Analysis of the long-term dynamics of ungulates
in Sikhote-Alin Zapovednik, Russian Far East
P.A. Stephens, O.Yu. Zaumyslova, G.D. Hayward and D.G. Miquelle
Collaborators:
Sikhote-Alin State Biosphere Zapovednik
Wildlife Conservation Society
University of Wyoming
USDA Forest Service
Analysis of the long-term dynamics of ungulates in Sikhote-Alin Zapovednik,
Russian Far East
A report to the Sikhote-Alin Zapovednik and USDA Forest Service
Philip A. Stephens*
Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA
Olga Yu. Zaumyslova
Sikhote-Alin State Biosphere Zapovednik, Terney, Terneiski Raion, Primorski Krai, Russia
Gregory D. Hayward
Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, USA;
USDA Forest Service, Rocky Mountain Region, PO Box 25127, Lakewood, CO 80225, USA
Dale G. Miquelle
Wildlife Conservation Society, Russian Far East Program, Vladivostok, Primorye Krai, Russia
2006
* Present address: Department of Mathematics, University of Bristol, University Walk, Bristol,
BS8 1TW, UK; philip.stephens@bristol.ac.uk
EXECUTIVE SUMMARY
Study and findings
1.
The winter transect count involves monitoring game species by counting tracks of
animals that intersect with a stable network of transects, surveyed during periods of snow
cover. It is the main method of estimating the number of many game animals in the
Russian Federation. For over four decades, this approach has been used consistently to
monitor a variety of species in Sikhote-Alin Zapovednik (SAZ), Russian Far East.
Hitherto, this extensive data set has not been rigorously analysed to assess trends and
ecological relationships in a variety of species, or to assess its potential and limitations
with regard to informing management of SAZ. We present such an analysis, focused on
six of the larger game species occurring in SAZ: red deer (Cervus elaphus), wild boar
(Sus scrofa), roe deer (Capreolus pygargus), musk deer (Mochus moschiferus), sika deer
(Cervus nippon) and moose (Alces alces).
2.
The principle objectives of this work were to examine spatial pattern in the occurrence of
the species of interest; to investigate methods for estimating population densities from the
track encounter data; to assess factors underlying temporal changes in populations of the
more abundant species; to analyse the survey protocol and recommend practices whereby
it might be improved; and to determine the likely impact of Amur tigers (Panthera tigris
altaica) on potential prey species. Through these analyses, we aimed to inform
understanding of the distribution and dynamics of the ungulates within SAZ, to aid
ongoing efforts to manage the area for the benefit of the endangered Amur tiger, and to
integrate the disparate Russian and English language literatures on estimating animal
abundance from indirect sign, thereby contributing to this important yet contentious field.
3.
Comparisons of track encounter rates among forest types and drainages suggested few
consistent patterns of animal distribution beyond those already recognised by accepted
divisions of SAZ into three broad habitat zones (the coastal, oak-birch zone; the central
belt, dominated by mixed Korean pine and deciduous forests; and the north-western,
higher altitude areas, dominated by spruce and fir forests). Within the oak-birch zone,
however, sika deer show pronounced differences in their use of the coastal oak forests
and mixed birch and aspen forests further inland. Though less marked, the data
suggested that other species may also show differences in their use of these areas.
Consequently, we recommend that, in future, the oak-birch zone should be divided into
two separate survey units, recognising the existence of four (rather than three) broad
habitat zones for survey purposes.
4.
Three methods for estimating ungulate absolute population densities from track counts
were compared, including a correction factor based on the relationship between track
counts and total counts of deer in experimental plots; the established FormozovMalyeshev-Perelshin (FMP) formula based on records of animal daily movement
distances; and a computationally-intensive simulation approach based on twodimensional records of animal daily movements. The simulation and FMP approaches
gave very similar estimates, supporting the existing belief in Russia that the FMP formula
is theoretically sound and generally robust to the different movement patterns of ungulate
species. The correction factor tended to overestimate densities but this is unsurprising,
i
given that data used to develop the correction factor came from other study areas, where
animal movements may be very different.
5.
We stress that no method for estimating density from indirect sign is robust to violations
of underlying assumptions. In particular, no method can fully compensate for biases
arising from a survey network that does not adequately represent the area of interest. All
methods based on indirect sign also require independent validation, ideally using
monitoring based on direct sightings. Specific recommendations for enhancing the
validity of the track count surveys are given below.
6.
Two of the methods for estimating ungulate abundance from track encounter rate depend
on good data on animal 24-hour movements. These data are currently limited for SAZ
but preliminary analyses indicated that movement distances may be affected by time of
year and group size (for red deer and roe deer), and a combination of habitat type and
time of year (for wild boar). Understanding how travel distances are affected by different
conditions is essential for improving the accuracy of density estimation and we urge
further collection of these data in a range of conditions.
7.
Differences between ungulate densities in the three major habitat zones of SAZ are
pronounced and we assumed that data would always be stratified at this level, at the very
least. Finer levels of stratification, including stratification by drainage basin and by forest
formation were compared. These different types of stratification seldom had strong
effects on estimates. However, analyses indicated that stratification by forest formation
could be vulnerable to outliers and, consequently, stratification by drainage basin is
recommended. It remains to be seen whether this will be necessary, if a four zone
approach to the surveys is adopted (see further below).
8.
Non-parametric bootstrapping was used to derive confidence intervals around estimates
of ungulate densities. This method is free from many of the assumptions required by
other suggested methods for estimating confidence intervals about estimates derived
using the FMP formula. Using non-parametric bootstrapping also avoids the requirement
for estimates of parameters such as average group size and average crossing rate for the
paths of individual animals, both of which can be very difficult to obtain.
9.
Overall, densities of ungulates tend to be highest in coastal areas and lowest in the
spruce-fir, montane forests. Red deer were the most abundant species (1.5 to 3.0 km-2
throughout SAZ), followed by roe deer (1 to 2.5 km-2). At present, sika deer occur only
in the oak-dominated forests on the coast but their population appears to be growing
rapidly (now exceeding 1 km-2 in that area). Less is known about musk deer daily
movements but analyses indicated that this species shows the opposite trend to the other
ungulates in SAZ, with the highest densities in montane, spruce-fir forests, and the lowest
densities towards the coast. Overall, mean musk deer density throughout SAZ is
approximately 1 km-2. Wild boar show substantial fluctuations throughout the coastal
and central areas but are at generally low abundance in both, seldom exceeding 0.1 to 0.5
km-2. Finally, moose tracks are encountered too rarely to analyse. That moose track
encounters have virtually ceased since 1980, suggests that this species (which is at the
southern extent of its range in SAZ) may have shifted northward in response to increasing
temperatures.
10.
Analyses of changes in track encounter rates within years suggested that encounters of
the tracks of several species (including red deer, roe deer and musk deer) show
ii
pronounced declines from early to late winter. Although this results partly from changes
in travel distances as winter progresses, it is also possible that species distributions shift
throughout winter. Survey routes that accurately represent the entire area of interest are
essential if this phenomenon is to be understood (see further below).
11.
In spite of the rigour with which SAZ is surveyed, the track data are prone to census error
and resultant estimates of density are noisy. This leads to difficulties in determining the
major factors dictating the dynamics of each species. Nevertheless, evidence for density
dependent processes was found in several populations.
Additionally, climate,
competition, quality of mast crops and protection from poaching all influence the studied
populations. Dynamics of the red deer and sika deer populations are currently best
understood. There is evidence for competition between these species and, also, for
climate effects acting in different directions. In particular, increasing temperatures
appear to have a positive effect on the sika deer population but a negative effect on red
deer populations in the coastal and central zones. By contrast, red deer in the spruce-fir
zone are positively affected by increasing temperatures, suggesting that the species may
be shifting its distribution northwards and to higher altitudes as mean temperatures
increase.
12.
Assessments of the survey protocol and of the relationship between survey effort
(kilometres of transects conducted per year) and precision, emphasised two major points.
First, that survey design depends critically on the goals of monitoring, in particular,
whether relative indices of abundance are sufficient or absolute estimates of abundance
are desired, and whether it is necessary to detect trends in animal abundance. If the
detection of trends is a goal of the monitoring, then it is important to establish what
magnitude of trend should be detectable and over what time period. Secondly, analyses
also highlighted the fact that, for a given set of goals, required survey effort is affected by
the density, movement behaviour and grouping behaviour of the species considered. Low
densities, short daily travel distances and clumped distributions all increase the
uncertainty in abundance indices. Thus, some species will be harder to monitor as
accurately as others. Different monitoring goals will be relevant to different species (see
further below).
13.
Simple analyses of the likely effects of tigers on prey populations indicated that these are
likely to be small relative to the estimated effects of other large carnivores on their prey.
This accords with findings from the temporal analyses, which showed no evidence for a
strong effect of tigers on prey populations. Although the social intolerance of tigers may
play a role in limiting their local density and, hence, their effects on prey, this is unlikely
to be important at the relatively low prey densities in SAZ. More likely, the generally
low impact of tigers on prey results from their relatively low energetic requirements when
compared to many other large carnivores.
Specific recommendations
This study highlighted a variety of improvements that could be made to the monitoring work
conducted in SAZ. Ultimately, the goals of Zapovednik monitoring are for the managers of the
Zapovednik system to designate. However, some suggested goals and recommendations include:
iii
1.
Use a four-zone classification of SAZ for ungulate monitoring. This is discussed in more
detail in the report but the zones would include the coastal zone (dominated by oak
forests), the inner-coastal zone (dominated by birch-aspen forests), the central zone
(dominated by Korean pine-deciduous forests) and the montane zone (dominated by
spruce-fir forests).
2.
Define an overall goal for monitoring ungulates. This should specify whether monitoring
should produce only an index of relative abundance, or estimates of absolute abundance
also. It should also specify the units of interest (both species and zones) and whether
trend detection is important. If trend detection is important, the magnitude of trends and
the time periods over which these should be detected must also be defined. We suggest
that the goal be defined as follows: Ungulate monitoring in SAZ will provide estimates of
the absolute abundance in winter of ungulates in the four major habitat zones. At least
1000 km of surveys will be conducted annually, distributed equally over the four zones.
The aim of this will be to give the maximum power to detect trends in numbers of the
more abundant species in the habitats most important to that species. A design capable of
detecting a 15% annual decline after 5 years of monitoring will be achievable for most
species.
3.
Recognise limitations and adapt to priorities and changing conditions. It is vital that the
limitations of the monitoring be recognised including, in particular, that density estimates
are associated with considerable uncertainty, and that species at lower abundance, with
shorter daily travel distances and with highly clumped behaviour will be subject to
greater uncertainty, such that trends are harder to detect with confidence. The monitoring
protocol should also be adaptable to changing priorities and to changes in conditions
(such as increasing or decreasing densities of certain species).
4.
Validate the relationships between track counts and density estimates. Independent
estimates of density must be generated using alternative methods, in order to indicate
how accurately density is estimated by current methodologies. In particular, we
recommend the use of distance sampling and aerial surveys (combined with sightability
models) as potential methods for validating the track count index.
5.
Assess bias in transect network. Assess bias in the transect network using GIS analyses
and by comparing results of randomly placed transects to the existing network within a
number of basins of the reserve. If a significant bias is detected, there are two
alternatives to address this bias: (i) if the bias is stable and predictable across all areas and
all conditions, apply a simple correction factor; (ii) if the bias is not stable and is difficult
or impossible to predict, relocate transects to approximate a random sampling effort.
6.
Improve data base on daily travel distances. Daily travel distances must be collected
during the time frame in which surveys are conducted, as there is evidence that travel
distance drops in late winter. Data on travel distances must also be collected across the
range of environmental parameters that are likely to affect movements. Our initial
analyses suggest that group size, time of year and habitat type are the primary drivers of
daily travel distance. Collecting data over the full range of possible values for each of
these parameters will be important in deriving appropriate estimates of travel distance for
ungulates within the Zapovednik.
7.
Collect data on the numbers of animals that made each set of tracks encountered. To
collect data not only on the number of sets of tracks of each species encountered on
iv
transects but, also, on the number of these that were made by single animals or groups of
various sizes, is likely to be awkward, especially from the point of view of data storage.
Nonetheless, our analyses showed that size of the travelling group may be important in
dictating the travel distance of some species. Consequently, collecting such data will be
helpful for improving the accuracy of density estimates. The data could also be useful for
determining group size distributions, which will have important implications for error
calculations and other aspects of understanding demography of the studied species.
8.
Eliminate the recording of “nabrods”, or multiple, uncountable crossings. Eliminate
records of “nabrod” in SABZ dataset by training all observers to circle nabrods and report
actual numbers of tracks to the best of their ability.
v
ACKNOWLEDGEMENTS
This monograph is the result of a long-term collaborative effort between Sikhote-Alin
Zapovednik and the Wildlife Conservation Society.
We thank A.A. Astafiev, Director of
Sikhote-Alin, for continual support of these mutually beneficial, ongoing efforts. We also thank
M. Hornocker and H. Quigley, who had the wisdom and courage to initiate the Siberian Tiger
Project, and select Sikhote-Alin Zapovednik as its base. M.N. Gromyko, and L.V. Potikha have
both acted as Assistant Directors of Science for Sikhote-Alin Zapovednik and facilitated our
collaborative efforts. E.N. Smirnov, our scientific collaborator for the Amur Tiger Project, has
been instrumental in all phases of the work. A.E. Myslenkov provided much data on daily travel
distances of ungulates, a pivotal part of the database which is used here. T. Merrill provided the
first GIS database training for Zapovednik personnel, and helped design and implement database
development.
We thank other members of the Zapovednik staff for their help and advice
including, especially, Luba Khubotnova, whose assistance with translation during meetings was
invaluable.
This work was funded by the U.S. Forest Service, International Programs, part of the U.S.
Department of Agriculture, to whom we are most grateful. In particular, we would like to thank
Liz Mayhew, Lara Peterson and Jen Peterson for all of their support and logistical advice
throughout the project.
The bulk of the analytical work was conducted at the University of Wyoming, USA, and
we thank the University for support. In particular, we are grateful to heads of the Zoology and
Physiology Department, N. Stanton and G. Mitchell, as well as S.D. Hutton in International
Student Services.
Translations were completed by E. Nikolaeva, A. Murzin, and D. Karp. G. Contraras
facilitated the translation of Russian scientific articles into English. Many others provided advice
on research approaches, translation of materials and statistical techniques. In particular, we thank
the following: C. Nations, C. Martínez del Rio, S. Buskirk, R. Freckleton, R. King, A. Cardinali,
C. Anderson, J. Crait and K. Gerow.
Finally, PAS and GDH would like to thank all those in Terney and Vladivostok who
made their visits so enjoyable and useful. Many of those are already listed but, additionally, we
thank John Goodrich, Marina Miquelle, Galia Safanov, Zheny Gishko, Kolya Reebin, Sasha
Reebin, and Volodia Melnikov.
vi
PREFACE
The Russian Zapovednik system is renowned throughout the world for its dedication to preserve
representative intact ecosystems. As impressive as the conservation goal is the secondary goal of
Zapovedniks to monitor and observe those ecosystems, and the changes that occur within them.
Long-term observations provide an opportunity to understand the impact of humans on natural
processes by comparing protected and unprotected areas, but they also provide unique
opportunities to better understand long-term dynamics of animal populations that reside in
preserves relatively free of human influence. Most Zapovedniks have retained a trained scientific
staff that has collated vast archives of data of great potential in understanding long-term dynamics
of natural ecosystems.
Such is the case with Sikhote-Alin Zapovednik. Since 1962, annual winter transect
routes (beli trappa), have been conducted to monitor populations of wildlife. The value of such
data may not have been immediately apparent to those who initiated data collection, but who
nonetheless went to painstaking lengths to insure that this data was archived and saved for future
generations. Thus, a “treasure” of data resided in the archives of Sikhote-Alin, mainly to be
found in the yearly “Chronicles of Nature” that are produced each year to document the biological
and ecological “status” of the reserve.
The Amur Tiger Project began in 1992 as a collaborative program between the Wildlife
Conservation Society (initially the Hornocker Wildlife Institute, which has since merged with
WCS), and Sikhote-Alin Zapovednik to study the ecology of the Amur tiger within the
boundaries of the Zapovednik. From the beginning, it was clear that understanding the relation of
tigers to their prey would be a primary component of our efforts. In Sikhote-Alin Zapovednik, in
particular, it was clear there were unique opportunities to study long-term dynamics of tigers and
their prey. Not only were there winter transect routes that provided a standardized means of
assessing prey abundance, but since 1966 E. N. Smirnov had collated all observations of tigers to
vii
derive yearly estimates of tiger abundance. Thus, the opportunity to assess and understand
temporal changes in abundance of both predator and prey populations was enormous.
To make effective use of the archived information from Sikhote-Alin Zapovednik, it was
clear that transformation into a digital geo-referenced dataset would be necessary. Therefore, the
Wildlife Conservation Society and Sikhote-Alin Zapovednik worked jointly to develop such a
GIS database, one of the first in the Russian Far East, which could be used to record all data from
winter routes, and link them to other geographic and biological features of the reserve. Olga
Zaumyslova took primary responsibility for overseeing this transformation of data, with the
assistance of many GIS and computer specialists, both Russian and American. This process took
seven years to reach its present stage and is, in fact, ongoing. We now have a 40-year database
that provides a record of ungulate and tiger abundance within Sikhote-Alin Zapovednik. Such
long-term databases on carnivores and prey are exceedingly rare, and in fact, this particular
dataset represents the only tiger-prey database of its kind in the world.
To maximize effectiveness of this database, we requested additional assistance for
analyses from the University of Wyoming. Specific aims of the analyses were discussed by
representatives of Sikhote-Alin, WCS, and University of Wyoming at the SAZ headquarters in
Terney, Primorski Krai, on the 17th of March, 2003, where it was agreed that the principal aim of
this study was to use the extensive data from the winter transect counts to analyse the long-term
population dynamics of ungulates within SAZ. We were interested first in determining the most
appropriate means to convert track abundance indices of ungulates to estimates of absolute
abundance - a theme that has concerned practical and theoretical Russian biologists for years.
While it was initially unclear how much we had to contribute to this extensive Russian literature,
we felt there was an opportunity to compare existing approaches to controlled simulations, and to
explore alternative statistical approaches to estimating abundance.. The Sikhote-Alin database
represented a unique opportunity to compare various approaches to estimating ungulate
abundance, and to assess variation in these approaches. With the most accurate information on
viii
ungulate densities possible, we would then be ready to assess the relationship between predators
and prey, and specifically, what, if any, parameters could explain numerical changes in both
predators and prey. In summary we were interested in addressing the following objectives:
examining spatial pattern in the occurrence of the species of interest; investigating methods for
estimating population densities from track encounter data; assessing factors underlying temporal
changes in populations of the more abundant species; assessing the potential impact of tigers on
ungulate populations; and analysing the existing survey protocol to assess its capacity to detect
change in ungulate populations, and to make recommendations to improve the survey protocol.
This report represents our first attempt to address these issues. While there are still many
questions, we believe that this work provides a useful contribution to our understanding of how to
estimate ungulate abundance, of the factors affecting ungulate abundance, and about the
relationship between tigers and their prey.
Dale G. Miquelle
Terney, 2006
ix
TABLE OF CONTENTS
Executive Summary
Study and findings
Specific recommendations
Acknowledgements
Preface
Table of Contents
i
i
iii
vi
vii
x
1. General introduction
1.1
Background and aims
1.2
Study area
1.3
Data and data collection
1.4
Structure of the report
1
1
4
4
9
2. Spatial analyses of ungulate distributions
2.1
Background
2.2
Methods
2.2.1
Analysis of track encounter rates among drainage basins
2.2.2
Analysis of track encounter rates among forest types
2.3
Results
2.3.1
Comparison of track encounter rates among drainage basins
2.3.2
Encounter rates in different forest formations
2.4
Discussion
10
10
10
10
11
15
15
17
18
3. Track encounter rates and ungulate densities
20
3.1
Background
20
3.2
Methods
22
3.2.1
Movement data
22
3.2.2
Estimation of deer density using a correction factor
24
3.2.3
Confidence intervals for density estimation
25
3.2.4
Stratification and weighting of density estimates
28
3.2.5
Estimation of density using the FMP formula
29
3.2.6
Estimation of density using simulations
32
3.3
Results
33
3.3.1
Movement data
33
3.3.2
Estimating density: comparison of weighting approaches
38
3.3.3
Parameters for density estimation by the FMP formula and simulation methods
42
3.3.4
Comparison of estimators
46
3.3.5
Final estimates of density
47
3.4
Discussion
47
4. Temporal analyses of ungulate population dynamics
4.1
Background
4.2
Methods
4.2.1
Within-year variation in track encounters
4.2.2
Linear trend analysis
4.2.3
Detecting density dependence
x
54
54
62
62
63
64
4.2.4
Time-series analysis
4.2.5
Putative factors influencing population growth
4.2.6
Selection of data sets for density dependent and time-series analyses
4.3
Results
4.3.1
Within-year variation in track encounters
4.3.2
Linear trend analysis
4.3.3
Density dependence
4.3.4
Time-series analysis
4.4
Discussion
4.4.1
Within-year variation in track encounters
4.4.2
Linear trend analyses
4.4.3
Density dependence
4.4.4
Time-series analysis
Appendix 4A
Appendix 4B
69
72
78
80
80
82
84
87
94
94
95
96
98
102
105
5. Survey protocol
5.1
Background
5.2
Methods
5.2.1
Zero counts and the length of transect segments
5.2.2
Survey effort and associated error
5.2.3
Power analyses and required survey effort
5.3
Results
5.3.1
Zero counts and the length of transect segments
5.3.2
Survey effort and associated error
5.3.3
Power analyses and required survey effort
5.4
Discussion
112
112
113
113
113
115
116
116
116
119
121
6. Tiger-prey relationships
6.1
Background
6.2
Methods
6.2.1
Estimating the requirements of tigers
6.2.2
Estimating the impacts of tigers
6.3
Results
6.3.1
Requirements of tigers
6.3.2
Estimated impacts of tigers
6.4
Discussion
125
125
126
126
128
130
130
132
134
7. General discussion
7.1
Ungulate densities and the utility of the survey protocol
7.1.1
Accuracy of data
7.1.2
Precision of estimates
7.2
Estimating animal density from sign
7.3
Ungulate dynamics and tiger conservation
7.4
Specific recommendations
7.5
Concluding remarks
139
139
140
143
145
146
148
150
References
152
xi
Analysis of ungulate dynamics
1. GENERAL INTRODUCTION
1.1
Background and aims
The winter transect count involves monitoring game species by counting the number of sets of
tracks of those species that intersect with a stable network of transects, surveyed during periods of
snow cover. It is the main method of estimating the number of many game animals in large
territories of the Russian Federation (Lomanov, 2000). In Sikhote-Alin Zapovednik (Reserve)
(SAZ), winter transect counts have been conducted each winter since 1962. In SAZ, tracks of
approximately 20 species of mammals have been recorded during winter transect counts,
including six species of ungulates: red deer (Cervus elaphus), wild boar (Sus scrofa), roe deer
(Capreolus pygargus) (Nowak, 1999), musk deer (Mochus moschiferus), sika deer (Cervus
nippon) and moose (Alces alces).
These data have been analysed previously to investigate the population dynamics of one
or more ungulate species (e.g. Zaumyslova, 2000; Zaumyslova et al., 2001) but, for three reasons,
we have extended these investigations and subjected all of the long-term data on ungulate species
to further, rigorous analyses. Our principal motivations included: (i) the importance of gaining
accurate knowledge regarding the densities of ungulates in SAZ and the utility of the survey
protocol; (ii) the broader contribution that our analyses can make to the field of estimating animal
population density from indirect sign; and (iii) the importance of understanding ungulate
dynamics in SAZ, in order to inform management of the Amur tiger (Panthera tigris altaica).
First, there is a need to determine the relationship between track encounter rates derived
from winter transect counts and absolute abundance of wildlife, a topic that has received
considerable attention in other parts of the Russian Federation (e.g. Chelintsev, 1995; Smirnov,
1973) but not in SAZ. Here, we present a rigorous analysis of the methods available to relate
track encounter rates to indices of abundance. This process allows us to assess the constraints on
1
Analysis of ungulate dynamics
further analyses of the long-term data and to make recommendations for improving the survey
protocol.
Secondly, in areas where ungulates are abundant or occur in open terrain, they are often
surveyed using direct count methods, such as aerial counts (e.g. Noyes et al., 2000; Rabe et al.,
2002; Walter & Hone, 2003). For populations at lower density or in heavily vegetated terrain,
aerial surveys are still possible using thermal imaging (e.g. Dunn et al., 2002; Haroldson et al.,
2003; Havens & Sharp, 1998) but this technology is seldom available. Instead, researchers often
rely on extrapolating from indirect sign, such as tracks or scat (e.g. De Young et al., 1988;
Mandujano & Gallina, 1995; Marques et al., 2001; Mooty et al., 1984). Issues arising from these
techniques have broad applicability to surveying a large number of low density or low-visibility
species by indirect sign, including many species of carnivore. The use of indirect sign to estimate
abundance is an important but highly contentious field (e.g. Barnes, 2001; Buckland et al., 1993;
Carbone et al., 2001; Carbone et al., 2002; Collie & Sissenwine, 1983; Diefenbach et al., 1994;
Frantz et al., 2004; Jennelle et al., 2002; Ogutu & Dublin, 1998; Patterson et al., 2004; Sadlier et
al., 2004; Schwarz & Seber, 1999; Thompson et al., 1998; Wasser et al., 2004; Wilson &
Delahay, 2001). The SAZ monitoring data set is unusual in its length and in the consistency with
which surveys have been conducted (cf. Stephens et al., 2001, for example). As a result, using
the SAZ data to analyse methods for estimating density from sign provides a rare opportunity to
contribute to this debate by analysis of a very extensive data set and by combining recent
developments from both the Russian and English literatures.
Finally, six ungulate species in SAZ are all potential prey of the Amur tiger. The tiger is
listed as an endangered species (IUCN, 2002) and, among its subspecies, the Amur tiger appears
to be one of the rarest. Long-term data from track surveys throughout the Amur tiger’s range
indicate that the population declined to a bottleneck of 20-30 individuals in the 1930s and 1940s
but has since shown a substantial recovery (Kucherenko, 2001; Smirnov & Miquelle, 1999).
However, traditional methods of monitoring were not standardised, preventing calculation of
2
Analysis of ungulate dynamics
error associated with population estimates; hence, the exact magnitude of the Amur tiger’s
recovery remains uncertain (Hayward et al., 2002). Increasingly, it is recognised that prey
availability is a key factor dictating tiger distribution (Karanth & Nichols, 1998; Karanth et al.,
2004; Karanth & Sunquist, 1992), with tiger densities positively related to the densities of
ungulate prey (Miquelle et al., 2005). For the Amur tiger, in particular, detailed analyses of
distribution in relation to a suite of habitat variables indicated that the distribution of prey is the
single most important factor determining the tiger’s geographic range (Miquelle et al., 1999).
Specifically, the Amur tiger shows an overlap of approximately 61% with the distribution of red
deer which has previously been shown to make up the majority of its diet (Miquelle et al., 1996).
Furthermore, within their broader geographic range, tigers appear to select home ranges that
contain a greater than average proportion of riverine forest, a habitat noted for its potentially high
prey abundance (Miquelle et al., 1999). Simple models of population dynamics also indicate that
the tiger may be more vulnerable to depletion of its prey than to commercial poaching, a factor
usually cited as its greatest potential threat (Karanth & Stith, 1999). Clearly, knowledge of the
distribution, dynamics and abundance of prey species is of crucial importance to the conservation
of tigers. Indeed, it has been suggested that “enhancing and monitoring the tiger's prey base is
perhaps the single most important task facing wildlife managers across Asia” (Karanth, 1999).
The principal aim of this study was to use the extensive data from the winter transect
counts to analyse the long-term population dynamics of ungulates within SAZ. Within this main
aim, five inter-related objectives were identified, as follows:

Spatial analyses of ungulate distributions.

Analyses of the relationship between track encounter rates and ungulate densities.

Temporal analyses of ungulate population dynamics.

Assessment of the current survey protocol, with suggestions for improvement.

Theoretical assessment of the prey requirements of tigers and the potential impact of
tigers on prey.
3
Analysis of ungulate dynamics
1.2
Study area
Sikhote-Alin State Biosphere Zapovednik is located in north-eastern Primorski Krai (Province) in
the southern Russian Far East, some 400 km northeast of Vladivostok. Portions of SAZ border
the Sea of Japan (Fig. 1.1) but its major feature is the Sikhote-Alin Mountains, a low range (most
peaks are below 1200m) running through Primorski and Khabarovski Krais and paralleling the
Sea of Japan. Created in 1935 as a one million hectare Zapovednik, and approved as a Biosphere
Zapovednik in 1978, SAZ has varied greatly in size over time (Gromyko, 2005), but the current
size of the Reserve is 4,000 km2.
Vegetation within the reserve is classified into seven dominant forest formations (see
further in Section 2), based on a Forest Inventory (Lesostroitsva) conducted on the Zapovednik in
1979. However, for the majority of our analyses we used a greatly simplified classification,
dividing the area into three broad habitat zones (Fig. 1.1). The coastal forest zone below about
250m above sea level (a.s.l.) has withstood severe impacts from fire and human disturbance, and
is dominated by Oak-birch forests. Further inland and at slightly higher altitudes, the central belt
of SAZ is dominated by mixed Korean pine-deciduous forests. Finally, the most westerly and
high altitude areas of SAZ (from 800 up to approximately 1300m a.s.l.) are dominated by mixed
spruce and fir forests. The lower portion of the Kolumbe Basin, added to the Reserve in 1996, is
also dominated by spruce-fir forests but, because long-term data have not been collected there by
reserve staff, this portion of the reserve is not included in our analyses.
1.3
Data and data collection
The main database consists of survey data spanning the period from 22-Jan-1963 to 4-Mar-2003.
Biological years are usually taken to run from spring to spring and, hereafter, we refer to any
winter period from October to April by the year at the start of that winter. It follows that the data
span the period of the biological year 1962 to the biological year 2002. Data from the biological
4
Analysis of ungulate dynamics
years 2001 and 2002 were added following the preliminary analyses. Most analyses incorporate
these data but where they do not, that absence is indicated in the report.
Figure 1.1.
Map of SAZ showing the major regions of different habitat types.
5
Analysis of ungulate dynamics
Winter transects were broken into transect “segments” each of which is intended to
represent a continuous sample of a single habitat type and/or aspect. Collectively, the database
consists of records from 9,612 transect segments. The total length of transects surveyed in any
one year varied from just under 100 km in 1964 to nearly 1800 km in 1985. In general, the total
length of transects increased throughout the 1960s to 1971, after which time it averaged 872 ±
294 (standard deviation; SD) km per year, with a low in 1982 and a high in 1985 (Fig. 1.2).
Route locations are shown in Section 2, Fig. 2.1).
For each winter transect count, tracks of each ungulate species were recorded if the
fieldworker assessed that the tracks were created in the previous 24-hour period. Along each
transect segment, in addition to the counts of tracks, habitat type, relief and snow depth, as well as
date, route and location, were recorded. Encounter rates during the study period (averaged over
all habitat types) are shown in Fig. 1.3 for the six principal ungulates.
In addition to the main database, several other data sources were developed to aid
analyses. These include records of 24-hour movements for four ungulate species, assessment of
mast crops in SAZ, data on human populations in Terney Raion (county), potential human
impacts on the reserve (e.g. road abundance in proximity to the reserve, level of poaching), and
climate from three weather stations in the region of SAZ.
Total length of transects (km)
2000
1800
1600
1400
1200
1000
800
600
400
200
0
1960
Figure 1.2.
1965
1970
1975
1980
1985
1990
1995
2000
2005
Year
Total length of all transects surveyed in SAZ during the study period.
6
4.0
Analysis of ungulate dynamics
(a)
3.0
2.0
1.0
0.0
1962
Mean encounter rate (km-1)
2.0
1972
1982
1992
2002
1972
1982
1992
2002
1972
1982
1992
2002
(b)
1.5
1.0
0.5
0.0
1962
0.8
(c)
0.6
0.4
0.2
0.0
1962
Year
Figure 1.3.
Annual track encounter rates for: (a) red deer (solid line) and wild boar (dashed
line); (b) roe deer (solid line) and musk deer (dashed line); (c) sika deer (solid line) and moose
(dashed line).impacts on the reserve (e.g. road abundance in proximity to the reserve, level of
poaching), and climate from three weather stations in the region of SAZ.
7
Analysis of ungulate dynamics
Daily movement data for red deer, roe deer, sika deer and wild boar were collected by
two methods. The first of these was used primarily for wild boar and involved locating a set of
fresh tracks and following it backwards to the previous night’s bed site. This location was
recorded and the following day, the tracks were followed from that point until the next bed site
(from the intervening night) was reached. The second method was similar but involved visual
observations of animals. The location and time of the observation were recorded and, the
following day, tracks were followed from that point until the animal was seen again, ideally at
approximately the same time as on the previous day. Use of radio-collared red deer increased the
efficiency of data collection for that key species (Myslenkov & Voloshina, 2005). The data were
stored as vectors, with each total path broken down into moves (e.g. see Turchin, 1998), defined
by an angle and a distance. Both straight line and total lengths of each move were recorded. For
each path, data were also collected on factors that could influence path characteristics. These
included species, sex and age of the individual(s) tracked, time of year, habitat and snow
conditions.
Data on mast abundance were also available for SAZ from throughout the study period.
Mast abundance was measured for both oak and Korean pine, using a system of regularly
assessed plots, each 1m2.
The numbers of acorns and pine cones within these plots were
measured and, since 1934, have been equated to an ordinal scale for each mast type, with 1
indicating a very low density of nuts and 5 indicating an exceptionally good year.
Finally, data on climate were available from two weather stations in the region of SAZ:
Terney weather station (close to the town of Terney, Fig. 1.1) and Melnichnoye weather station in
the main mountain range, approximately 18 km due west of the northwest boundary of SAZ.
Data available from these weather stations include mean snow depths for each 10 day period
during winter, as well as temperature and precipitation data from throughout the year.
8
Analysis of ungulate dynamics
Correlations between weather records from the two stations are high and, as the data from
Melnichnoye are more reliable, these are the data that were used for our temporal analyses of
ungulate dynamics (Section 4).
1.4
Structure of the report
The remaining sections of this report are divided between the five objectives listed in Section 1.1
(Sections 2 to 6) and a broad discussion of the findings (Section 7). The sections on individual
objectives present the background, methods, results and conclusions relevant to that section, and
are intended to be readable on their own. There is, however, considerable overlap between
sections and, consequently, cross-references are included where relevant. The aim of Section 7 is
to bring the individual objectives together in a more coherent manner. Where necessary, species
and habitat codes are used in tables and figures. These are summarised in Tables 1.1 and 1.2,
respectively.
Table 1.1
Table 1.2
Species codes used in the report
Species
Code
Moose
Musk deer
Red deer
Roe deer
Sika deer
Wild boar
MO
MD
RE
RO
SD
WB
Habitat codes used in the report
Habitat
Oak-birch
Korean pine-deciduous
Spruce-fir
Code
OB
KD
SF
9
Analysis of ungulate dynamics
2. SPATIAL ANALYSES OF UNGULATE DISTRIBUTIONS
2.1
Background
Understanding the spatial pattern of ungulate abundance is important for two reasons. First,
knowledge of the relative abundance of different species within different parts of SAZ has
implications for management and for developing the sampling protocol.
Secondly, spatial
analyses are required to determine a suitable approach for stratification of the winter transect
count data for further analyses.
Many spatial divisions based on geographical or habitat
boundaries are recognised within SAZ.
Perhaps the most striking differences in ungulate
abundance are seen between the three habitat zones identified in Section 1.2. Even a cursory
examination of track encounter rates throughout the study period suggests that track encounter
rates vary greatly among the three zones annually, and supports division of the reserve into those
three zones for data analyses. For that reason, further analyses employ the habitat zone as the
most basic level of data stratification. Further stratification of the data is possible on the basis of
both drainage basins and finer-scale habitat divisions (e.g. vegetation types). In this section, we
assess data within these subdivisions in more detail and analyse the importance of further
stratification of the data. In doing this, we also provide an indication of the heterogeneity of
ungulate distributions, suggesting which drainage basins and habitats are most important for the
various ungulate species.
2.2
Methods
2.2.1
Analysis of track encounter rates among drainage basins
To assess whether there are consistent differences in ungulate encounter rates between
drainage basins, we compared annual track encounter rates in each drainage with those in the
broader habitat category to which it belongs. In spite of the chance that certain drainages will
deviate from the mean for the overall category in certain years, only deviations in consistent
10
Analysis of ungulate dynamics
directions across multiple years will indicate that the drainage shows a clear tendency to have
ungulate densities that differ from the annual mean.
SAZ was divided into 13 major drainage basins, each of which occurs entirely within one
of the habitat zones (see Table 2.1 and Fig. 2.1). Where Eh,y is the average track encounter rate
for a given habitat type (h) and year (y), and Eb,y is the average track encounter rate for a given
drainage basin (b) and year, the overall encounter rate in a given basin relative to the mean for the
habitat zone is given by:
Y
Eb , y / E h , y
y 1
Y
b  
(2.1)
where  b is the mean deviation for basin b and Y is the total number of years during which a
given species occurred in the habitat and was surveyed in that basin. That the mean deviation is
calculated from annual ratios will tend to normalize the data and, consequently, we used a
standard approach for calculating confidence intervals, where the confidence intervals are
symmetric, and of magnitude I, given by:
I = s / √n ∙ τ
(2.2)
Here, s is the standard deviation, n is the sample size and τ is the α = 0.025 t-statistic associated
with n-1 degrees of freedom.
2.2.2
Analysis of track encounter rates among forest types
A number of classifications of vegetation type have been used in SAZ. In addition to the broad
habitat zones discussed above (Fig. 1.1), vegetation can be characterised more specifically by
dominant forest formations (referred to here as “forest types”) (Fig. 2.2 and Table 2.2). To a
large extent, the relative prevalence of these forest types defines the major habitat zones in SAZ
and, consequently, analyses of the relative preference of forest types can be conducted without
11
Analysis of ungulate dynamics
Figure 2.1. Fourteen drainage basins (including the new addition of lower Kolumbe, which was
not used in analyses) and primary survey routes used to assess variation in track encounter rate
across Sikhote-Alin Zapovednik, based on winter transect routes, 1962 to 2002.
12
Analysis of ungulate dynamics
stratification by the major habitat zone in which each forest type is found. For this reason, mean
deviation for any forest type f, was calculated as:
Y
E f ,y / Ey
y 1
Y
f  
(2.3)
where Ef,y is the average track encounter rate for a given vegetation type and year, Ey is the overall
average track encounter rate for that year, and Y is the total number of years during which that
vegetation type was surveyed.
Table 2.1
Major drainage basins in SAZ
Habitat category
Drainage
number
Oak-birch
1
2
3
4
7
8
9
Korean pine-deciduous
5
10
11
12
13
Spruce-fir
Table 2.2
Drainage name
6
Drainage size
(km2)
Abrek
Blagodatnoe
Khuntami
Inokov
Kunaleyka
Kuruma
Lianovaya
42.7
53.7
75.4
55.2
104.0
302.9
135.8
Jigitovka
Serebrianka
Tayozhnaya
Yasnaya
Zabolochennaya
152.5
922.0
115.0
106.2
309.0
Kolumbe
1099.0
Forest types in SAZ
Description
Riverine
Oak
Birch/aspen
Pine-deciduous
Northern pine
Larch
Fir
Area of forest type within each zone (km2):
Oak-birch
Korean pine-deciduous Spruce-fir
13.1
379.7
239.3
6.7
23.4
27.9
9.9
7.0
65.0
128.1
145.9
699.8
116.3
364.4
17.2
52.2
25.0
555.5
203.6
784.3
13
Analysis of ungulate dynamics
Figure 2.2. Map showing distribution of major vegetation groups within SAZ
14
Analysis of ungulate dynamics
2.3
Results
2.3.1
Comparison of track encounter rates among drainage basins
Average ratios between encounter rates in each basin and mean encounter rate for the whole
major habitat category are shown in Fig. 2.3. Analyses were conducted for the entire study period
(biological years 1962 – 2002) and, also, for the most recent five years (1998 – 2002). Clearly,
the ratio of encounter rates in the Kolumbe basin to the encounter rates in spruce-fir areas is
always unity, as the Kolumbe drainage makes up the entire spruce-fir zone in SAZ.
Consequently, no results are shown for the spruce-fir area. For species in the other habitats, Fig.
2.3 suggests few consistent patterns of occurrence which must, in any case, be treated with
caution and interpreted only in light of the limitations on sample sizes within each basin.
Nevertheless, a few general observations are possible on the basis of this analysis. These include
first, that patterns have not always remained consistent throughout the study period. Perhaps a
striking example of this is the relative decrease in red deer use of Abrek, to the point that they are
relatively uncommon in that drainage now. By contrast, sika deer appear to have become
relatively more common in that area in recent years, a fact that may account for the reduction in
red deer numbers. Elsewhere, sika deer appear to have a selective advantage over red deer
(Abernathy, 1994) and a decline in red deer in south-western Primorye appears to be the result of
an increase in sika deer (Pikunov et al., 2000). A second finding is that, at least for roe and sika
deer, several of the oak-birch drainages along the southern border of SAZ appear to have
relatively low abundances. This may be indicative of source-sink dynamics, with areas to the
south of SAZ acting as a sink due to higher rates of off-take where human populations and access
are relatively high. Thirdly, although they are seldom strikingly different from the average for
any one species, both Blagodatnoe and Khuntami appear to be good areas for several of the
ungulates that are common in oak-birch habitat (i.e. red deer, roe deer, sika deer and wild boar).
Finally, there appear to be few obvious patterns in the relative abundance of any species in
Korean pine-deciduous areas.
15
6.0
4.0
(a)
5.0
(d)
4.0
3.0
2.0
2.0
1.0
1.0
Jigitovka
Serebrianka
Tayozhnaya
Yasnaya
Zabolochennaya
Jigitovka
Serebrianka
Tayozhnaya
Yasnaya
Zabolochennaya
Jigitovka
Serebrianka
Tayozhnaya
Yasnaya
Zabolochennaya
Lianovaya
Lianovaya
Lianovaya
Kuruma
Kuruma
Kuruma
Kunaleyka
Kunaleyka
Kunaleyka
Inokov
Inokov
Inokov
Huntami
Huntami
(e)
8.0
Blagodatnoe
Abrek
10.0
Huntami
3.0
Zabolochennaya
Yasnaya
Tayozhnaya
Serebrianka
Jigitovka
Lianovaya
Kuruma
Kunaleyka
Inokov
Huntami
(b)
Blagodatnoe
4.0
0.0
Abrek
0.0
6.0
2.0
4.0
1.0
2.0
Zabolochennaya
Yasnaya
Tayozhnaya
Serebrianka
0.0
Jigitovka
0.0
Lianovaya
1.0
Kuruma
1.0
Kunaleyka
2.0
Inokov
2.0
Huntami
3.0
Blagodatnoe
3.0
Blagodatnoe
(f)
4.0
Blagodatnoe
5.0
Abrek
Zabolochennaya
Yasnaya
Tayozhnaya
Jigitovka
Lianovaya
Kuruma
Kunaleyka
Inokov
Serebrianka
4.0
Huntami
(c)
Blagodatnoe
Abrek
5.0
Abrek
0.0
0.0
Abrek
Mean ratio of encounter rate in basin to encounter rate in habitat zone
3.0
Figure 2.3.
Ratios of track encounter rate in basins to major habitat encounter rate, averaged over all years in which the species occurred in
the habitat and surveys were conducted in each basin. Oak-birch habitat (green bars) and Korean pine-deciduous habitat (brown bars) are shown
for full study period (dark bars) and last five years (light bars) Panels show: (a) red deer, (b) roe deer, (c) sika deer, (d) musk deer, (e) moose, (f)
wild boar. Broken lines show ratios of one and error bars show 95% confidence intervals. Some very large confidence intervals have been
truncated for clarity.
Analysis of ungulate dynamics
2.3.2
Encounter rates in different forest formations
For several ungulate species, the analysis of track encounters within different forest types (Fig.
2.4) provided more striking patterns of preferences than those seen in the comparison of drainage
basins. With a few exceptions, patterns are generally as expected from what is known about the
ecology of the species and are summarised in Table 2.3. Red deer preferred riverine habitat
types, and avoided larch and spruce-fir forest types. Roe deer preferred both riverine and oak
forests, and avoided not only larch and spruce-fir, but also both pine forest types. Sika deer
preferred only oak forest, and avoided all but riverine forests (which were used approximately in
accordance with availability). In contrast, musk deer preferred northern pine, larch, and sprucefir forests, used Korean pine-deciduous in proportion to availability, and avoided riverine, oak,
and birch forests. Moose preferred only larch and spruce-fir forests, and avoided all others except
Korean pine-deciduous forests. Wild boar showed a preference only for Northern pine forests.
That these patterns were evident in spite of the potentially confounding effects of different
encounter rates in different habitat zones and drainage basins suggests that forest type is an
informative factor and that stratification of data by forest type (within habitat zones) may help to
increase the accuracy of density estimates.
Table 2.3
Summary of relationships between encounter rate and forest type for ungulate
species (+ indicates preferred habitats, - indicates avoided habitats)
Vegetation type
Red deer
Roe deer
Riverine
Oak
Birch/aspen
Pine-deciduous
Northern pine
Larch
Fir
+
+
+
-
-
Species
Sika deer Musk deer
+
-
+
+
+
Moose
Wild boar
+
+
+
-
17
Analysis of ungulate dynamics
2.4
Discussion
In this section, we have shown how the long term track survey data from SAZ can be used both to
assess the need for post-stratification of data, and to gain some insight into the heterogeneity of
ungulate distributions. Within habitat zones, different species of ungulate show some consistency
in the drainage basins in which they are encountered most frequently, although for the majority of
species and basins, variation between years (as indicated by the error bars in Fig. 2.2) is
2.0
3.0
(a)
(d)
1.5
2.0
1.0
1.0
0.5
0.0
2.5
0.0
10
(b)
2.0
8
1.5
6
1.0
4
0.5
2
0.0
0
4.0
3.0
(c)
(e)
(f)
3.0
2.0
2.0
1.0
1.0
0.0
Fir
Larch
Northern pine
Pine/deciduous
Birch/aspen
Oak
Riverine
Fir
Larch
Northern pine
Pine/deciduous
Birch/aspen
Oak
0.0
Riverine
Mean ratio of encounter rate in forest type to encounter rate in Zapovednik
sufficiently large to suggest that no strong preferences exist for any drainage. Rather, it is likely
Figure 2.4.
Relative encounter rates within vegetation groups for: (a) red deer, (b) roe deer,
(c) sika deer, (d) musk deer, (e) moose, (f) wild boar.
18
Analysis of ungulate dynamics
that populations move among drainages in response to temporal heterogeneity in habitat quality.
Nevertheless, some patterns were seen in the use of different drainages, including a tendency for
Blagodatnoe and Khuntami to have relatively high populations of several species, whilst several
of the drainages further inland but within the same habitat zone, had relatively low abundances,
especially of deer. This finding may be explained by the distribution of forest types within the
oak-birch zone (see Fig 2.1). In particular, although we have considered the oak-birch zone as a
single habitat zone, it is clear that oak predominates in the coastal area, whilst birch and aspen
dominate more inland parts of the zone. The distinct nature of this separation, visible in Fig. 2.2,
might suggest that a four zone habitat classification would be more useful in SAZ. Alternatively,
the variation in distribution within the oak-birch habitat zone may reflect preference with coastal
areas, where snow density is generally less throughout the winter. Probably some combination of
variation in snow density, mast distribution (in some years) and perhaps some other features of
the forest types explain this pattern. Again, however, different climatic influences (particularly
that of the coast) might support division of the oak-birch zone into two zones. We return to these
ideas in Section 7.
The strong influence of habitat in explaining patterns seen among different drainages,
together with the striking disparities in encounter rates among forest types (Fig. 2.4), suggest that
forest type is a fundamentally important factor explaining variation in ungulate abundances
within the different zones. The patterns of apparent preference and avoidance are largely what
would be expected, although there are some unexpected results, such as the apparent preference
of wild boar for northern pine areas, in contrast to its average abundances in mixed pine and
deciduous areas. This type of anomaly is likely a result of much finer scale patterns in the mosaic
of habitats and would require a higher resolution of analysis than is possible using the winter
transect count data alone. Overall, however, it appears likely that stratification of survey data by
either drainage basin or vegetation type will improve the accuracy of density estimates, and we
build on this finding in the following section.
19
Analysis of ungulate dynamics
3. TRACK ENCOUNTER RATES AND UNGULATE DENSITIES
3.1
Background
Caughley (1977, p.12) observed that “The majority of ecological problems can be tackled with
the help of indices of density, absolute estimates of density being unnecessary luxuries.” For
three reasons, however, it is important to know the relationship between track encounter rates and
absolute densities of ungulates within SAZ. First, the process of converting track encounter rates
into estimates of density may help to identify sources of error in the estimates of density. As
such, the process may help with constructing confidence boundaries for predicted population
densities and identifying required differences in track encounter rates necessary to infer a
difference in population density. Secondly, analysing the long-term dynamics of ungulates within
SAZ will, necessarily, require some form of standardisation of abundance indices between
different areas within the reserve. Converting indices of relative abundance into estimates of
density will provide this standardisation. Thirdly, if it is possible to estimate absolute densities
from the winter transect count data, these would also be very useful in their own right for
management in SAZ. In particular, emerging evidence suggests that tiger numbers may be
closely related to prey biomass (Karanth et al., 2004; Miquelle et al., 1999) and it would be useful
to determine with greater accuracy how tiger and prey densities fit this pattern in SAZ (see further
in Section 6).
Although the question of how best to convert track data into density estimates has been
considered by Russian biologists for decades (e.g. Formozov, 1932), in the English language
scientific literature the topic is surprisingly rare, as is evidenced by the paucity of coverage the
subject receives in recent reviews (Schwarz & Seber, 1999) and textbooks (Williams et al., 2002).
In North America, some of the most elaborate work on this subject has used probability sampling
to estimate the size of a number of low density populations, using data on track encounters and
daily movement (e.g. Anderson & Lindzey, 1998; Becker, 1991; Becker et al., 1998; Garant &
20
Analysis of ungulate dynamics
Crete, 1997; Van Sickle & Lindzey, 1991).
Becker (1991) described two approaches to
probability sampling but both are reliant on a systematic survey design, in which transects are laid
out parallel to each other. Probability sampling is, thus, most practical when aerial surveys are
possible and is less relevant to the surveys conducted in SAZ. Consequently, we used three
approaches that are derived largely from the Russian literature on estimating ungulate population
densities from survey data, all of which could be directly applied to the data from SAZ.
The first and simplest method for estimating density from track encounters is an
empirical correction factor, used to translate combined encounter rates of deer tracks into
estimates of deer density and associated confidence intervals. This correction factor was derived
by regressing observed numbers of deer within a plot (determined by expert assessment of tracks
entering and leaving the plot) on numbers of tracks encountered when the plot perimeter was
walked (Gerow et al., 2005). The second method to estimate ungulate densities from survey data
uses a formula known variously as the Formozov (Mirutenko, 1986) or Formozov–Malyashev–
Pereleshin formula (Kuzyakin, 1983). All of these authors were involved in prompting the
derivation of the formula but it was perhaps most comprehensively set out by Chelintsev (1995).
The formula is based on probabilistic encounters between randomly placed and orientated animal
paths and surveyed routes. Hereafter, we refer to it as the FMP formula. The third approach that
can be used to assess the relationship between track encounters and population density is
simulation modelling. Using empirical records of movement patterns, large numbers of simple
simulations can be performed to provide a relationship between track encounter rates and
densities of paths. Simulation modelling is a computerised version of graphical techniques which
have a long history in Russia (e.g. Kuzyakin, 1983).
The second and third of these methods require estimates of daily travel distance and
actual daily travel routes, respectively. In this section, we begin by detailing the analysis of the
movement data, before going on to describe the estimation of population density by each of the
three methods described above.
21
Analysis of ungulate dynamics
3.2
Methods
3.2.1
Movement data
Movement data were collected as described in Section 1.3 and stored as vectors, with each total
path broken down into moves (e.g. see Turchin, 1998), defined by an angle and a distance. Both
straight line and total lengths of each move were recorded. Total lengths were used when
assessing the total distance travelled on any path but for assessing the probability of track
encounters, straight line distances were sufficient.
This is because local re-crossings were
ignored when transect data were collected.
To assess which factors influenced path characteristics, we first assessed general effects
on both travel distance and tortuosity (or curvilinearity) of the paths. Tortuosity was expressed in
terms of the turning rate (klinokinesis), measured as the mean degrees turned per metre travelled
(Murdie & Hassell, 1973). Initial analyses indicated that travel distance was the most important
characteristic likely to affect the probability of encountering paths during transects (see Section
3.3.1). Consequently, further analyses were conducted to compare the performance of a variety
of simple, one- or two-factor models, in explaining travel distances.
Two of the factors measured were mast abundance and snow depth. The data on mast
abundance have been described above (Section 1.3). Unfortunately, daily movements have not
been recorded in a wide range of mast conditions. Consequently, the five-point indices for oak
and Korean pine mast were collapsed into just two categories each: good or poor. Specifically,
the indices were taken to indicate a poor mast crop in years when the recorded mast index was
between zero and two, inclusive. All other years, with mast scores of from three to five, were
categorised as good mast years.
Daily movements were also recorded in relatively few snow depths, preventing the use of
snow depth as a continuous variable. Analyses of energy expenditure suggest that costs of
locomotion increase abruptly in snow depths above a certain proportion (40 – 60%) of ungulate
breast height (Parker et al., 1984). We decided to classify snow depth into shallow or deep on the
22
Analysis of ungulate dynamics
basis of whether it fell above or below an approximate threshold related to size. For red deer, we
used a value of 45cm as the threshold (Parker et al., 1984) whilst for roe deer, we used 25cm. For
wild boar, the threshold used was 20cm.
Models were compared using Akaike’s Information Criterion (AIC), modified for small
sample sizes (AICc). AIC and AICc converge as sample size increases, so it is generally better to
use AICc (Burnham & Anderson, 2002). All the models proposed were simple linear models, for
which AICc can be calculated as follows (Burnham & Anderson, 2002):
AIC c  AIC 
2 K ( K  1)
n  K 1
(3.1)
where K is the number of parameters (including the constant and an error term), n is the sample
size (or number of data points) and AIC is given by the formula:
AIC  2  log( )  2 K
(3.2)
where log(ℓ) is the log-likelihood of the model calculated (for linear models) as:
n
log( )    log( ˆ 2 )
2
and
ˆ 2 
RSS
n
(3.3)
(3.4)
where RSS is the residual sum of squares.
Models were ranked according to their Δi scores (calculated as the difference between
their AICc score and that of the model with the lowest AICc) and relative likelihood of models
was determined as:
 1 
exp    i 
2 
wi  R 
 1 
 exp   2  r 
r 1
(3.5)
where R is the set of all models for comparison. Models were compared and their relative support
used solely to infer which parameters explained the data most convincingly and, thus, which (if
23
Analysis of ungulate dynamics
any) parameters should be used to stratify movement data sets for further analyses (in particular,
for analyses of the relationship between track encounters and density).
All of the factors
examined are likely to affect animal movements in some way, so here, AIC was effectively used
as a magnitude of effects estimator (sensu Guthery et al., 2005).
3.2.2
Estimation of deer density using a correction factor
The correction factor used was derived by Gerow et al. (2005) to estimate combined densities of
red, roe and sika deer from encounter rates of their tracks. Plots were randomly selected in southeastern Primorye Krai (Olginski and Lazovski Raions), in oak/deciduous forests and mixed
conifer/deciduous forests.
During winter the plot boundary was traversed and tracks were
recorded to estimate the number of animals entering and leaving the plot during the previous 24
hours. Plot size and shape were chosen to minimize the chance that deer within the plot would go
undetected (i.e. not cross the plot boundary during the previous 24h period). Expert assessments
of the density of animals within the plot were then regressed on the number of tracks encountered.
A log-log plot was used to ensure homoscedasticity and the regression (and associated confidence
intervals) were used to derive the correction factor. The formula derived for the combined
density of red, roe and sika deer, D̂ , is (Gerow et al., 2005):
Dˆ  x  exp( 0.56  0.11)
(3.6)
where x is the combined encounter rate of paths of the three species. The upper and lower 95%
confidence intervals are given by using the upper and lower values of the exponent.
In practice, there are several ways in which equation 3.6 may be applied to field data
consisting of multiple samples (transect segments) for the study area and period in question.
Different methods are available to calculate both the mean and its associated confidence intervals.
Firstly, all transect segments could be considered to be sections of a single sample; in that case,
we can apply the equation exactly as written, calculating a single overall mean estimate of
24
Analysis of ungulate dynamics
density. Secondly, we might consider each transect segment to be a single sample. In this case,
we can use equation 3.6 to generate an estimate of density for each sample. We can then find the
mean of these estimates. Finally, because the transect segments are of different lengths, we may
wish to find a weighted mean of the estimates from each. This assumes that longer segments are
likely to be closer to the true encounter rate and, thus, give a better estimate of mean density in
the area. In fact, the weighted mean gives the same overall estimate of density as when the
samples are combined to give an overall mean. In general, we believe that weighting by transect
length is the best method and we discuss this approach (together with other forms of weighting)
in Section 3.2.4, below.
3.2.3
Confidence intervals for density estimation
Deriving confidence intervals associated with mean estimated densities is a problematic issue.
Some authors (e.g. Smirnov, 1973) have suggested that track encounters should be well described
by a Poisson distribution.
If this were the case, then given certain properties of Poisson
distributed data (for example, that the variance is approximately equal to the mean), confidence
intervals would be reasonably straightforward to estimate. However, there are several reasons to
believe that track encounters will not conform to a Poisson distribution. In particular, the
potential for multiple crossings of a single path (see further in Section 3.3.3), as well as the
possible non-independence of paths (e.g. Chelintsev, 1995), are both likely to cause deviations
from the Poisson distribution. One consequence of this is that the distribution of estimates of
density generated by independent transects is unknown and unlikely to conform well to a known
distribution. Furthermore, sample size for some areas in some years is also low, with the result
that the central limit theorem (leading to approximate normality of estimates when sample size is
high) is unlikely to apply. Owing to these complications, there is no tractable method for
estimating confidence intervals about the mean estimate of density. For that reason, we used
bootstrapping (Efron & Tibshirani, 1991, 1993) to determine estimates for confidence intervals.
25
Analysis of ungulate dynamics
Bootstrapping is a flexible procedure that uses computational power to reduce the number
of assumptions inherent in many other statistical approaches (Efron & Tibshirani, 1991). The
procedure may be conducted parametrically (by repeated re-sampling from the type of
distribution from which the experimental data are presumed to have been drawn) or nonparametrically (by repeated re-sampling from the available data set). The latter approach makes
no assumptions about the form of the distribution from which the data have been taken and so is
particularly appropriate for constructing confidence intervals for the estimates of ungulate
density. Four different methods for bootstrapping confidence intervals have been recommended
by Efron & Tibshirani (1993). Of these the BCA (“bias-corrected and accelerated”) approach is
generally believed to be the most accurate (Efron, 2003). ‘Bias-correction’ refers to adjustments
that are made to account for the discrepancy between the proportion of B bootstrap samples (see
further below) that lie below the mean and the proportion that lie above the mean (an indicator of
bias). ‘Acceleration’ refers to an adjustment made for heteroscedasticity in the data. Details of
the construction of confidence intervals by BCA can be found in Efron & Tibshirani (1993).
Here we give a brief overview with specific reference to bootstrapping confidence intervals for
the mean ungulate density, D.
We assume that N transect segments each give rise to an estimate of total deer density,
D̂ , and that these estimates form a vector, D̂ n (n = 1, 2, … N), with N elements. The arithmetic
mean of the estimates is D . Bootstrapping involves re-sampling with replacement from D̂ n to
produce B bootstrap replicates of the set of estimates, denoted D̂*b n (b = 1, 2, … B). From each
of these replicates, we can calculate a mean, D *b . The simplest way to create a 95% confidence
interval about the overall mean D , is known as the percentile method. A 95% confidence
interval is constructed assuming that 2.5% of the distribution at each tail is beyond the confidence
interval (this uses an α-level of 0.025, therefore). For percentile confidence intervals, the B
26
Analysis of ungulate dynamics
values of D *b are ordered and the estimate of D corresponding to Bα is selected as the lower
confidence limit, whilst that corresponding to B(1 – α) is selected as the upper confidence limit.
For example, if B = 1000 and α = 0.025, then the 25th lowest value of D will be the lower
confidence limit and the 975th lowest estimate will be the upper confidence limit. As noted
above, the BCA approach improves on this by correcting the values of α used to account for both
bias and heteroscedasticity. Specifically, two further parameters are calculated: z0 is the biascorrection and a is the acceleration. Bias-correction is given by (Efron & Tibshirani, 1993):
 # ( D *b  D ) 

z 0   1 

B


(3.7)
where # indicates the number of values of D *b that conform to the given condition (i.e. the
number that are less than the overall estimated mean) and Φ-1(x) indicates the inverse function of
a standard normal cumulative distribution function (i.e. the standardised number of standard
deviations giving the cumulative probability x. Note that if exactly half of the bootstrapped
estimates of density are less than the mean density, there is no bias and z0 = 0).
The acceleration is determined by a jackknife procedure, whereby i resampled sets of the
original set of estimates, each of size N-1, are generated by sequential deletion of the N elements.
The ith jackknifed replicate is thus equal to the original set of estimates, with the ith element
removed. The mean, Di , of each replicate is calculated and the mean of all means is denoted
D()  i 1 Di / N . The acceleration is then given by (Efron & Tibshirani, 1993):
N
i 1 D()  Di  
a
N
2 3/ 2
6i 1 D()  Di  
N
3
(3.8)
The two values determined by equations 3.7 and 3.8 are then used to adjust the α-values used for
determination of confidence limits in the percentile method. Specifically, α 1 and α2 are used for
the lower and upper limits, respectively, and are calculated by:
27
Analysis of ungulate dynamics
z 0  z ( )

1    z 0 
( )


) 
1  a( z 0  z


z 0  z (1 ) 
 2   z0 

1  a( z 0  z (1 ) ) 

(3.9)
where Φ(x) represents the number of standard deviations of a standardised normal curve
associated with the cumulative probability x, and z(c) is equivalent notation for cumulative
probability c.
Efron and Tibshirani (1993) suggest that accurate bootstrapping of confidence intervals
requires a large number of bootstrap replicates. For all BCA bootstrapping reported here, we
used B = 5000. As we used a weighted mean for estimating overall density, we also drew
bootstrap samples from a weighted pool, with both length and number of crossings used to make
up the bootstrap samples and find the bootstrap means.
3.2.4
Stratification and weighting of density estimates
Our analyses in Section 2 indicated that within a given broad habitat zone, species may not be
distributed uniformly between either drainage basins or forest types. For this reason, estimates of
density were derived in three different ways, as follows: (i) using weightings by segment length
alone; (ii) using weighting by segment length and drainage basin size (equivalent to stratification
by drainage basin); and (iii) using weighting by segment length and forest type (stratification by
forest type). The difference between these approaches is summarised by the following equations,
which indicate how mean estimated density for a given habitat zone, D̂ , was derived in each
case. First, for the simple case of weighting by transect length:
T
Dˆ 
 Dˆ .S
t 1
T
t
S
t 1
t
(3.10)
t
28
Analysis of ungulate dynamics
where T is the total number of transect segments surveyed in the area during the time period, D̂t
is the point estimate of density resulting from segment t (calculated by equation 3.6), and St is the
length of segment t.
Where estimates of density were stratified by drainage basin size, equation 3.10 was used
to calculate a new parameter, D̂b , the estimated density within the drainage basin for the given
period, based on the T transect segments conducted in that basin. Overall density for the habitat
zone was then calculated using:

Dˆ 
 Dˆ . A
b
b 1
b

A
b 1
(3.11)
b
where β is the total number of drainage basins in the habitat zone in which surveys were
conducted during the time period, and Ab is the area of drainage basin b. Clearly, both approaches
(described by equations 3.10 and 3.11) required similar modifications to the way that bootstrap
and jackknife means were calculated for use in equations 3.7 and 3.8. Where stratification by
drainage basin was used (equation 3.11), bootstrap and jackknife means were also calculated
using that stratification. Finally, for stratification by forest type, data were grouped using the
seven vegetation categories shown in Table 2.2. Density estimation was equivalent to that
illustrated by equation 3.11, except that D̂b was defined as the density within a forest type, Ab
was the total area dominated by that forest type within the habitat zone, and β was the number of
different forest types present within the zone.
3.2.5
Estimation of density using the FMP formula
The derivation of the FMP formula has been described in detail by Chelintsev (1995). All theory
presented here is derived from that paper. In brief, it is assumed that an animal’s daily travel path
(of length L) can be broken down into a large number (m) of moves which are effectively linear.
29
Analysis of ungulate dynamics
Each move has length Mi. A transect segment (of length S and any shape) can similarly be broken
down into t component parts, each of length Tj. Any move is assumed to lie at an angle, α, to a
given section of transect.
The probability, P(mi,tj,α), that a given move (mi) crosses a given section of transect (tj) at
angle α is therefore calculated as:
P(mi , t j ,  ) 
M i T j sin(  )
A
(3.12)
Note that the top part of this equation is the area of a parallelogram formed by mi and tj, whilst the
bottom (A) is the study area. Thus, the probability is the ratio of the area within which the move
must start (in order to cross the transect section) to the whole study area, and is thus the
probability that a randomly located move starts close enough to the transect section to cross it.
Given an equal probability of travel in any direction (i.e. any angle, α, between the move and
transect section), the average probability of a crossing for any value of α is given by integrating
equation 3.12 for the interval of 0 to 2π, and dividing the result by 2π. As the integral of |sin(α)|
from 0 to 2π is 4, this yields:
P(mi , t j ) 
2M i T j
A
(3.13)
Given a density of animals in the study area of D = N/A and summing the probability given by
equation 3.13 for all m sections of the movements of all N animals in the area, it is possible to
show that the estimated density is given by:
 x
Dˆ 
2SLˆ
(3.14)
where x is the number of tracks encountered, S is the length of a transect (or transect segment)
and L̂ is the estimated daily travel distance of the species monitored. This is the FMP equation.
30
Analysis of ungulate dynamics
Here, error in the estimated density may arise from two sources, both error in x and error
in L̂ . In this case, however, the resultant variance in D̂ is derived by the multiplicative rule of
error propagation:
 x2
 Dˆ 2  Dˆ 
 x


 Lˆ 2 
Lˆ 
(3.15)
The above derivation applies to situations in which each path (and each move within a path) is
randomly located. Track encounters in such situations are likely to be well explained by a
Poisson distribution and, hence (using a property of Poisson distributions), variance in the
estimated track encounter rate will be equal to the mean encounter rate itself. However, these
relationships are complicated by two factors: the non-independence of multiple crossings of a
single path, and the non-independence of multiple paths when animals travel together.
Chelintsev (1995) discussed the derivation of error calculations for such circumstances in
some detail. Unfortunately, his resultant formula for variance depends on several parameters that
may not be known in empirical surveys of animal tracks. These include estimates of the number
of times that each path is crossed and estimates of average group sizes. As with estimates derived
using the correction factor, the uncertainty surrounding these parameters and, by extension, the
form of the resultant distribution, means that determining confidence intervals about mean
estimates of density is most accurately performed using the BCA bootstrap procedure (Section
3.2.3). Consequently, this method was used to generate confidence intervals for mean estimates
of density produced by the FMP formula. As with estimates based on the correction factor, each
transect segment from a given time period and area was assumed to represent an independent
estimate of density. Mean estimates and associated confidence intervals were again calculated in
three ways: first by weighting in proportion to the length of the transect segment and then, also,
using stratification by either drainage basin area or by area of forest type (Section 3.2.4).
31
Analysis of ungulate dynamics
3.2.6
Estimation of density using simulations
Estimating density using simulations requires several steps. First, it is necessary to determine a
suitable sample of movement data with which to estimate densities. Methods for analysing
available movement data in order to identify suitable samples are presented in Section 3.2.1,
above. Next, track encounter probabilities must be estimated by simulating transects through a
survey area containing a given number of movement paths. If animals are distributed randomly
within an area of habitat, it is expected that mean encounter rates of individual paths will increase
linearly with density and that the number of encounters of individual paths (either one or more
times) will conform to a Poisson distribution. It was necessary to test both of these predictions
and to determine the relationship between transect (or transect segment) length and the
distribution of multiple encounters of a single path (assuming the path is encountered at least
once). Finally, the most probable density given any encounter rate on a transect of given length
can be estimated. To do this, it was assumed that the total number of track encounters, x, is given
by:
Y
x   ni
(3.16)
i 1
where Y is the total number of unique tracks encountered and n is the number of times that each
of those unique tracks is encountered. For any density, the most probable value of x will be the
expectation of x, E(x), given by:
E(x) = E(Y) × E(n)
(3.17)
If Y increases linearly with density for a given transect length and n is constant for a given
transect length, then E(x) will also increase linearly with density. Thus, where x is known and Y
and n can be predicted, the most probable density ( D̂ ) leading to x can be estimated. That value
was taken to be a point estimate of density. As with the previous approaches, estimates arising
from independent transect segments were then bootstrapped using the BCA technique, in order to
determine confidence intervals about a weighted mean.
32
Analysis of ungulate dynamics
Unique path encounter probabilities, p(Y), and probabilities of multiple encounters with
unique paths, p(n), were determined by simulation. The simulated survey area was 2,500 km2 (50
× 50 km).
Movement paths recorded in the field were converted into schematics, each
comprising m straight line moves. These were read into the model as m+1 sets of coordinates
(x1,y1 – x2,y2; x2,y2 – x3,y3; … xm,ym – xm+1,ym+1). To simulate the required density of paths, a
given number of movement paths were picked at random (from a set of paths appropriate for the
particular analysis) and randomly placed in the survey area, ensuring that the entire path was
within the area. Transects of a given length were then designated randomly and compared to each
move of each path to determine whether they crossed the section. Encounter rates were expressed
per km of transect.
Pilot tests were run using all of the red deer movement paths. A range of path densities
from 0.25 km-2 to 10 km-2 and a range of transect lengths from 100 m to 5 km, were simulated to
ensure that encounter rates with unique paths increased linearly with both path density and
transect length.
For each density and transect length, 100,000 replicate simulations were
performed, with path and transect locations randomised for each replicate.
Thereafter,
simulations used only relatively low path densities (1 km-2) and were performed using subsets of
the movement paths available for each species. Relatively low path densities were used as
simulations of low densities required fewer comparisons (between transects and path sections)
than when high densities were used. Subsets of the movement paths available for a species were
used where analyses indicated that one or more factors had a substantial bearing on the
characteristics of paths collected under different circumstances (see results, Section 3.3.1).
3.3
Results
3.3.1
Movement data
Detailed records of 280 daily (24-hour) movements of individuals or groups of animals were
collected during the winters of 1999/2000 to 2003/4. These included records of the movements
33
Analysis of ungulate dynamics
of four ungulate species, in two areas (Lazovski Zapovednik and SAZ). Records are summarised
in Table 3.1, and their main features (length and tortuosity) are shown in Fig. 3.1. No data on
daily movements of moose or musk deer are available from this study. However, observations of
musk deer in SAZ suggest that the mean 24-hour travel distance for males and females is
approximately 1.5 km (Zaitsev, 1991). This figure was used for analysing musk deer survey data
but moose are not considered further in this section.
Although sample sizes are small for Lazovski Zapovednik, the data appear to reflect quite
different movement patterns to those indicated for SAZ. In particular, both red deer and roe deer
show much longer average movements in Lazovski Zapovednik than SAZ, whilst wild boar move
much smaller distances in Lazovski Zapovednik. Tortuosity of movement is similar in the two
areas for these three species, indicating similar patterns of movement despite the different
distances. By contrast, sika deer have similar mean movement lengths but apparently dissimilar
tortuosity in the two areas. The differences are less marked in this species and may reflect the
smaller sample sizes. However, given the general differences apparent from Fig. 3.1, as well as
the limited data available from Lazovski Zapovednik, further analyses of dynamics in SAZ were
conducted using only the data from SAZ.
Within SAZ, tortuosity was remarkably consistent among movement records (note the
narrow confidence intervals about the mean in Fig 3.1) for each species. Furthermore, for species
for which the most data were available, tortuosity and length of movements were significantly
negatively correlated (red deer, Pearson’s r = -0.213, p < 0.05; wild boar, r = -0.347, p < 0.001),
suggesting that distance travelled is a good general parameter characterising movement. By
contrast to tortuosity, distance moved in 24 hours was relatively variable, especially for sika deer
and wild boar. This factor is particularly important in influencing estimates of density generated
from track encounter rates. Consequently, we analysed these data further, in order to investigate
the impact of different factors on distance moved.
34
Analysis of ungulate dynamics
Table 3.1
24-hour movement data collected
Species
Number of records from:
Lazovski
SAZ
Zapovednik
Red deer
Roe deer
Sika deer
Wild boar
(a)
7
9
14
3
90
62
10
85
5000
Length (m)
4000
3000
2000
1000
(b)
3.5
Tortuosity (ºm-1)
0
3
RE (n = 7, 90)
RO (n = 9, 62)
SD (n = 14, 10)
WB (n = 3, 85)
RE (n = 7, 90)
RO (n = 9, 62)
SD (n = 14, 10)
WB (n = 3, 85)
2.5
2
1.5
1
0.5
0
Species and sample sizes
Figure 3.1.
Mean length (a) and tortuosity (b) for paths of the four different species in
Lazovski Zapovednik (filled bars) and SAZ (open bars): RE, red deer; RO, roe deer; SD, sika
deer; WB, wild boar. Error bars show 95% confidence interval. Figures in parentheses show
sample sizes for Lazovski and SAZ, respectively.
35
Analysis of ungulate dynamics
Factors that might be expected to affect travel distance include snow depth, habitat type,
quality of mast crop, time of year and size of the travelling unit (whether a solitary animal or
multiple animals). Unfortunately, the data do not provide an even representation over a range of
values for each of these parameters. Furthermore, a full analysis of the importance of all factors
is impossible without larger sample sizes (numbers of 24-hour movement records). Sample sizes
currently available restrict the potential for sub-dividing movement records on the basis of more
than one or two parameters. For sika deer, we reasoned that sample size was so small, that
dividing the data for further analyses (for example, for estimation of densities from transects
conducted during different periods of winter, or from transects conducted in different habitats)
would render the mean distance unacceptably sensitive to outlying values of distances moved
under those conditions. Consequently, we did not subdivide the sika deer movement data for
further analyses.
To discern which parameters might be of greatest importance in dictating travel distance
for the other three species, we used AICc to compare a range of simple, one- or two-factor models
to explain the distance moved by red deer, roe deer and wild boar. Models were designated a
priori and were restricted by the range of possible causal parameter values for which data were
available. All possible one- and two-factor models were assessed, except where a factor had no
contrasting variable values. Results of the model comparisons are given in Table 3.2.
The comparison of models indicated that for red deer, no factor explained much of the
observed variance in travel distance (which was, in any case, very limited). Time of year did
feature in all of the best supported models and, as such, we divided the red deer movement data
into subsets from early and late winter for further analysis. We note, however, that this is likely
to bring only a very slight improvement to the accuracy of density estimates. Models were more
successful in explaining variation in roe deer movements, with time of year alone explaining over
50% of observed variance and group size providing additional explanatory power. Effect of
36
Analysis of ungulate dynamics
Table 3.2
Comparison of simple, single factor models for the travel distances of three
species
Species
Model variables
K
AICc
Δi
wi
R2
Red deer
Time of year
Time of year, individual or group
Time of year, snow deptha
Time of year, mast qualityb
Time of year, habitat typec
Individual or group
Snow depth
Mast quality
Habitat type
Snow depth, individual or group
Habitat type, individual or group
Mast quality, individual or group
Habitat type, mast quality
Habitat type, snow depth
Snow depth, mast quality
3
4
4
4
4
3
3
3
3
4
4
4
4
4
4
-131.45
-130.17
-129.32
-129.28
-129.26
-128.67
-127.51
-127.11
-127.04
-126.94
-126.49
-126.48
-125.60
-125.37
-125.32
0.00
1.28
2.13
2.17
2.19
2.78
3.94
4.34
4.41
4.50
4.96
4.97
5.85
6.08
6.13
0.279
0.148
0.096
0.095
0.094
0.070
0.039
0.032
0.031
0.029
0.023
0.023
0.015
0.013
0.013
0.048
0.058
0.049
0.048
0.048
0.018
0.005
0.001
0.000
0.023
0.018
0.018
0.008
0.006
0.005
Roe deer
Time of year, individual or group
Time of year
Time of year, habitat type
Time of year, snow depth
Habitat type, snow depth
Habitat type
Habitat type, individual or group
Snow depth, individual or group
Snow depth
Individual or group
4
3
4
4
4
3
4
4
3
3
-95.64
-90.42
-89.21
-88.74
-52.16
-49.98
-49.00
-47.73
-46.10
-45.45
0.00
5.22
6.43
6.90
43.48
45.66
46.64
47.91
49.54
50.19
0.873
0.064
0.035
0.028
0.000
0.000
0.000
0.000
0.000
0.000
0.585
0.532
0.540
0.537
0.164
0.102
0.120
0.102
0.044
0.033
Wild boar
Time of year, habitat type
Time of year, mast quality
Habitat type
Habitat type, snow depth
Habitat type, individual or group
Habitat type, mast quality
Time of year, individual or group
Time of year
Snow depth, mast quality
Mast quality
Time of year, snow depth
Mast quality, individual or group
Individual or group
Snow depth
Snow depth, individual or group
4
4
3
4
4
4
4
3
4
3
4
4
3
3
4
150.96
153.11
155.39
155.77
156.97
157.04
158.38
159.66
159.97
160.12
161.61
161.71
165.22
165.74
166.13
0.00
2.15
4.43
4.81
6.00
6.08
7.42
8.69
9.00
9.16
10.65
10.74
14.25
14.78
15.16
0.585
0.200
0.064
0.053
0.029
0.028
0.014
0.008
0.006
0.006
0.003
0.003
0.000
0.000
0.000
0.188
0.167
0.122
0.140
0.128
0.127
0.114
0.077
0.097
0.071
0.079
0.078
0.014
0.008
0.029
a
Categorical variable indicating shallow or deep snow. For red deer, the threshold was set at 45cm. For
roe deer, the threshold was 25cm.
b
Categorical variable indicating quality of mast crop, either acorn or pine nut dependent on the dominant
trees in the habitat in which data were collected. No roe deer movement data have yet been collected in
poor mast years.
c
Movement data have so far been collected only in the Oak and Korean pine habitat zones.
37
Analysis of ungulate dynamics
group size cannot be applied currently to refine density estimates because such data were not
reported in the track count surveys. In future, however, it would be beneficial to record such
information. As with red deer, we based analyses of roe deer densities on subsets of the
movement data for early and late winter. Finally, for wild boar, the model based on both time of
year and habitat type received markedly more support than competing models. Consequently, the
wild boar movement data were divided into four subsets (defined by these two variables) for
further analysis.
3.3.2
Estimating density: comparison of weighting approaches
Three different weighting methods (by segment length alone, or by segment length in conjunction
with stratification by either drainage basin area or area of forest type) were used to generate
estimates of density from the survey data. We begin by comparing the predictions made using
these three weighting approaches in conjunction with the correction factor estimator.
Table 3.3 shows the main features of predicted density using the correction factor to
estimate combined density of red, roe and sika deer. Typically, estimates derived using the three
weighting approaches were highly similar for each habitat zone, with no strong tendency for one
method to produce consistently higher or lower results than another, or to have consistently larger
confidence intervals than the others. However, an examination of overall correlations between
the three different weighting approaches (Table 3.4) suggests some of the limitations of the
method involving post-stratification by forest type. Although correlations between the methods
are generally high (Pearson’s r > 0.86 in most cases), this is not the case for correlations between
estimates derived for the Korean pine-deciduous habitat using post-stratification by forest type,
and those derived for the same habitat using the other two weighting approaches (Pearson’s r <
0.63 in both cases). The reasons for this can be seen by looking at the time-series of predictions
made (Fig. 3.2), and are largely attributable to a single prediction (see Fig. 3.2c, 1994). This
38
Analysis of ungulate dynamics
Table 3.3
Habitat zone
Oak-birch
Comparison of combined red, roe and sika deer density estimates derived using
the correction factor in combination with different weightings (SL, segment
length; DB, drainage basin area; FT, forest type area). Figures in parentheses
show one standard error.
Mean estimated density (km-2):
whole
last 5
Weighting
period
years only
Mean CI proportionsa:
lower
upper
SL
SL + DB
SL + FT
6.29 (± 0.76)
6.59 (± 0.81)
6.14 (± 0.74)
11.21 (± 1.15)
9.46 (± 0.92)
10.51 (± 1.09)
0.29 (± 0.03)
0.31 (± 0.02)
0.30 (± 0.03)
0.51 (± 0.08)
0.45 (± 0.04)
0.52 (± 0.08)
Korean pinedeciduous
SL
SL + DB
SL + FT
Spruce-fir
SL
SL + DB
SL + FT
3.26 (± 0.24)
3.27 (± 0.22)
3.22 (± 0.34)
0.98 (± 0.16)
0.98 (± 0.16)
0.93 (± 0.14)
5.61 (± 0.75)
5.39 (± 0.63)
5.17 (± 0.78)
2.80 (± 0.35)
2.80 (± 0.35)
2.33 (± 0.33)
0.27 (± 0.01)
0.27 (± 0.02)
0.31 (± 0.02)
0.48 (± 0.03)
0.48 (± 0.03)
0.49 (± 0.03)
0.40 (± 0.03)
0.41 (± 0.04)
0.44 (± 0.03)
0.87 (± 0.09)
0.87 (± 0.09)
0.78 (± 0.09)
a
Proportional size of confidence interval is given as deviation divided by mean. Note that upper
confidence intervals are generally larger than lower confidence intervals as (i) the latter are bounded by
zero when bootstrapping; and (ii) the former tend to be exaggerated when distributions are clumped.
estimate of 12.8 km-2 (CI: 12.1 - 14.3) contrasts starkly with those for the same year made using
no stratification or stratification by drainage basin area: 2.9 km-2 (2.1 - 4.5) and 4.0 km-2 (2.7 7.2), respectively. Predictions for this year and habitat are clearly varied, due to a number of
short transect segments on which the tracks of large herds of deer were encountered. However,
the prediction made using post-stratification by forest type stands out as an anomalous result. A
further note of caution regarding this approach to weighting data is illustrated by Fig. 3.2d. For
this figure, the vegetation code associated with a single transect from the Korean pine-deciduous
habitat in 1994 was altered. Specifically, a transect segment designated as running through oak
forest (a relatively rare forest type, accounting for less than 5% of the Korean pine-deciduous
zone), was recoded to northern pine (which dominates closer to 50% of the habitat zone; see Fig.
2.1 also), in order to see what effect this would have. The consequences of this minor alteration
were substantial, reducing the predicted density for the year and habitat from almost 13 km-2 to
39
Analysis of ungulate dynamics
just 3.0 km-2 (2.0 - 5.0) (Fig 3.2d), a prediction much more in line with those derived using the
alternative weighting approaches. In addition, this slight adjustment increased the correlation
coefficients between predictions derived using stratification by forest type, and those derived
using no stratification or stratification by drainage basin area, respectively, to r = 0.92 and r =
0.81.
The findings above illustrate several points regarding the best methods for density
prediction. First, in contrast to the concerns raised in Section 2, which suggested that ungulates
are far from uniformly distributed between drainages and vegetation types, the generally high
correlations between predictions made using different methods are reassuring. These correlations
suggest that the distribution of survey effort between different drainages and forest types is
broadly representative of the relative areas of these different features within SAZ. Secondly, and
perhaps most importantly, our findings illustrate the extreme sensitivity of predictions made using
stratification by forest type, to the designation of dominant vegetation type along transects. By
comparison to defining the boundaries of drainage basins or major habitat zones (a process which
is assisted by major geographical features such as watersheds, and physical features such as
altitude), defining the boundaries of different forest types is relatively subjective.
These
boundaries are neither static in time nor, typically, are they clearly demarcated by abrupt
Table 3.4
Correlations between combined red, roe and sika deer densities predicted using
the three different weighting approaches
Habitat
Oak-birch
Weighting
SL
SL + DB
Korean pine-deciduous SL
SL + DB
Spruce-fir
SL
SL + DB
Weighting:
SL + DB SL + VT
0.913
0.915
1.000
-
0.983
0.864
0.615
0.626
0.961
0.961
40
16
16
Estimated density (km-2)
(a)
12
12
8
8
4
4
0
1962
16
1972
1982
1992
2002
0
1962
1972
1982
1992
2002
1972
1982
1992
2002
16
(b)
(d)
12
12
8
8
4
4
0
1962
(c)
1972
1982
1992
2002
0
1962
Year
Figure 3.2
Estimates of combined red, roe and sika deer density in the Korean pine-deciduous habitat, derived using the correction factor
method and: (a) weighting by transect segment length only; (b) weighting by segment length and drainage basin area; (c) weighting by segment
length and forest type (unaltered data set); (d) weighting by segment length and forest type (single data point recoded to alter vegetation
designation - see text for further details). Error bars show confidence intervals.
Analysis of ungulate dynamics
transitions. Furthermore, some areas do not correspond to any of the seven main forest types
used in our analyses and, consequently, a small proportion of data points had to be excluded from
analyses based on forest type. Overall, these findings (and especially those illustrated by Fig. 3.2)
cast doubt on the merits of post-stratification by forest type and we do not consider that method
further.
Finally, although our results illustrate a high degree of similarity between predictions
made using unstratified data and those derived using data stratified by drainage basin, we suggest
that the differences between these approaches could be important. In particular, stratification by
drainage basin tends to produce more conservative estimates, especially for more recent years
when ungulate densities have reached relatively high levels (see Table 3.3). More importantly,
outliers predicted using the unstratified data are often less extreme when stratification by drainage
basin is used (see, for example, 1982 in Fig. 3.2a,b), and this is reflected in slightly lower
variance associated with mean estimates over either the whole period or, more strikingly, over the
past five years (Table 3.3). For these reasons, and because our spatial analyses (Section 2)
indicated some degree of heterogeneity in ungulate densities between basins, we recommend that
stratification by drainage basin is used. Consequently, further results presented in this section
were all derived using that weighting method.
3.3.3
Parameters for density estimation by the FMP formula and simulation methods
For the FMP method, estimates of density were made using equation 3.14, which requires
estimates of total length of transect segments, travel distance and numbers of path intercepts.
Based on the findings from Section 3.3.1, data on movements were divided into subsets as
appropriate, with mean travel distances used as indicated in Table 3.5. As discussed in Section
3.2.3, each transect segment was treated as an independent sample for estimates made using the
FMP approach. For this reason, uncertainty in each estimate (arising from variance in travel
distances) is unimportant relative to uncertainty between estimates (arising from spatial and
42
Analysis of ungulate dynamics
temporal heterogeneity in ungulate distributions).
Overall estimates of density will have
confidence limits dictated by the variance between estimates, and it is sufficient to use mean
distances to calculate the expected estimate associated with each transect segment. Consequently,
variation in travel distance (as given in Table 3.5) was unimportant for the estimation of densities;
it is shown only for clarity.
For the simulations, pilot tests indicated that, as expected, path encounters increased
linearly with density, such that doubling the number of paths per unit area led to doubling the rate
with which unique paths were encountered.
Consequently, further simulations were only
conducted by varying transect length (as transect length was an important predictor of multiple
encounters of the same path). Simulations were conducted using the subsets of movement data
indicated in Table 3.5.
In general, the approach used to estimate density is that described by equations 3.16 and
3.17. The simulations were used to derive formulae predictive of E(Y) and E(n), as defined in
equation 3.15. The first of these describes the relationship between path density, transect length
and numbers of encounters with unique paths. Simulations indicated that for red deer tracks in
Table 3.5
Estimates of daily travel distances used for calculations based on the FMP
formula. Confidence intervals are given for information only.
Species
Conditions
Red deer
Red deer
Roe deer
Roe deer
Sika deer
Musk deer
Wild boar
Wild boar
Wild boar
Wild boar
Early winter
Late winter
Early winter
Late winter
All
All
Early winter, OB habitat
Late winter, OB habitat
Early winter, KD habitat
Late winter, KD habitat
Sample size
Mean
27
63
11
51
10
6
36
8
35
1.52
1.29
2.19
0.89
2.78
1.50
3.63
3.00
7.13
4.40
Travel distance, km
95% confidence interval
1.30
1.18
1.63
0.79
1.50
-
1.74
1.40
2.75
0.99
4.06
0.86
2.42
3.89
3.57
- 6.39
- 3.59
- 10.36
- 5.22
43
Analysis of ungulate dynamics
early winter, the mean number of unique paths encountered path-1 km-2 km-1, λ = 0.559. Note that
the units of λ are path-1 km-2 km-1, indicating that it is a function both of the number of paths per
km2, and that it depends on the transect length (in km). For any given density (D) and transect
length (S), the expected number of unique paths encountered by a transect is (Fig. 3.3a):
E (Y )  DS
(3.18)
Rates of encounter of unique paths made by roe deer, sika deer and wild boar were also
determined and the mean encounter rates for each species are given in Table 3.6.
The second variable to be predicted, E(n), describes the relationship between transect
length and multiple encounters of a single path. As transect length increases, so the probability
that a path, once encountered, will be repeatedly crossed, also increases. Obviously, above a
certain transect length (corresponding to the widest chord of a path), numbers of crossings of a
given path will not increase.
Thus, the relationship between E(n) and transect length is
asymptotic and is well described by a Michaelis-Menton function (Fig. 3.3b) of the form:
E ( n)  1 
aS
bS
(3.19)
where a and b are constants for a given set of movement paths, and S is transect length. Once
again, parameters were determined for the movement data for each species, or the relevant
subsets, as described above. Parameters are summarised in Table 3.7.
The parameters in Table 3.6 and 3.7 were used (with equation 3.17) to predict expected
numbers of track encounters on a transect of given length at a high density of track abundance.
Actual encounter rates on any transect were then used to interpolate, providing a point estimate of
density. Point estimates of density for a given time period and area were bootstrapped to provide
confidence intervals about the mean estimated density.
44
Analysis of ungulate dynamics
(a)
Mean number of unique paths
encountered by a transect
10.00
1.00
0.10
0.01
0.1
1
10
Mean frequency with which
individual paths, once encountered,
are crossed
(b)
2.0
1.8
1.6
1.4
1.2
1.0
0
1
2
3
4
5
Transect length, km
Fig. 3.3
Estimating parameters for density estimation from simulations. The example
given is for red deer in early winter (N = 27 daily movement records). (a) Number of unique
paths encountered by a transect of length S = 1km, when path density is D =1km-2 was estimated
as the gradient of the relationship illustrated (in this case, λ = 0.5592). (b) Parameters of the
function relating mean number of encounters per path encountered to transect length were solved
by least squares fitting of equation 3.19 to simulated data.
45
Analysis of ungulate dynamics
Table 3.6
Mean encounter rates of unique ungulate paths determined by simulation
Species
Conditions
Red deer
Early winter
Late winter
Early winter
Late winter
All
Oak-birch, early winter
Oak-birch, late winter
Korean pine-deciduous, early winter
Korean pine-deciduous, late winter
Roe deer
Sika deer
Wild boar
Table 3.7
0.559
0.503
0.596
0.353
0.819
1.639
1.111
2.651
1.395
Parameters underlying multiple encounter rates of unique paths, as determined by
simulation. See main text for further details.
Species
Conditions
Red deer
Early winter
Late winter
Early winter
Late winter
All
Oak-birch, early winter
Oak-birch, late winter
Korean pine-deciduous, early winter
Korean pine-deciduous, late winter
Roe deer
Sika deer
Wild boar
3.3.4
Estimated mean (λ) for 1 km
transect, when density is 1 km-2
Parameter estimates
a
b
0.807
0.698
1.475
0.676
1.359
0.671
0.964
1.011
1.251
0.212
0.233
0.244
0.198
0.415
1.748
0.884
1.142
0.633
Comparison of estimators
We began by comparing density estimates produced by the FMP and simulation methods (Fig.
3.4). Clearly, the estimates produced by the two methods were very similar. A line through the
origin with a gradient of unity (indicating an exact match between the two methods) had an R2 >
0.995 in each case. Owing to these similarities and to its relative simplicity, estimates produced
using the FMP formula were used for further analyses.
46
Analysis of ungulate dynamics
Combined red deer, roe deer and sika deer density was estimated using the correction
factor and FMP methods. In the latter case, estimates were derived independently for each deer
species and these were summed for each transect segment.
Combined totals were then
bootstrapped. Comparisons of point estimates are shown in Fig. 3.5. In all habitats and across
the full range of densities, the correction factor produced estimates of density in the order of 1.6
times as high as those produced by the FMP formula.
3.3.5
Final estimates of density
In the previous section, we showed that estimates of density produced by the FMP and simulation
methods were highly similar. Consequently, final estimates of the density of each species over
time were produced using the FMP formula. Specifically, we used the travel distances given in
Table 3.5 and the BCA bootstrapping method for determining confidence intervals. Estimates of
density were determined for all species except moose (for which no data on travel distance are
available from SAZ). All estimates are shown in Fig. 3.6. Red deer are clearly the most
abundant ungulate in SAZ, followed by roe and musk deer. Sika deer are restricted to the
southern, coastal, low altitude areas, whilst wild boar are generally the least abundant of the
species analysed. Musk deer show the least consistency in patterns of abundance, possibly owing
to the lack of information concerning their movements. More detailed information on differences
in movements between years may well improve our understanding of musk deer dynamics.
3.4
Discussion
Our results suggest that relatively simple approaches can be used to convert track encounter rates
into estimates of absolute density in SAZ.
The most complex and time-consuming of the
conversion methods was the simulation approach but the results suggest that estimates derived
using the FMP formula are extremely similar, and that this much simpler, more tractable
47
Analysis of ungulate dynamics
10.0
(a)
8.0
4.0
2.0
3.0
1.5
2.0
1.0
1.0
0.5
6.0
4.0
2.0
0.0
0.0
0.0
6.0
2.0
4.0
6.0
8.0
10.0
0.0
0.0
1.0
2.0
3.0
4.0
3.0
(b)
0.0
0.5
1.0
1.5
2.0
0.5
0.4
Density estimates derived using simulations (km-2)
4.0
2.0
0.3
0.2
2.0
1.0
0.1
0.0
0.0
0.0
1.0
2.0
4.0
6.0
0.0
0.0
1.0
2.0
3.0
0.0
0.1
0.2
0.3
0.4
0.5
(c)
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.5
0.6
0.1
(d)
1.0
0.4
0.5
0.2
0.0
0.0
0.0
0.5
1.0
1.5
0.0
0.0
0.2
0.4
0.6
0.0
0.1
-2
Density estimates derived using the FMP formula (km )
Figure 3.4
Comparisons of population density estimates derived using the FMP formula and
the simulation approach, for oak-birch habitat (left), Korean pine-deciduous habitat (centre) and
spruce-fir habitat (right). Panels show: (a) red deer, (b) roe deer, (c) sika deer and (d) wild boar.
Estimates derived using data stratified by drainage area. Broken lines show expected relationship
if estimates were identical.
48
Analysis of ungulate dynamics
3.0
3.0
Ratio of correction factor estimate to FMP estimate
(a)
2.5
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
0
5
10
15
3.0
0
5
10
3.0
(b)
2.5
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
0
1
2
3
4
5
6
3.0
0
1
2
3
0.0
0.5
1.0
1.5
3.0
(c)
2.5
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
0.0
0.5
1.0
1.5
2.0
2.5
-2
Combined deer density (km ) derived using the FMP formula
Figure 3.5.
Comparison of methods for predicting combined densities of red deer, roe deer
and sika deer in (a) oak-birch, (b) Korean pine-deciduous, (c) spruce-fir habitat. Open circles are
individual data points (for one year), broken line indicates a ratio of unity, expected if the two
methods produce matching results.
49
2
18
3
Analysis
of ungulate dynamics
8
(a)
6
12
2
4
6
1
2
0
1962
1972
1982
1992
2002
8
Estimated density (km-2)
1972
1982
1992
2002
7
(b)
(c)
0
1962
0
1962
1972
1982
1992
2002
1972
1982
1992
2002
1992
2002
1992
2002
1992
2002
3
6
6
5
2
4
4
3
1
2
2
1
0
1962
1972
1982
1992
2002
2.0
1.5
0
1962
1972
1982
1992
2002
0
1962
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
1.0
0.5
0.0
1962
1972
1982
1992
2002
3.0
0.0
1962
1972
1982
1992
2002
12
(d) 2.5
0.0
1962
1972
1982
6
9
2.0
4
1.5
6
1.0
2
3
0.5
0.0
1962
1972
1982
1992
4
2002
0
1962
1972
1982
1992
0
2002 1962
1
1972
1982
0.6
(e) 3
0.4
2
0.2
1
0
1962
1972
1982
1992
0
2002 1962
1972
1982
1992
2002
0.0
1962
1972
1982
Year
Figure 3.6.
Estimates of population density in oak-birch habitat (left), Korean pinedeciduous habitat (centre) and spruce-fir habitat (right), (a) red deer, (b) roe deer, (c) sika deer,
(d) musk deer and (e) wild boar. Estimates derived using the FMP formula, with BCA
bootstrapping for confidence intervals. Data stratified by drainage area.
50
Analysis of ungulate dynamics
approach can be used instead of simulations. Thus, the major problems with density estimation
are those concerned with obtaining accurate estimates of daily travel distance (and the factors
affecting this parameter), together with designing accurate, unbiased and correctly stratified
survey methodologies (see further in Sections 5 and 7).
Overall, the estimates suggest that (of the species examined) densities are highest in the
coastal oak-birch areas, typically lower in the mid-elevation Korean pine-deciduous area, and
lowest in the spruce-fir forests that dominate the western macroslope of the Sikhote-Alin
Mountains within SAZ. Red deer were the most abundant species, with an average density in
SAZ in recent years of around 1.5 to 3.0 km-2. Roe deer were next most abundant, occurring at
densities of nearer 1 to 2.5 km-2. Neither sika deer nor wild boar are very abundant at all, both
occurring at about 1 per 8 or 9 km2 overall. Musk deer appear to be present at an average density
of about 1 km-2 but this must be regarded as a very preliminary estimate, pending further
information on musk deer daily movements.
Comparisons between methods using stratified and unstratified data showed that
stratification by forest type is not a viable approach, as results are far too sensitive to this
relatively subjective classification. Owing to the difficulties inherent in demarcating forest types,
estimation of the area dominated by each forest type is also subject to errors that may be
propagated by extrapolation. Furthermore, forest types form a mosaic in a way that is very
distinct from features with a more geographical basis. It is likely that animals will often move
between elements of the mosaic in a way that they would not move between drainage basins, for
example. Less favoured forest types may be used extensively, if they are often found between
patches of preferred types. Thus, the value of forest type as a stratification or weighting factor, is
dependent on the precise configuration of the mosaic in any area. By contrast, estimates derived
using the other weighting approaches were generally in very good agreement. This suggests that
within each major habitat zone, the transect system is currently well designed (in terms of effort
in km km-2) to reflect the relative size of different drainages. Nevertheless, including weightings
51
Analysis of ungulate dynamics
by drainage basin size might have some influence over final estimates and this is the weighting
approach that we recommend.
That the correction factor tended to overestimate density may be due to a combination of
factors. First, data used to determine the correction factor came from different study areas in
Primorye Krai (Gerow et al., 2005). We have determined that the movement of animals can be
markedly different, even between relatively proximal areas (see Section 3.3.1) and, potentially,
among different habitats.
It is likely that grouping data from different areas can obscure
substantial variation in the relationships between track encounters and density in those different
areas. Secondly, the data used to derive the correction factor came from areas of relatively low
density (typically less than 2 km-2, with associated track encounter rates less than 1.5 km-1)
(Gerow et al., 2005). Had data been available from areas of higher density, the relationship may
have appeared to be rather different. Finally, that insufficient data were available to determine
correction factors independently for different species is likely to have reduced the utility of the
correction factor substantially. Movement distances differ markedly between the three species
(Fig. 3.1) and, consequently, the three are likely to show very different relationships between
track encounters and density. That the correction factor is currently unable to account for this
variation greatly limits its utility.
Although the FMP formula is easy to apply, determining confidence intervals associated
with mean estimates is relatively complex. However, comparisons between BCA and standard
confidence intervals suggest that these can often be markedly different and, thus, the extra effort
required to determine BCA intervals is likely to be worthwhile. Routines for determining these
intervals are increasingly available for standard statistical software (e.g. Efron & Tibshirani,
1993) but they can also be derived reasonably easily by anyone familiar with programming.
Despite the close agreement between density estimates derived by the FMP and
simulation methods, limitations of this study continue to restrict our confidence in the estimates
of density produced. The first of these is the finer-scale heterogeneity in densities of ungulates.
52
Analysis of ungulate dynamics
Although we have assessed correlations between encounter rates and forest types (Section 2), it is
possible that there may be relationships between the habitats used by ungulates and those through
which transects were run. At the extreme, if all transects were run through valley bottoms and all
ungulates concentrate in valley bottoms during winter, our estimates of density would be
substantially inflated. The second limitation on estimating density arises from limits to our
understanding of the factors underlying movement patterns. In this chapter, we reported on a
simplistic analysis of pairs of variables important in influencing travel distance. The most
important factor influencing travel distance among species appeared to be time of year. Other
factors are also likely to be important but, without additional data on 24-hour movements, it is
difficult to identify these effects. We note that group size also appeared to be an important factor
and we strongly suggest that future surveys collect data on the numbers of animals responsible for
each set of tracks encountered. Such data will be helpful for improving the accuracy of density
estimation by the FMP formula and will also provide useful data on group size distributions.
Kuzyakin and Lomanov (1986) have shown that in more favourable areas, moose move shorter
distances during the day than in less favourable environments, presumably because they need not
travel so far in order to find browse. It seems likely that this would also apply to the species we
studied. It is also interesting to note that snow depth did not receive strong support as a factor
affecting travel distance. Previously, this factor has been shown to have a strong effect on
ungulate movements (e.g. Mysterud, 1999; Parker et al., 1984). It may be that over-riding factors
and interactions between variables mask the effects of this parameter; only with larger sample
sizes, recorded in a greater variety of snow depth conditions, will it be possible to tease out the
relative importance of all putative factors.
Collecting additional data on animal 24-hour
movements is crucially important. It is likely that determining predictive models for the distances
moved in different areas and at different times would substantially increase the accuracy of
density estimates determined on the basis of movement.
53
Analysis of ungulate dynamics
4. TEMPORAL ANALYSES OF UNGULATE POPULATION
DYNAMICS
4.1
Background
In this section, we concentrate on two aspects of the temporal dynamics of ungulates. First, we
examine changes in track encounter rate within years. This is important largely in relation to
standardising the monitoring protocol but also for detecting intra-annual movements of ungulates
between different habitat areas. Secondly, we assess between-year variation in ungulate density.
Long-term datasets on the abundance of ungulates are increasingly available and a number have
been subjected to rigorous analyses of their population dynamics.
Several of these are
summarised in Table 4.1. Evidently, ungulate dynamics may be influenced by a combination of
density dependence and stochastic variation in the environment (Gaillard et al., 1998; Sæther,
1997), as well as by competition and predation. In particular, density dependent effects were
found to be important in 27 of the 30 analyses listed in Table 4.1, and were important factors in
all of the most elaborate, individual-based studies (e.g. Coulson et al., 2001; Coulson et al., 2000;
Forchhammer et al., 2001). In spite of this, density dependence remains difficult to demonstrate
with survey data and, consequently, controversial (e.g. Shenk et al., 1998). Similarly, climatic
effects were found to be important in a large proportion (22 of 30) of the analyses listed in Table
4.1. The long-term data from SAZ, comprising large numbers of surveyed transects each year,
present an important opportunity to assess new ways of determining the role of density
dependence in ungulate dynamics. Analyses of factors important in ungulate dynamics will also
contribute information from an ecosystem with very different climate and species composition to
the vast majority of previous analyses (which have used data from Europe or North America, see
Table 4.1).
54
Table 4. Analytical approaches used to assess long-term population dynamics of ungulates and their major influences1
Species
Data set details
Analytical approach2
Factors influencing dynamics
(and direction of influence)
Reference
Caribou
(Rangifer tarandus)
Aerial or ground counts of 8
populations
1970 – 1981
Norway
Detailed counts, including
individual recognition
1974 – 1984
Kruger NP, RSA
Detailed counts, including
individual tagging
1959 – 1968 & 1985 – 1990
Hirta, St Kilda, U.K.
Regression
Population density (-)
Severe weather (-)
Skogland (1985)
Regression and partial
correlation of population
change and survival on
putative influences
Key factor analysis of
mortality acting at each life
stage and regression of
mortality rates against
log (population density)
3rd degree polynomial fitted
to population estimates, in
order to derive conservative
estimates of population
growth. Pearson partial
correlations to identify
contributions of different
factors
As above
Preceding population biomass
density (-)
Preceding annual rainfall (+)
Owen-Smith (1990)
Population density (-)
Clutton-Brock et al. (1991)
Relative wolf (Canis lupus)
density (-)
Messier (1991)
Wolf predation (-)
Population density (-)
Messier (1991)
Comparative study of areas
with an without high wolf
predation
Wolf predation (-)
Seip (1992)
Greater kudu
(Tragelephus
strepsiceros)
Soay sheep
(Ovis aries)
White-tailed deer
(Odocoileus virginianus)
Aerial counts
1975 – 1986
Superior National Forest,
USA
Moose
Skeletal remains
1959 - 1968
Aerial counts
1969 – 1986
Isle Royale NP, USA
Triannual aerial counts
1984 – 1989
Southeastern BC, Canada
Caribou
(Continued overleaf)
Species
Data set details
Analytical approach2
Factors influencing dynamics
(and direction of influence)
Reference
Elk
Mark-recapture censuses
1963 – 1985
Grand Teton NP, USA
Meta-analysis of 27 North
American studies of moosewolf interactions
As above
Population density (-)
Dennis and Taper (1994)
Regression of population
growth against population
size; curve fitting for
functional and aggregative
responses of predators
Logistic regression (to look
for density dependent growth)
and multiple regression (to
look at the effects of climatic
factors)
Visual analyses of population
trends
Population density (-)
Predator density (-)
Messier (1994)
Population density (-)
Autumn and winter
temperatures (+)
Snow cover (-)
Markov (1997)
Predator density (-)
McLaren and Peterson (1994)
Regressions of density and
population growth against
extrinsic factors; multiple
regressions; PLR
randomisation tests for
density dependence
As above
Population density (-)
Political instability (-)
Annual temperature (+)
Density of other ungulates (-)
Jedrzejewska et al. (1997)
Population density (-)
Political instability (-)
Annual temperature (+)
Density of other ungulates (-)
Wolf density (-)
Jedrzejewska et al. (1997)
Moose
Wild boar
Winter track counts
1988 – 1996
Sverdlosk Oblast, Russia
Moose
Skeletal remains
1959 - 1981
Aerial counts
1982 – 1994
Isle Royale NP, USA
Archival data and hunting
statistics 1798 – 1940
Track counts and ad-hoc
sightings 1946 – 1993
Białowieża Primeval Forest,
Poland and Belarus
As above
European bison
(Bison bonasus)
Moose
(Continued overleaf)
Species
Data set details
Analytical approach2
Factors influencing dynamics
(and direction of influence)
Reference
Roe deer
As above
As above
Jedrzejewska et al. (1997)
Wild boar
As above
As above
Wildebeest
(Connochaetes taurinus)
Point counts along transects
every 2 weeks through the
dry season
1960 – 1998
Soay sheep
Detailed counts, including
individual tagging
1959 – 1968 & 1985 – 1996
Hirta, St Kilda, U.K.
Annual counts and individual
marking
1971 – 1997
Rum, U.K.
Aerial surveys
1976 – 1996
Betpak-dala, Khazakhstan
Key factor analysis of
mortality acting at each life
stage and regression of
mortality rates against
log (population density)
Logistic regression with fixed
effects, and logistic
regression with fixed and
random effects
Structured demographic
accounting as a method of
key factor analysis
Population density (-)
Political instability (-)
Annual temperature (+)
Lynx (Lynx lynx) density (-)
Population density (-)
Annual temperature (+)
Acorn crop in preceding year (+)
Snow cover (-)
Political instability (-)
Population density (-)
Dry season grass biomass (+)
Population density (+)
NAO index3 (-)
Milner et al. (1999)
Population density (-)
Albon et al. (2000)
Population density (-)
Mean December-January
temperature lagged by
1 year (+)
Population density (-)
Mean December-April
temperature lagged by
2 years (+)
Coulson et al. (2000)
Red deer
Saiga antelope
(Saiga tartarica)
Soay sheep
Detailed counts, including
individual tagging
1985 – 1998
Hirta, St Kilda, U.K.
Linear regression with
weather covariates; models
selected using AIC4
As above
Jedrzejewska et al. (1997)
Mduma et al. (1999)
Coulson et al. (2000)
(Continued overleaf)
Species
Data set details
Analytical approach2
Factors influencing dynamics
(and direction of influence)
Reference
Red deer
Annual counts and individual
marking
1971 – 1997
Rum, U.K.
As above
Coulson et al. (2000)
Soay sheep
Detailed counts, including
individual tagging and markrecapture
1986 – 1996
Hirta, St Kilda, U.K.
Detailed counts, including
individual tagging and markrecapture
1985 – 1996
Hirta, St Kilda, U.K.
Age-structured Markov
modelling and comparisons
with actual trajectories
Population density (-)
Previous year’s population
density (-)
Winter temperature lagged by
2 years (+)
Interactions between:
Population density (-)
NAO index (-)
Sex-ratio
Forchhammer et al. (2001)
Mule deer
(Odocoileus hemionus)
Roadside count index
1964 – 1989
South-central Oregon, USA
Elk
Aerial censuses
1964 – 1995
Northern Yellowstone, USA
DO analysis of 12 Rickertype models including a
density independent model,
selected using both AIC and
SIC5
DT analysis using SIC to
select between various Ricker
and Gompertz models with
up to 2 terms influencing
intercept, slope and error,
respectively.
Population density in the winter
preceding a cohort’s
birth (-)
NAO index in the winter
preceding a cohort’s
birth (-)
Population density (-)
Z-scored6 precipitation in June
and August (+)
Forage biomass (+)
Population density (-)
Spring precipitation (+)
Spring precipitation squared (+)
Taper and Gogan (2002)
Soay sheep
Generalised linear models
differentiated using AIC
Coulson et al. (2001)
Peek et al. (2002)
(Continued overleaf)
Species
Data set details
Analytical approach2
Factors influencing dynamics
(and direction of influence)
Reference
Ibex
(Capra ibex)
Annual total counts
1920 – 1990
Swiss NP, Switzerland
Population density (-)
February – April precipitation (-)
Sæther et al. (2002)
Elk
Annual aerial surveys
1985 – 2000
Banff NP, Canada
Parametric bootstrapping to
estimate all parameters in a logistic regression; weather
factors used as covariates of
an error term.
Generalised linear modelling
with log-change in population
size as the response variable.
Hebblewhite, Pletscher &
Paquet (2002)
Caribou
Hunting records
1908 – 1957 or 1989
Western and Southern
Greenland
AIC used to compare multiorder autoregressive models
incorporating NAO values
and population size
Musk oxen
(Ovibos moschatus)
Counts during military sledge
patrols
1961 – 1989
Northeastern Greenland
Aerial counts plus shorterterm, smaller-scale
monitoring of individuals
1985 – 2000
Laikipia District, Kenya
Annual Autumn census by
direct sighting
1956 – 2000
Gran Paradiso NP, Italy
As above
Population density (-)
Presence of fencing along
highway (+)
Snow depth (-)
Rate of predation by wolves (-)
Cold and snowy winters (+/- in
populations at different
locations; lagged)
Population size (-, delayed in
some populations)
Warm snowy winters (-, delayed)
Population size (-, delayed in
some populations)
Population density (-)
Mean annual rainfall (+)
Georgiadis, Hack & Turpin
(2003)
Population density (-; although
weak support from tests
for density dependence)
Snow cover (-)
Jacobson et al. (2004)
Zebra
(Equus burchelli)
Ibex
Comparative fitting of density
dependent and densityindependent, stage and sex
structured matrix models to
time-series data.
Bulmer’s R and R* tests, plus
DO analysis of Ricker and
Gompertz models, compared
using AIC.
Forchhammer et al. (2002)
Forchhammer et al. (2002)
Analysis of ungulate dynamics
Notes from Table 4.1
1
Data from many long-term ungulate studies have been analysed repeatedly. Here, I present only
those analyses that have employed novel techniques or presented new findings. I omit studies
that have assessed environmental or population effects on one or more proxy for population
performance (e.g. body weight, fecundity) but have not assessed influences at a population level.
2
see main text for further details.
3
NAO values are an index of the North Atlantic Oscillation; higher values indicate worse (wetter
and windier) winter weather.
4
Akaike Information Criterion.
5
Schwartz Information Criterion (Schwarz, 1978).
6
Z-scores achieved by subtracting the mean and dividing by the standard deviation for the month
in question.
In this section, we analyse long-term dynamics in three ways. First, we establish overall
trends during the study period. These are determined for each major habitat area separately, and
for the reserve as a whole. Using these, it will be possible to determine the overall trajectories of
the studied species and, also, to see if these have been similar among the different habitat zones.
Secondly, we assess evidence for density dependence in the data, using various approaches to see
if each population shows signs of density dependent regulation. Finally, we analyse the timeseries of abundances in more detail, to determine whether the data show support for the effects of
other environmental correlates in dictating population growth.
A variety of methods have been developed to examine the influence of density dependent
processes in time-series data (e.g. Bulmer, 1975; Dennis & Taper, 1994; Pollard et al., 1987;
Vickery & Nudds, 1984) and these methods have been tested and compared on several occasions
(e.g. Shenk et al., 1998; Slade, 1977; Vickery & Nudds, 1984). Owing to the need to use seriallyautocorrelated data for detecting density dependence (Eberhardt, 1970), there is considerable
concern over the potential for Type I error resulting from many of the tests, especially where
observation error (or sampling error) is large relative to process error (or stochastic variation in
population density) and where long data sets are available (Shenk et al., 1998). However, the
observation that many populations exist for long periods and yet remain finite is evidence of the
60
Analysis of ungulate dynamics
ubiquity of density dependence (Royama, 1977) and, consequently, some authors have observed
that estimating the size of negative autocorrelations in time series data remains interesting in its
own right (Langton et al., 2002). In particular, estimating the magnitude of such negative
autocorrelations may be interesting, when it also permits estimates of the contribution to growth
rates of other environmental correlates.
Due to the concerns over the use of tests for density dependence, we employ two methods
to assess evidence for its impact on the population growth of ungulates in SAZ. First, we use the
tests of Bulmer (1975) to analyse whether density dependence is strongly illustrated by any of the
populations. In contrast to many alternatives, Bulmer’s R* test has been shown to have low Type
I error rates for a wide range of conditions but, also, to lack power (Shenk et al., 1998). As such,
it represents a very conservative test for the role of density dependence in a tested population.
Our second approach is motivated by the fact that previous tests developed to assess evidence for
density dependence in population processes have all been designed on the basis that only one
estimate of density is available for each year. As a result, these tests have been limited by an
inability to confront the role of observation error (error in the annual estimates) explicitly. By
contrast, the data from SAZ are based on large numbers of independent samples (surveyed
transect segments) conducted annually.
We have already shown that non-parametric
bootstrapping can use these independent samples to derive confidence intervals around annual
estimates (Section 3).
Similarly, non-parametric bootstrapping presents an opportunity to
determine how often observed characteristics of the data that indicate density dependence could
have been produced if the underlying processes were density independent. As such, multiple
annual samples provide the means for controlling for Type I error (false rejection of the null
hypothesis that dynamics are density independent), the major flaw of the majority of existing tests
of density dependence.
Our final set of temporal analyses uses a method employed in a large number of the
studies in Table 4.1; this is the stochastic population modelling approach of Dennis & Taper
61
Analysis of ungulate dynamics
(1994) (the “DT approach” in Table 4.1). The DT approach permits analysis of the influence of
various factors underlying population growth, by determining which of these factors are
important for predicting the observed time-series of population size. Dennis & Taper’s (1994)
approach has been used to analyse several long-term datasets on ungulate abundance (e.g. Dennis
& Taper, 1994; Jacobson et al., 2004; Taper & Gogan, 2002). It has also been modified to
include weather covariates (Dennis & Otten, 2000) (the “DO approach” in Table 4.1) and this
approach has been applied to indices of ungulate abundance (Peek et al., 2002). The DT
approach now seems to be the main method for assessing factors important to the long-term
population dynamics of a broad range of taxa, e.g. house mice (Mus domesticus) (Choquenot &
Ruscoe, 2000), common wasps (Vespula vulgaris) (Barlow et al., 2002), merlin (Falco
columbarius) (Wiklund, 2001).
4.2
Methods
4.2.1
Within-year variation in track encounters
As in Section 2, where subdividing data spatially led to small sample sizes, subdividing data
temporally also leads to small sample sizes, which confound inferences about the effect of time of
year on track encounter rate. Again, however, patterns can be assessed for individual years and
pooled across years to see if they occur consistently. To determine whether consistent patterns
exist in survey results within years, we divided the encounter rate data into months. Very few
surveys have been conducted in October, so for each biological year, we used data from the six
months from November to April. We then used the approach summarised in equation 2.1 to
determine whether average encounter rates for each month differed consistently from annual
average encounter rates.
62
Analysis of ungulate dynamics
4.2.2
Linear trend analysis
Linear trend analysis is intended to give a very general indication of overall trajectories of the
different surveyed species, over long periods.
To determine these trajectories, we used a
modification of the bootstrapping approach (described in Section 3.2.3) for linear regression. For
those species for which we have estimates of movement (red deer, roe deer, sika deer, musk deer
and wild boar), the raw data were estimates of density derived in Section 3.3.5, using the FMP
formula with weighting by transect length and stratification by drainage basin area, as well as
daily movement model averaging for red deer and wild boar. For the other species (moose), the
raw data consisted of track encounter rates. For each year (and habitat where appropriate), the
raw data consisted of n samples (each from an independent transect). From these, we generated B
bootstrap samples, each also of size n. Each bootstrap sample was post-stratified by drainage
basin area to give an average density (or encounter rate), D *b , for each year. Linear regression
was used to determine the slope (β1*b) and intercept (β0*b ) for each bootstrap sample and the
mean slope ( ˆ1 ) and mean intercept ( ̂ 0 ) over all B bootstraps were used to indicate the mean
trend for that species.
To generate confidence intervals about the linear trends, each bootstrap estimate of slope
(β1*b) and intercept (β0*b ) was used to generate a prediction for the density (or encounter rate)
associated with each year. The 95% confidence limits for each year were then calculated as
described in Section 3.2.3 (equations 3.7 – 3.9). Trend analysis was conducted for each species in
each of the three main habitat zones and then for each species for the whole of SAZ combined. In
the latter case, bootstrap samples from each year were generated by sub-sampling from each of
the three habitat zones and adjusting the year’s mean estimate according to the relative areas of
each habitat zone. Clearly, for those species for which we do not have good estimates of travel
distance, this assumed that track encounter rate and density were related by the same function in
all zones. In Section 5, we discuss the annual survey effort required to allow trends to be detected
63
Analysis of ungulate dynamics
over five year periods. Early on in the monitoring of SAZ, survey effort in many years was
insufficient for that purpose and, consequently, it is likely that trends will not be detected
accurately. By contrast, surveys in recent years have generally been adequate for the detection of
trends (Section 5). For these reasons, we split the study period into four subsections for trend
analysis. These were: 1962 - 1982; 1983 - 1992; 1993 - 1997; and 1998 - 2002.
4.2.3
Detecting density dependence
The derivation and statistical basis of Bulmer’s tests for density dependence have been discussed
in detail elsewhere (Bulmer, 1975; Pollard et al., 1987; Shenk et al., 1998; Slade, 1977; Vickery
& Nudds, 1984). Here we present only a brief outline of the methods. The main approach is to
calculate a statistic, R (or R*, see further below), which has been assessed by simulation and
shown to be indicative of density dependence. The calculated statistic is compared to a critical
value to determine whether the null hypothesis (that the data were produced by a density
independent process) can be rejected. For a time-series of length q, it is assumed that the annual
logged estimates of population size are denoted xt (i.e. x1, x2 … xq). Bulmer (1975) defines the
following parameters:
q 1
U   ( xt 1  xt ) 2
t 1
q
V   ( xt  x ) 2
t 1
R  V /U
(4.1)
The distribution of the R statistic was examined by simulation, and Bulmer suggested that critical
values of the R statistic should be calculated as:
Rcrit = 0.25 + (q - 2)RL
(4.2)
For α = 0.05, RL is given as 0.0366 and significance (rejection of the null hypothesis of density
independence) is assumed where R < Rcrit.
64
Analysis of ungulate dynamics
Bulmer (1975) also noted that the presence of observation error in the estimates of xt will
tend to exaggerate the appearance of a density dependent signal in the data. This is a wellrecognised problem (e.g. Eberhardt, 1970) that arises because overestimates of population size in
any year will generally lead to underestimates of the change in population size between that and
the following year. Similarly, underestimates will lead to exaggerated corresponding changes.
Thus, smaller estimates of population size will be correlated with larger estimates of change and
vice versa, leading to the appearance of density dependence, even where this plays no role in the
underlying process. To remedy this, Bulmer (1975) defined additional parameters as:
q 2
W   ( xt  2  xt 1 )( xt  x )
t 1
R*  W / V
(4.3)
The distribution of R* was also determined by simulation and the test was assumed to be
significant when R* < R*crit, where, for α = 0.05, this is given by:
R *crit  
13.7 139 613
 2  3
q
q
q
(4.4)
Bulmer’s R test has been shown to have high Type I error rates but can indicate the
possibility of a density dependent signal, whilst the R* test has been shown to be highly
conservative, having generally low power (Shenk et al., 1998).
One of the limitations of
Bulmer’s tests (in keeping with all other tests developed to assess the influence of density
dependence in time-series data) is that they were developed for application to data consisting of a
single annual estimate of population size. As the data from SAZ comprise multiple independent
estimates for each year, the possibility arises to develop a test that explicitly accounts for
observation error. Our test draws on approaches discussed by Dennis & Taper (1994) and Pollard
et al. (1987) but is novel, in that it uses non-parametric bootstrapping of multiple annual samples,
in order to determine the significance of an apparent density dependent signal.
65
Analysis of ungulate dynamics
There is little consensus regarding the best type of underlying model when testing for
density dependence in vertebrates. Due to its analytical tractability, many authors (e.g. Pollard et
al., 1987) have used a Gompertz-type model, in which population growth is logarithmically
dependent on population size. Dennis & Taper (1994) noted that, by contrast, a Ricker model (a
standard logistic growth model, in which population growth depends on absolute population size)
allows for stronger density dependence, and is therefore preferable. The Ricker approach was
used by Peek et al. (2002). In practice, however, the two processes (Ricker and Gompertz) can
lead to very similar dynamics (e.g. see Fig. 4.1); consequently, some authors have suggested
examining both possibilities (Jacobson et al., 2004) and that is the approach that we take. Using
the notation given above, the Ricker and Gompertz models, respectively, are described by the
following autoregressive processes:
xt 1  r  xt  N t  Z t
(4.5)
xt 1  r  xt  Z t
(4.6)
where r and β are constants and Zt is a normally distributed random number, with a mean of zero
and a standard deviation of one. Values of Zt are assumed to be uncorrelated between years. In
either case, three different models can be distinguished:
r = 0, β = 0 (Ricker) or β = 1 (Gompertz)
(model 1)
r ≠ 0, β = 0 (Ricker) or β = 1 (Gompertz)
(model 2)
β ≠ 0 (Ricker) or β ≠ 1 (Gompertz)
(model 3)
Model (1) is a random walk, model (2) is a random walk with drift (an exponential growth or
decline model, with mean growth rate r) and model (3) is a density dependent population model
(with a carrying capacity of -r / β for the Ricker process, or exp[r / (1 - β)] for the Gompertz
process). We now discuss the detection of either of these density dependence processes. For
brevity, our discussion focuses on the Gompertz model but is readily adapted to the Ricker model
66
Analysis of ungulate dynamics
also, by noting the effects of the different values of β associated with each model (see models 1 to
3, above).
4.0
(a)
Population density, Nt
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
10
20
30
40
Time, t
Log-change in population density, dt
0.25
(b)
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
0
1
2
3
4
Population density, N t
Figure 4.1. Sample simulations of populations following a Ricker process (solid lines) or a
Gompertz process (broken lines): (a) a single time-series for each process; (b) best fit regressions
showing the mean relationships between population growth and population size (Ricker shown
with linear regression, Gompertz with logarithmic regression). For both processes, initial
population density, N1 = 1, carrying capacity, K = 3, and process error, σ = 0.07. Additional
parameters: Ricker, r = 0.3, β = -0.1; Gompertz, r = 0.22, β = -0.8.
A common approach to testing for Gompertz density dependence, is to regress dt on xt.
This regression has slope b = β - 1 and intercept r. The mean squared residual is equivalent to σ.
In both models 1 and 2, defined above, β = 1 and, hence, we might expect that a regression of
density independent data would have a slope of b = 0. However, two processes can affect this.
Firstly, stochasticity can lead to slopes that are different from zero, although this will be
increasingly unlikely in longer data sets. Secondly, and more importantly, the consequences of
67
Analysis of ungulate dynamics
observation error (discussed above) will invariably lead to a negative slope. The key requirement
of a test for density dependence is to determine whether a slope of b could have been produced
merely as a consequence of stochasticity and sampling error, or whether it is likely to reflect a
clear density dependent process. As we already have estimates of the amount of sampling error
inherent in our data, we can use a combination of simulations and bootstrapping to determine the
frequency with which slopes less than or equal to the observed slope could be generated by
density independent processes. This is effectively a modified form of the randomisation test of
Pollard et al. (1987), adapted to include a known distribution of sampling error.
Once again, we consider the case of a time-series of length q, consisting of annual
estimates of population size, Nt. As we explicitly incorporate the availability of multiple annual
estimates, we assume that each overall annual estimate (Nt) is the arithmetic mean (or weighted
arithmetic mean if the data are stratified) of i annual estimates, n1,q, n2,q, … ni,q. As above, we
define xt = ln(Nt), and annual changes in these values are given by dt = xt+1 - xt. Given an actual
time-series of data, Nt (hereafter referred to as the test data set), the test requires the following
steps:
(i)
Determine the coefficients of the regression of dt on xt, analysed by each of the three
models given above. For clarity, we term these coefficients σ1 (for model 1), σ2 and r2 (for model
2) and σ3, r3 and b3 (for model 3).
(ii)
Beginning with N'1 = N1, simulate a random data set (N'1, N'2, … N'q), based on either
model (1) (using the value of σ1) or model 2 (using the values of σ2 and r2). Note that if N1 = 0,
the simulated set should be conditioned on the first non-zero estimate of Nt.
(iii)
For each year, populate an array of independent samples that would have led to the
simulated annual estimate. These will take the values n'i,q = ni,q ∙ N't / Nt (where ni,q are the i
independent samples from year t of the test data set).
(iv)
Non-parametrically bootstrap the independent samples (n'i,q) for each year, to produce a
bootstrapped set of the simulated annual estimates, N*t.
68
Analysis of ungulate dynamics
(v)
By taking logs of N*t (denoted x*t), estimate b̂ * for this bootstrap.
By repeating the bootstrap process B times and the simulation of a data set G times, we
can estimate the probability p(I) = #( bˆ*  b3 ) / B∙G, where # indicates the absolute number of
times that the given condition is satisfied. In this way, it is possible to estimate the overall
probability, given the actual distribution of sampling errors, that a slope as negative as that
observed could have been produced by a density independent process. Preliminary assessments
showed that some slopes (b3) calculated from test data sets were extremely sensitive to individual
data points. For that reason, all parameters for each test data set were calculated after having
removed the data point that contributed the most to the negative value of b3. This conservative
estimate of the slope for each test data set was termed b(j). Using b(j) instead of b3 affected the
outcome of only one test, where the removal of a single data point vastly altered the value of b3
(see further in Section 4.3.3). Overall, evidence suggests that this modified-Pollard test has low
Type I error rates, except where survey error is extremely high, but that test power is high only
when density dependence is strong (P.A. Stephens, unpublished data). Consequently, we use α =
0.10 as our significance threshold.
4.2.4
Time-series analysis
Analyses of most data sets to account for the factors underlying density dependent changes in
population estimates (whether they are due to a density dependent population growth process, or
to autocorrelations in sampling error) can tell us little about the environmental factors that affect
population growth. More thorough analyses of time-series data aim to determine which intrinsic
and extrinsic factors are likely to underlie the time-series of observed population size (or indices
of population size). Many methods exist for such analyses but here, we focus on the stochastic
69
Analysis of ungulate dynamics
population modelling approach of Dennis and colleagues (Dennis & Otten, 2000; Dennis &
Taper, 1994).
Dennis & Taper (1994) presented their analytical approach based on an underlying
Ricker process (equation 4.5). The approach can be modified for use with a Gompertz process
(Jacobson et al., 2004) but here, we follow Dennis and colleagues, and build on the notation given
in equation 4.5, above. Dennis & Otten (2000) extended this to incorporate density independent
environmental correlates of population growth. In general, the extended model can be written as:
xt 1  xt  r  N t  c1 E1  c2 E2  ...  ci Ei  Z t
(4.7)
where c1, c2, … ci are constants, and E1, E2, … Ei are environmental correlates, such as weather
indices, forage biomass, predator abundance, etc. It is possible to identify a range of competing
hypotheses based on equation 4.2, according to whether the various constants differ from zero.
Maximum likelihood estimates of the constants may be obtained using linear regression.
Specifically, multiple linear regression is conducted using dt as the response variable, with Nt and
E1 to Ei as the independent variables (note that a Gompertz process would use xt rather than Nt as
the independent population size variable).
This yields coefficients equivalent to maximum
likelihood estimates of r (the intercept), β (the coefficient of Nt) and c1 to ci (the coefficients of E1
to Ei, respectively). Error (σ2) is given by the mean sum of squared residuals. Lagged density
dependence may also be incorporated by including βlNt-l terms, for a density dependent lag of
order l+1. Competing models can be compared using AIC (see further below) and, thus, the ‘best
model’ or set of models will indicate support for the importance of various constants from the full
(or global) model (equation 4.7).
Having assessed the extent of support for density dependence acting within the
populations (see Sections 4.2.3 and 4.3.3), the aim of our time-series analyses was to determine
which other factors are important for explaining annual changes in population size. For this
reason, we included both an intercept (equivalent to r in equation 4.7) and an autoregressive term
70
Analysis of ungulate dynamics
(βNt or βxt) in all models. Whether or not there is strong evidence for density dependence, the
autoregressive term also accounts for serial autocorrelation in survey error, allowing remaining
variation to be accounted for by other factors in the model. Our choice of whether to use a Ricker
or a Gompertz process as the underlying model was guided by regressions of dt on Nt and xt. The
autoregressive metric (Nt or xt) that explained the greater amount of variation in dt (i.e. had the
higher R2 value) was then used in all models of that population.
Models including various combinations of factors were compared using AIC (equations
3.2-3.5). As data sets were small (40 data points at best but less where shorter time periods were
considered, lag terms were included or data were missing), AICc was used in all cases. Model
comparisons were run using the statistical software package R (http://www.r-project.org/) and
AIC values were taken directly from the model output. AICc was then calculated as shown in
equation 3.1. Models can be considered to have strong support if their AIC c value is within two
units of that of the best model (Anderson et al., 2000). Models with low AICc values may,
nevertheless, be rejected if they do not conform to prior biological understanding. For example,
if a covariate is initially assumed to have a positive effect on population growth but features in
models as a negative influence, it is likely that the model fit is an artefact of spurious regression
(a relationship between two variables that is due to chance, rather than to any biologically
meaningful process).
In these cases, such models were removed from the set of strongly
supported models (or ‘confidence set’). Where confidence sets included a variety of candidate
models, average models were obtained by multi-model averaging (Burnham & Anderson, 2002).
Specifically, a weighted average of the models’ predictions is calculated using weightings
obtained by formula 3.5, calculated only for the group of models of interest. Model averaging
permitted large sets of models to be condensed to a single model indicating the approximate
effect sizes of well-supported parameters. Only strong effects, typically occurring in several
models within the confidence set, were still visible in average models.
71
Analysis of ungulate dynamics
4.2.5
Putative factors influencing population growth
In model selection, the prior determination of candidate model sets is extremely important
(Burnham & Anderson, 2002).
Candidate models were discussed during meetings at the
Zapovednik offices in Terney during September 2004. Although not all correlates were thought
likely to affect all species, here we describe factors likely to affect one or more of the ungulates
surveyed in SAZ, together with the derivation of appropriate indices. Where parameters are
identified, this is done in light of the general aim to predict log population change from year t to
year t+1, dt. The following sets of factors were thought likely to have an impact on population
growth in one or more species. “Global model” refers to the full set of factors included in models
for a given species in a given habitat zone.
Density dependence.
For ungulates, it is possible that density dependence is more
complex than first-order lags and several of the studies listed in Table 4.1 show evidence for
higher order lags. All global models included lags of up to three orders. This required using Nt,
Nt-1 and Nt-2 (or xt, xt-1 and xt-2), as predictors for dt. The choice of scale (absolute or logarithmic)
was determined as described in the previous section.
Mast abundance. Mast is an important food resource for ungulates in SAZ, especially
wild boar. As discussed in Section 1.3, indices of both oak and Korean pine mast abundance
have been collected annually in SAZ. As a predictor variable, we used the categorical index, Mt,
for the predominant mast type in the habitat analysed (oak in the oak-birch habitat zone, and
Korean pine in the Korean pine-deciduous zone). The exception to this was wild boar. Biologists
in SAZ have observed that wild boar depend largely on oak mast but, in years when oak mast
fails, a good crop of pine nuts can alleviate problems of food shortage. Consequently, some
biologists assess wild boar dynamics in relation to a modified mast index, equivalent to the oak
mast in all but three years when this failed completely; in those years, the mast index is modified
upwards, according to the quality of the pine mast. As wild boar dynamics in oak-birch and
Korean pine-deciduous habitats were analysed together (see further below), all three mast indices
72
Analysis of ungulate dynamics
(oak, pine and the alternative, amalgamated index) were compared for this species, in order to see
which was most informative. Note that a good mast in year t is expected to improve the condition
of animals emerging from the biological winter of year t and, consequently, to increase
recruitment (and, hence, population change, dt) from t to t+1. Mast index values are shown in
Fig. 4.2a-c.
Predator abundance. Tigers in the case of red deer, sika deer and wild boar, and lynx
(Felis lynx) in the case of roe deer (and possibly musk deer), are significant predators.
Abundance indices are available for both: estimates of absolute tiger numbers are available for
each year, and lynx tracks (of less than 48 hours old) are recorded on the winter transect counts.
The latter can be expressed as tracks km-1, to give an approximate relative index of the likely
level of predation from year to year. Tiger abundance was highly non-stationary throughout the
study period. Consequently, we used log-change in tiger population size from t to t+1 as our
index of tiger abundance. Lynx abundance is relatively stationary. Again, however, abundance
in both the previous winter and the current winter could be argued to be the relevant index for
looking at effects on population growth. In practice, fluctuations in predator populations are
likely to be slow and, consequently, we smoothed the index by using an average of these two
values (i.e. Lynx = [Lynx (t) + Lynx (t+1)] / 2). Predator indices are shown in Fig. 4.2d,e.
Competitor abundance. Different species are likely to compete to different extents with
other members of their guild and other species that exploit the same resources. In addition to
competition between the larger ungulates, wild boar may compete (at least for mast) with small
rodents. Where C was the abundance of a competitor, we used Ct as our index of competition.
Abundance indices for ungulates were the densities calculated in Section 3 of this report. For
small rodents, trapping has been conducted every year since 1965 (E. Smirnov, unpublished data).
Numbers of rodents trapped per 100 trap nights have been recorded for three species: the Korean
field mouse, Apodemus peninsulae; the northern red-backed vole, Clethrionomys rutilus; and the
grey red-backed vole, C. rufocanus. Although trapping success has shown a more dramatic
73
Analysis of ungulate dynamics
increase for the mouse than for the voles since monitoring began, all three species tend to show
highs in similar years (Fig. 4.2). As trapping is conducted in the summer preceding the ungulate
winter survey, we used as our index of competition, the combined trap success for all three
species in the year from which change was measured, i.e. year t. The Z-scored index of rodent
abundance (see further below) is show in Fig. 4.2f.
Winter severity. Two aspects of winter weather conditions were deemed particularly
important. These were snow cover (which limits access to resources) and temperature (which
dictates demand for resources). These might act independently, or in concert. Consequently, we
compared models containing any one of four different indices of winter weather. The indices
were winter snow (WS, total precipitation for October to March in biological year t), winter
temperature (WT, mean temperature for October to March in biological year t), a combined winter
conditions index [defined as WC = Z(WT) – Z(WS), where Z(x) is the Z-score for x (see further
below)], and the winter North Pacific Oscillation Anomaly (WNPO). WNPO data are available
from
the
USA’s
National
Centre
for
Atmospheric
Research
website
(http://www.cgd.ucar.edu:80/cas/climind) and have been shown to have a strong influence on elk
dynamics in parts of North America (Hebblewhite, 2005). On that continent, higher NPO indices
are associated with poorer conditions in winter but in the Russian Far East, higher NPO values are
associated with milder winters with less snow. Although correlations with winter variables from
the Melnichnoye and particularly the Terney weather stations are not strong, the NPO index was
used to provide a broader indication of winter weather, in contrast to these very localised
measures. Note that all winter weather variables (from year t) were assumed to affect the
condition in which ungulates emerge from winter and, consequently, their reproductive success
(and population growth) from t to t+1.
Spring conditions. Weather conditions during April and May can have an important
effect on survival of newborn young, especially for the smaller species. If snowy conditions
74
3
2
1
1972
1982
1992
1.2
(g)
0.9
Number of reports
Log (population change)
4
0
1962
0.6
0.3
0
-0.3
1962
2002
1972
1982
1992
(e) 8
5
1
0
1962
Alternative mast index
(c)
1972
1982
1992
(f)
3
2
1
1962
1972
1982
Year
1992
2002
4
8
4
1972
1982
1992
2002
1972
1982
1992
2002
1972
1982
1992
2002
32
24
16
2
8
0
1962
2002
12
40
6
Illegal entries
2
16
(h) 48
1972
1982
1992
0
1962
2002
3
(i)
2
Estimated protection
3
Total abundance
Pine mast index
4
20
0
1962
2002
-1
(b)
(d)
5
Abundance (tracks km )
Oak mast index
(a)
1
0
-1
-2
1962
1972
1982
Year
1992
2002
10
8
6
4
1962
Year
Fig. 4.2. Covariates used in time-series models (excluding weather and ungulate competitor covariates): (a) oak mast; (b) pine mast;
(c) alternative mast index (note reduced number of categories); (d) tiger population growth; (e) lynx abundance; (f) rodent abundance (Z-scored);
(g) reports of poaching; (h) incidences of illegal entry; (i) expert assessments of efficacy of protection.
Analysis of ungulate dynamics
persist, warm springs could also be problematic, reducing the mobility of some species. We
incorporated both spring precipitation and mean temperature from April and May (at the start of
the biological year t+1) as model covariates.
Summer conditions. Both summer temperatures and precipitation might be important for
vegetative productivity and, hence, might be expected to affect the condition in which animals
enter winter and, thus, recruitment in the following year. Our indices were for June to September
in the biological year t (i.e. the summer preceding the winter of biological year t).
Human impacts. At times, poaching of animals from within SAZ may have had an effect
on ungulate population dynamics. To examine this, we used several indices of human impact that
may correlate with either poaching or hunting pressure. These were: annual reports of poaching
in SAZ, RP; annual numbers of illegal entries into SAZ, IE; and an expert assessment of the
efficacy of protection of SAZ, EP. The latter index was the average of five independent, year by
year assessments, given by Zapovednik employees familiar with the enforcement history in SAZ.
Time series of these factors are shown in Fig. 4.2g-i.
In addition to the specific seasonal weather variables discussed above, annual mean
temperature was also used as a broader climatic index. Climatic variables are shown in Fig. 4.3.
All parameters (including autoregressive parameters) were Z-transformed to remove the effect of
scale.
This allows the magnitude of effects to be compared more easily.
In general,
Z ( x)  ( x  x ) / s , where Z(x) is the Z-score for a given value of x, x is the mean of all x, and s
is the standard deviation of x.
The factors listed summarise the full range of correlates designated a priori, for which
data exist to compare population models. Not all factors were included in the global model for
any population. Our general approach was to include three autoregressive terms (for density
dependence and lagged density dependence), together with spring and summer weather indices, in
76
-16
-12
-8
-4
0
1962
1972
1982
1992
2002
(g)
14
Mean summer temperature, °C
(d)
-20
Winter NPO anomaly index
Mean winter temperature,
°C
(a)
12
10
8
6
4
2
0
1962
1972
1982
1992
2002
18
17
16
15
14
13
12
1962
1972
1982
1992
2002
1992
2002
0
(e)
Winter precipitation, mm
300
250
200
150
100
50
0
1962
1972
1982
1992
2002
10
-2
-4
-6
-8
6
-10
-12
4
-14
-16
-18
1972
1982
1992
1982
1992
2002
(h)
8
2
1962
1972
950
Summer precipitation, mm
350
Mean spring temperature, °C
(b)
1962
750
550
350
150
1962
2002
1972
1982
-20
0
(c)
(f)
5
350
1962
(i)
1972
1982
7
1992
2002
1
-1
-3
-5
1962
1972
1982
1992
2002
300
-4
250
-6
200
-8
150
-10
-12
100
-14
50
-16
0
1962
-18
1972
1982
1992
2002
-20
Year
Year
Annual mean temperature, °C
3
Spring precipitation, mm
Winter conditions index
-2
5
3
1
-1
-3
1962
0
1962
-2
1972
1982
1992
2002
1972
1982
1992
Year
-4
-6
-8
-10
-12
-14
-16
Fig. 4.3. Weather covariates used in time series analyses. Note that in each case, the solid line represents Melnichnoye (used for analyses of
population in the spruce-fir zone) and the broken line represents Terney (used for analyses of data from the oak-birch and Korean pine-deciduous
zones). The exception is (d), the winter NPO anomaly index, which is independent of habitat zone.
-18
-20
2002
Analysis of ungulate dynamics
the global models for all populations. To these were added relevant predators (tigers for the
larger ungulates, but lynx for roe deer and musk deer) and relevant mast crops (only musk deer
were thought likely to be completely unaffected by mast crops). All of the larger deer were
included as competitors in global models for any other large deer. Whilst this competition might
not be direct, an array of indirect effects are possible, including foraging disturbances and
interactions with predators (for example, predator dilution). Rodents were also included as a
competitor in the wild boar global models. Musk deer were deemed unlikely to compete with
rodents or other ungulates and so no competitors were included in the musk deer global models.
In addition to these factors, winter weather variables and human impact variables were also
included in global models. To avoid the potential for over fitting that arises from having highly
correlated parameters, a maximum of one winter weather parameter and one human impact
variable was included in any one model. Thus, although all winter weather variables were
included in the global model, these were never included in any candidate model in combination.
Similarly, whilst all three human impact factors were included in the set of candidate models,
only one (at most) was ever used in any given candidate model. For clarity, further details of the
models compared are given in the results section.
4.2.6
Selection of data sets for density dependent and time-series analyses
Although Dennis and colleagues (Dennis et al., 1998) have developed their approach for use on
metapopulation data (see also Langton et al., 2002), they caution that this approach can lead to a
rapid inflation of the number of estimated parameters. This will be even more pronounced when
environmental correlates are included. In addition, trend analyses (Section 4.3.2) showed that for
most species, populations had markedly different trajectories in the different habitat zones of
SAZ. Amalgamating data for the whole of SAZ often led to less pronounced trends, obscuring
some of the detail evident amongst the different zones. Furthermore, it seems likely that different
factors may be important in different parts of SAZ (for example, mast crops are only expected to
78
Analysis of ungulate dynamics
be important in the habitat zone in which the masting species predominates). For these reasons,
we chose to analyse populations of each species separately for each zone. The exception to this
was wild boar, which exist in relatively low numbers in both the oak-birch and Korean pinedeciduous zones. Boar are also known to move large distances between zones in search of food.
Consequently, average density of wild boar over the two zones was used for analysis.
Analysing longer data sets is preferable, as multi-parameter models can be treated with
greater confidence when applied to larger data sets. Where possible therefore, full data sets were
used for analyses of the role of density dependence. However, for time-series analyses, we had
one very clear reason to divide the data set temporally. This was that important sections of the
oak-birch zone only received formal protection from 1980 onwards. These areas are known to be
important for many of the ungulate species and, consequently, had the potential to influence
populations throughout SAZ (either by recruitment or migration). Indeed, Fig. 3.11 suggests that
the dynamics of several species may have been different before and after 1980, seemingly in all
zones of SAZ. Consequently, for time-series analyses, all populations were divided into the two
periods, 1962 - 1979 and 1980 - 2002. The exception to this was musk deer, which are relatively
rare in the oak-birch zone and showed no sign of a change in dynamics after 1980 in either the
spruce-fir or Korean pine-deciduous zones. For both of those zones, time-series analyses were
conducted for musk deer for the entire period, 1962 - 2002.
Finally, analyses of the importance of density dependent and independent factors
affecting population growth depend critically on good quality data. For this reason, we elected
not to analyse data on moose (which are very sparse and, given current levels of survey effort,
unreliable; see further in Section 5). Other species were analysed only in the zones in which they
were abundant (where population data are likely to be more reliable). Specifically, red deer and
roe deer were analysed for all three zones, sika deer were analysed in the oak-birch zone only,
musk deer data from the oak-birch zone were not analysed, and wild boar were analysed only in
the oak-birch and Korean pine-deciduous areas. Several species occurred in certain habitat zones
79
Analysis of ungulate dynamics
in very low numbers during one of the two studied time periods. In particular, sika deer were
largely absent from the oak-birch zone until 1980, whilst roe deer were present in the Korean
pine-deciduous and spruce-fir zones in very low numbers prior to that point. Consequently, no
analyses were possible for these species in those habitats, during the first period. A small number
of conspicuous outliers were removed from remaining data sets. These included data points with
confidence intervals which overlapped with neither of their neighbouring data points, and which
also lay outside the confidence intervals of their neighbouring data points. Specifically, these
included: red deer, oak birch zone, 1987 and spruce-fir zone, 1979; roe deer, Korean pinedeciduous zone, 1994; sika deer, oak-birch zone, 1984; musk deer, Korean pine-deciduous zone,
1982 and spruce-fir zone, 1993.
4.3
Results
4.3.1
Within-year variation in track encounters
Relative track encounter rates for the months of November to April are shown in Fig. 4.4.
Relative monthly encounter rates differ substantially from unity in only a very few cases.
However, where temporal patterns are visible from the figure, a tendency for encounter rates to
decline from early winter to late winter is the most common pattern (approximately half of the
cases illustrated). That there are no corresponding increases in encounter rate in other areas,
suggests that this is not a consequence of movement between areas; however, we return to this
point in the discussion (Section 4.4). A reduction in travel distance over winter seems likely from
the daily movement data (Section 3.3.1) but other factors may confound attempts to determine the
magnitude of such declines. As a result, it is not possible to establish whether or not reductions in
travel distance are the sole cause of observed declines in encounter rate, or whether mortality
during the season or some other cause is implicated.
80
Analysis of ungulate dynamics
3
3
3
2
2
2
1
1
1
Encounter rate relative to annual mean, averaged over all years that species was present and surveyed
(a)
0
0
Nov
Dec
Jan
Feb
Mar
Apr
0
Nov
Dec
Jan
Feb
Mar
Apr
3
3
3
2
2
2
1
1
1
Nov
Dec
Jan
Feb
Mar
Apr
Nov
Dec
Jan
Feb
Mar
Apr
Nov
Dec
Jan
Feb
Mar
Apr
Nov
Dec
Jan
Feb
Mar
Apr
Nov
Dec
Jan
Feb
Mar
Apr
(b)
0
0
Nov
Dec
Jan
Feb
Mar
Apr
Nov
Dec
Jan
Feb
Mar
Apr
0
Nov
Dec
Jan
Feb
Mar
Apr
3
(c)
2
1
0
3
3
3
2
2
2
1
1
1
(d)
0
0
Nov
Dec
Jan
Feb
Mar
Apr
0
Nov
Dec
Jan
Feb
Mar
Apr
3
3
2
2
1
1
(e)
0
0
Nov
Dec
Jan
Feb
Mar
Apr
3
3
3
2
2
2
1
1
1
(f)
0
0
Nov
Dec
Jan
Feb
Mar
Apr
0
Nov
Dec
Jan
Feb
Mar
Apr
Month
Figure 4.4.
Relative encounter rates over winter. Oak-birch habitat (left panels), Korean
pine-deciduous (middle panels) and spruce-fir (right panels) for: (a) red deer, (b) roe deer, (c) sika
deer, (d) musk deer, (e) moose, (f) wild boar. Broken lines indicate a ratio of one, at which
encounter rates in a given month are equal to the average for the year. Some larger confidence
intervals are truncated.
81
Analysis of ungulate dynamics
4.3.2
Linear trend analysis
Linear trends and associated confidence intervals were generated for each species in each habitat
(Fig. 4.5). Confidence intervals for each period, including those for the five year periods, are
typically narrow, indicating that survey effort is currently sufficient to give a good indication of
trends on these timescales. There are exceptions, however, especially for species in habitats in
which they occur relatively infrequently (such as red deer in spruce-fir habitats, for example) and,
in particular, where the mean trend suggests that a species population density remained fairly
constant during the period. Beyond these observations, it is difficult to generalise about the
trends illustrated in Fig. 4.5. In the oak-birch zone, red deer and roe deer appear to have followed
similar trajectories, increasing initially but decreasing in recent years. This contrasts with sika
deer, which have increased rapidly in the oak-birch zone in the last decade. That red deer and roe
deer seem to have increased in the Korean pine-deciduous and spruce-fir zones in the last decade,
could indicate either improving conditions in those areas, or population movement in response to
a decline in conditions in the oak-birch zone. Wild boar in both the oak-birch and Korean pinedeciduous zones have followed fairly similar trajectories to red deer and roe deer in the oak-birch
zone, suggesting that similar factors are affecting the dynamics of the three species. Musk deer
show the least consistency in trends, possibly as a result of the limited data available on their
movements (see Section 3). Sharp discontinuities between musk deer trends in the different
periods are also a product of highly varying predictions between sequential years (for example,
between the final year of one period and the first year of the following period). Finally, moose
appear to have declined in the spruce-fir zone, the only zone in which they were sighted with any
regularity. A suggestion that they may be recovering slightly now is undermined by wide
confidence intervals. These are unsurprising, given the survey effort required to assess moose
dynamics with confidence (see further in Section 5).
The overriding trends in SAZ are more easily interpreted when the study areas are
combined (Fig. 4.6). From these results, it is readily apparent that only moose have shown a
82
Analysis of ungulate dynamics
(a)
10
4.0
2.0
8
3.0
1.5
2.0
1.0
1.0
0.5
6
4
2
0
1962
(b)
1972
1982
1992
2002
1982
1992
2002
0.0
1962
4.0
2.0
4.0
3.0
1.5
2.0
1.0
1.0
0.5
2.0
1.0
0.0
1962
Density (km-2) or track encounter rate (km-1)
1972
5.0
3.0
(c)
0.0
1962
1972
1982
1992
2002
1972
1982
1992
2002
0.0
1962
1972
1982
1992
2002
0.0
1962
1972
1982
1992
2002
1972
1982
1992
2002
1972
1982
1992
2002
1972
1982
1992
2002
1972
1982
1992
2002
1.6
1.2
0.8
0.4
0.0
1962
(d)
0.8
4.0
5.0
0.6
3.0
4.0
0.4
2.0
0.2
1.0
0.0
1962
0.0
1962
1972
1982
1992
2002
3.0
2.0
1.0
1972
1982
1992
2002
(e)
0.0
1962
0.25
0.20
0.15
0.10
0.05
0.00
1962
(f)
2.4
2.0
1.6
1.2
0.8
0.4
0.0
1962
1972
1982
1992
2002
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1962
0.15
0.12
0.09
0.06
0.03
1972
1982
1992
2002
0.00
1962
Year
Figure 4.5.
Linear trends during four periods (1962-82; 1983-92; 1993-97; 1998-2002).
Oak-birch habitat (left panels), Korean pine-deciduous (middle panels) and spruce-fir (right
panels) for: (a) red deer, (b) roe deer, (c) sika deer, (d) musk deer, (e) moose, (f) wild boar. Solid
lines show the mean trend from 5,000 bootstrapped regressions. Broken lines indicate the 95%
confidence intervals for predictions. All panels show trends in density except for moose (e),
which show trends in encounter rate. Trends for sika deer and moose are shown only for the
primary habitats in which they occur.
83
Density (km-2) or encounter rate (km-1)
Analysis of ungulate dynamics
2.5
4.0
(a)
3.0
2.0
0.4
(b)
(c)
0.3
1.5
2.0
0.2
1.0
1.0
0.1
0.5
0.0
1962
2.5
1972
1982
1992
2002
0.08
(d)
2.0
0.0
1962
1.5
1972
1982
1992
2002
0.0
1962
0.8
(e)
0.06
0.6
0.04
0.4
0.02
0.2
1972
1982
1992
2002
1972
1982
1992
2002
(f)
1.0
0.5
0.0
1962
1972
1982
1992
2002
0.00
1962
1972
1982
1992
2002
0.0
1962
Year
Figure 4.6.
Linear trends during four periods (1962-82; 1983-92; 1993-97; 1998-2002)
averaged over all habitats (weighted by area): (a) red deer, (b) roe deer, (c) sika deer, (d) musk
deer, (e) moose, (f) wild boar. Solid lines show the mean trend from 5,000 bootstrapped
regressions. Broken lines indicate the 95% confidence intervals for predictions. All panels show
trends in density except for moose (e), which show trends in encounter rate.
general decline throughout the study period, but that wild boar, musk deer and, to a lesser extent,
red deer, have all declined in recent years.
In the case of the wild boar, this decline is
disturbingly abrupt. Sika deer is the only species that has shown an uninterrupted increase over
recent years.
4.3.3
Density dependence
The results of Bulmer’s R and R* tests are shown in Table 4.2. Two-thirds (8 out of 12) of the
populations tested gave positive results of the R test but none of the R* tests gave positive results.
These findings are presented mainly for comparative purposes and accord with what is known
about the two tests. Given the potential for Type I error in the R test, the non-significant results
are perhaps more interesting than the significant results. In particular, that the R tests gave nonsignificant results for red deer, roe deer and sika deer in the oak-birch zone, as well as roe deer in
the spruce-fir zone is suggestive that, in the oak-birch zone in particular, some process may be
regulating all of the deer species at a level beneath the natural carrying capacity of the
84
Analysis of ungulate dynamics
environment.
That none of the R* tests gave significant results is unsurprising, given the
notoriously low power of this test, and we hesitate to conclude from this finding that there is no
evidence for density dependence in the population processes of the ungulates studied.
The modified-Pollard test was run using G = 250 simulated density independent data sets
(125 each of random walk and stochastic exponential growth or decline) and B = 400 bootstraps
of each data set, giving 100,000 estimates of b̂ * .
Random walk models and stochastic
exponential models gave similar results, and we present combined results. The proportion of all
density independent models yielding bˆ*  b( j ) for each tested data set is shown in Table 4.3.
Overall, half (6 of 12) of the tested populations showed evidence for either Ricker-type,
Gompertz-type, or both types of density dependence. Once again, there was no evidence for
Table 4.2
Bulmer’s R and R* tests for density dependence. Parameters as in main text.
†
denotes significant values (p  0.1; none of the R* tests yielded significant
results).
Species
Habitat
q-1
U
V
W
R
Rc
Red deer
Oak-birch
Korean pine-deciduous
Spruce-fir
Oak-birch
Korean pine-deciduous
Spruce-fir
Oak-birch
Korean pine-deciduous
Spruce-fir
Oak-birch
Korean pine-deciduous
41
40
36
40
40
25
29
40
37
40
40
17.60
9.62
43.74
15.39
54.09
16.94
35.65
23.02
23.87
40.75
146.41
39.01
6.86
31.81
27.54
71.34
39.11
78.13
17.51
20.85
50.72
70.84
0.59
-2.11
11.91
-0.75
5.48
-2.25
2.87
-6.34
-2.90
-9.74
5.67
2.22
0.71
0.73
1.79
1.32
2.31
2.19
0.76
0.87
1.24
0.48
1.68
1.64 †
1.49 †
1.64
1.64 †
1.09
1.24
1.64 †
1.53 †
1.64 †
1.64 †
Roe deer
Sika deer
Musk deer
Wild boar
R*
R*c
0.02
-0.31
0.37
-0.03
0.08
-0.06
0.04
-0.36
-0.14
-0.19
0.08
-0.62
-0.64
-0.75
-0.64
-0.64
-1.31
-1.04
-0.64
-0.72
-0.64
-0.64
85
Analysis of ungulate dynamics
Table 4.3
Species
Red deer
Modified-Pollard test for density dependence. Parameters as in main text.
†
denotes significant values (p  0.1).
Habitat
Oak-birch
Korean pine-deciduous
Spruce-fir
Roe deer Oak-birch
Korean pine-deciduous
Spruce-fir
Sika deer Oak-birch
Musk deer Korean pine-deciduous
Spruce-fir
Wild boar Oak-birch
Korean pine-deciduous
b
Ricker
b(j)
p(I)
-0.141
-0.476
-1.044
-0.198
-0.440
-0.573
-1.844
-1.092
-0.430
-1.218
-6.106
-0.126
-0.441
-0.777
-0.170
-0.321
-0.312
-0.268
-0.910
-0.396
-1.026
-5.283
0.288
0.208
0.089†
0.269
0.344
0.477
0.336
0.215
0.396
0.025†
0.018†
b
-0.245
-0.739
-0.728
-0.283
-0.380
-0.294
-0.268
-0.795
-0.672
-0.469
-0.987
Gompertz
b(j)
p(I)
-0.200
-0.687
-0.610
-0.227
-0.310
-0.157
-0.133
-0.656
-0.626
-0.406
-0.922
0.498
0.021†
0.268
0.710
0.526
0.966
0.959
0.091†
0.175
0.707
0.091†
density dependent regulation of red, roe or sika deer in the oak-birch zone, although wild boar
showed evidence of Ricker-type density dependence in this zone. Time-series for red deer
showed evidence of density dependence in both the Korean pine-deciduous zone and spruce-fir
zone, by at least one method. Roe deer gave no significant results, suggesting either that density
dependence is too weak to be detected in the studied populations of this species, or that
competition with other ungulates is currently the over-riding regulatory factor for roe deer.
Finally, it is interesting to note that the removal of the most extreme point from each test data set
generally made little difference to the slopes (typically reducing their absolute magnitude by
between 10 and 20%). The exception to this was the data set for sika deer in the oak-birch zone.
Removing a single outlying data point from this data set reduced the slope of the regression of dt
on Nt by over 80%, preventing the test from giving a significant result. This finding suggests
caution in the analysis of data sets subject to large sampling errors, and supports the removal of
outliers when conducting the modified Pollard test.
86
Analysis of ungulate dynamics
4.3.4
Time-series analysis
Variables used in the models are set out in Table 4.4. The actual variables considered within the
global model for any population are shown in Appendix 4A, together with hypothesised
directions of effects, given prior biological knowledge. Given the relatively small sample sizes,
models were restricted to contain a maximum of four parameters (in addition to the intercept and
error term). Higher numbers of parameters would have certainly led to overfitted models. Even
with four parameters, there was a danger of overfitting but fewer parameters would have greatly
limited the insights that could be gained from this analyses, showing only the most dominant
effects.
The best-supported models for each population are shown in Appendix 4B. Populations
varied from sika deer in the oak-birch zone, 1980-2002, for which a single model received
substantially higher support than any alternative, to roe deer in the oak-birch habitat, 1980-2002,
where 20 models received good support (based on AIC alone). There was also substantial
variation among populations, in terms of the amount of variation in population growth that was
explained by selected models. Models selected for roe deer in the Korean pine-deciduous zone,
1980-2002, typically explained over 80% of variation in population growth rates, whilst in the
spruce-fir zone during the same period, models selected for roe deer explained only 30 to 46% of
variation in population growth rates.
Typically, the set of models selected for a given population all contained two or three
common variables, together with one or two additional variables that varied among models.
Those variables that appeared consistently in all of the models selected for a population are likely
to be among the most important effects influencing that population. Other variables that did not
appear consistently among models were often associated with one another however, and
frequently highly correlated (such as different indices of the severity of winter). For each
87
Table 4.4.
Summary of variables used in time-series analyses. Further details on which variables were included in models of the different
populations are given in the appendices to this Section
Variable
Description
Variable
Description
dt
Dependent variable
Log change in population size from year t to year t+1
Nt
Nt-1
Nt-2
xt
xt-1
xt-2
Density dependence
Absolute population density in winter of year t
Absolute population density in winter of year t-1
Absolute population density in winter of year t-2
Logarithm of population density in winter of year t
Logarithm of population density in winter of year t-1
Logarithm of population density in winter of year t-2
Tig
Lynx
Predators
Log (change in tiger population from t to t+1)
Lynx abundance averaged between winters of biological years t and t+1
Red
Roe
Sika
Rdnt
Competitors
Red deer abundance in winter of biological year t
Roe deer abundance in winter of biological year t
Roe deer abundance in winter of biological year t
Rodent abundance in summer of biological year t
WT
WS
WC
VT
VP
ST
SP
AT
WNPO
Weather variables
Mean winter temperature in winter of biological year t
Total winter precipitation in winter of biological year t
Winter conditions index in winter of biological year t
Mean spring temperature in spring of biological year t+1
Total spring precipitation in spring of biological year t+1
Mean summer temperature in spring of biological year t+1
Total summer precipitation in spring of biological year t+1
Annual mean temperature in biological year t
Winter NPO index for winter of biological year t
Oak
Pine
AltMast
Mast indices
Oak mast abundance in summer of biological year t
Pine mast abundance in summer of biological year t
Alternative mast index in summer of biological year t
RP
IE
EP
Human impact variables
Reports of poaching for biological year t+1
Illegal entries for biological year t+1
Estimated efficacy of protection for calendar year t+1
Analysis of ungulate dynamics
population, models (shown in Appendix 4B) that were clearly contrary to prior hypotheses and,
hence, did not receive good biological support, were excluded from the confidence set.
Remaining models were then averaged. The results of this process are shown in Table 4.5.
The process of model averaging permits all of the major influences on each population to
be illustrated within a single model formulation. All variables were Z-transformed prior to
analysis, so the size of coefficients also gives an indication of the strength of an effect, relative to
a change in the underlying parameter of a given number of standard deviations. First order
autoregressive terms were included in all models and generally (though not always) had large
effects relative to other factors. All were negative, as would be expected from data with survey
error. We will not comment further on these here. More interesting were the small number of
populations that seemed to be affected by higher order density dependence. Positive second or
third order lags (associated with the estimated populations in years t-1 and t-2) are usually
associated with populations in which growth is limited by a shortage of reproductively mature
females. Such lags are seen in red deer in the oak-birch zone, 1962-1980, roe deer in the sprucefir zone, 1980-2002, musk deer in the Korean pine-deciduous zone, 1962-2002 and sika deer in
the oak-birch zone, 1980-2002. In three of these cases (red deer, roe deer and sika deer), the
populations considered appear to have been undergoing near-exponential increases and, thus,
positive lagged density dependence is unsurprising. By contrast, musk deer do not appear to have
been increasing, suggesting that the population was limited by some extrinsic factor.
The effects of competition feature in models of several populations. In the later period
(1980-2002), there is evidence of competition among all of the larger deer in the oak-birch zone
with, in particular, negative effects of red deer and sika deer on one-another, reinforcing the
findings of our spatial analyses (Section 2.3.1). In the spruce-fir zone during that period, red and
roe deer also showed positive responses to the numbers of sika deer in the oak-birch zone.
Although this is unlikely to be a direct effect, it might suggest that whatever factor underlies the
89
Table 4.5
Summary of best models describing dynamics of each population, determined using the methods of Dennis & Otten (2000).
Parameters are summarised in Table 4.4.
Population (models in the confidence set a)
Multi-model average b
R2
Red deer, Oak-birch habitat, 1962-1979
1-3
dt = 0.08 - 0.17 Nt + 0.23 Nt-1 + 0.22 Oak - 0.32 WS - 0.19 AT
0.71
Red deer, Oak-birch habitat, 1980-2002
1-7
dt = - 0.04 Nt - 0.27 Roe - 0.05 Sika - 0.02 ST + 0.06 EP
0.50
Red deer, Korean pine-deciduous, 1962-1979
1-3
dt = - 0.03 - 0.39 xt - 0.06 ST - 0.06 AT - 0.32 WS - 0.26 RP
0.78
Red deer, Korean pine-deciduous, 1980-2002
1, 3 - 5, 7
dt = 0.04 - 0.19 xt - 0.15 WS + 0.03 VP - 0.01 ST - 0.08 SP
0.82
Red deer, Spruce-fir, 1962-1979
1-3
dt = - 0.25 - 0.32 xt + 0.31 WNPO + 0.10 VP - 0.50 RP
0.77
Red deer, Spruce-fir, 1980-2002
1 - 3, 5
dt = 0.19 - 0.67 xt + 0.26 Sika + 0.02 WNPO + 0.05 ST
0.55
Roe deer, Oak-birch habitat, 1962-1979
1 - 11
dt = 0.07 - 0.12 Nt + 0.24 Oak + 0.05 Red - 0.30 WS + 0.08 WC - 0.15 VT + 0.10 ST
0.55
Roe deer, Oak-birch habitat, 1980-2002
1, 4, 5, 7, 8, 12 - 14, 16, 19, 20
dt = - 0.01 - 0.41 Nt - 0.04 Nt-2 - 0.01 Sika - 0.01 WS + 0.01 VP - 0.01 ST - 0.02 SP + 0.04 EP
0.49
Roe deer, Korean pine-deciduous, 1980-2002
3-5
dt = 0.13 - 0.55 xt - 0.28 Lynx - 0.40 WS + 0.10 VT + 0.04 AT
0.84
(Table continues …)
Population (models in the confidence set a)
Multi-model average b
R2
Roe deer, Spruce-fir, 1980-2002
1 - 7, 10
dt = 0.08 - 0.95 xt + 0.07 xt-2 + 0.27 Red + 0.16 Sika + 0.04 AT - 0.07 EP - 0.06 IE
0.34
Sika deer, Oak-birch habitat, 1980-2002
1
dt = 0.38 - 0.96 xt + 0.60 xt-1 - 0.30 Red + 0.24 ST
0.77
Musk deer, Korean pine-deciduous, 1962-2002
1, 3, 6, 7, 9
dt = 0.02 - 0.34 Nt + 0.43 Nt-1 - 0.23 WC + 0.03 VT + 0.39 ST + 0.30 AT + 0.11 EP
0.51
Musk deer, Spruce-fir, 1962-2002
1 - 12
dt = 0.11 - 0.47 xt - 0.02 WS + 0.01 WC - 0.01 VT + 0.01 VP - 0.03 ST - 0.01 IE
0.50
Wild boar, Oak-birch and Korean pine-deciduous habitats, 1962-1979
4
dt = 0.12 - 0.61 xt
0.45
Wild boar, Oak-birch and Korean pine-deciduous habitats, 1980-2002
1-6
dt = - 0.07 - 0.58 xt + 0.07 AltMast + 0.11 WT + 0.09 WC - 0.04 SP + 0.07 AT + 0.40 EP
0.50
a
Numbers of models in the confidence set refer to model numbers in the summary of all models in Appendix B. Some models reported in that
summary were excluded for reasons given in the Appendix.
b
Average models clearly contain more parameters than any one model reported in Appendix B. Parameters are not shown, however, where the
magnitude of their coefficients is less than 0.01.
Analysis of ungulate dynamics
rapid increase in sika deer in the oak-birch zone also accounts for the increasing utilisation of the
spruce-fir zone by red and roe deer. Intriguingly, roe deer show positive effects of red deer in
two areas. Although the dominant interactions between these species tend to be negative, roe
deer may benefit where red deer maintain paths through deep snow (Danilkin, 1995). Whether
such an effect underlies our results is difficult to determine but might form the basis of an
interesting behavioural study.
Oak mast featured as a factor in models of only a few populations, including red deer, roe
deer and wild boar (see Table 4.5). In the case of wild boar (in the more recent period), the
alternative mast index appeared to be more informative than the index of oak mast alone,
underlining the importance of pine nuts to boar in years of low acorn availability. Pine mast
alone did not feature as a positive effect in selected models but whether this reflects its relative
unimportance, or the difficulty of accurate estimation of pine mast quality, it is currently
impossible to say. In general, mast indices may be too coarse to capture the variation among
years adequately, or they may become more revealing if reduced to fewer categories (to reflect
more drastic differences between years). Predators also appeared in very few population models,
with only lynx remaining as a strong negative influence on the growth of roe deer in the Korean
pine-deciduous zone, 1980-2002. No other model for roe deer was as informative as for that
population (note the lower R2 values in Table 4.5); it may be that survey error inhibited the
accurate identification of influential factors in other roe deer populations, for which it seems
likely that lynx are also important predators. That tigers did not emerge as an important factor for
any of the populations may be associated with the relatively low impacts of tigers as predators
(see Section 6 and Miquelle et al., 2005). Alternatively, it may be that log-growth in the tiger
population is a poor predictor of the impact that they have on prey populations during any
biological year. Unfortunately, due to the highly non-stationary nature of tiger dynamics during
the study period, absolute abundances of tigers are prone to spurious regressions with ungulate
populations, and so could not be incorporated into our analyses.
92
Analysis of ungulate dynamics
Many relationships between weather variables and ungulate dynamics are possible,
especially given the broad array of weather variables considered in our analyses. Winter weather
variables appear in most of the averaged models in Table 4.5, typically with negative effects of
cold snowy winters. These relationships are most pronounced for red and roe deer. Two curious
exceptions to this general pattern are worth noting.
First, musk deer in the Korean pine-
deciduous zone seem to show a substantial negative reaction to milder, less snowy winters. It is
possible that movement in these small deer is inhibited by warmer winters, when snow is softer
and they may regularly break through the crust. More puzzling, is that all of the top models for
wild boar prior to 1980 (many of which had high R2 values, indicative of high explanatory power;
see Appendix 4B), contained parameters suggesting that milder winters with less precipitation
inhibited population growth. These associations were rejected as potentially spurious, but it
might be instructive to consider whether there could be biological support for such patterns,
perhaps indirectly through an interaction between colder winters and food availability in spring,
for example. Few other weather variables had strong influences on any populations and the
consequences of given weather variables often varied between zones or periods. Such patterns
may suggest non-linear effects and it may be beneficial to include non-linearities in subsequent,
more detailed analyses of any specific population. One interesting feature of selected models for
red deer, was that there appeared to be negative impacts of higher summer or annual temperatures
in the oak-birch and Korean pine-deciduous zones, whilst increased temperatures led to
population increases in the spruce-fir zone. This might suggest that rising summer temperatures
are leading to a gradual northward shift in red deer in SAZ.
Finally, human impact factors appeared in a large number of models, suggesting that
effective protection may be important for many of the ungulates in SAZ. The strongest effects
were seen among red deer and wild boar but all species apart from sika deer showed some
relationship with one of the indices of protection or poaching pressure.
An unexpected
relationship is that shown by musk deer in the Korean pine-deciduous zone, where the population
93
Analysis of ungulate dynamics
appears to decline in response to increasingly effective protection. It is possible that musk deer
(which are one of the primary targets of poachers, due to the highly valued musk glands of males,
e.g. Yang et al., 2003) have moved into the central belt, away from the oak-birch zone in more
recent years, in response to increasing poaching pressure in that area (which, since receiving
formal Zapovednik designation, may have been perceived as a potential haven for this prized
species).
4.4
Discussion
In this section, we have demonstrated a seasonal decline in the rate at which tracks of several
ungulate species are encountered, with important implications for winter surveys of ungulates.
We have also assessed the longer term, temporal dynamics of ungulates in SAZ, shedding further
light on the trajectories of different populations in the area, their interactions, and the factors that
affect their growth. Importantly, we have used the data from SAZ to provide evidence for the
role of density dependent effects in several populations.
Whilst the influence of density
dependence on population dynamics is generally accepted to be widespread, evidence for this is
notoriously difficult to derive. That we have done so here, underlines the value of rigorously
collected, long term data sets, such as that from SAZ.
4.4.1
Within-year variation in track encounters
Seasonal declines in track encounter rates suggest that consistency in the timing of surveys is
crucial for providing data that are comparable from one year to the next. In Section 3.3.1, we
assessed the effect of time of year on the movement of ungulates. Models based on time of year
received some support for red deer and strong support for roe deer (Table 3.2). With the limited
24-hour movement data available, it is currently difficult to interpret the importance of time of
year as a factor underlying decreasing track encounters over winter. It is likely that changes in
encounter rate throughout the sampling period are partially attributable to changes in movement
94
Analysis of ungulate dynamics
behaviour but, at least for red deer, the measured decrease in daily travel distances is not
sufficient to account for the magnitude of observed declines in track encounters.
Declines in
track encounters may also reflect changes in density, due either to mortality or migration. That
no commensurate increases in encounter rate were seen in any part of SAZ suggests that
migration is unlikely to account for the observed patterns. Although it is possible that, as winter
progresses, ungulates move to some part of SAZ that is not surveyed thoroughly, radio-tracking
data do not provide evidence of large-scale movements during the winter seasons.
Fall
migrations occur in October and November, and red deer remain within small winter home ranges
until late April (Myslenkov and Miquelle, unpubl. data). As more data (especially radio-tracking
data) on ungulate daily movements become available, it should become possible to determine
whether changes in distribution or travel distance are likely to affect track encounter rates.
Randomised survey routes in areas that are rarely surveyed would also help to establish whether
seasonal changes in ungulate distributions play a role in the observed declines in track encounter
rates over winter.
4.4.2
Linear trend analyses
Linear trend analyses must be interpreted with some caution, owing to the influence of the
placement of period boundaries. Our choice of period boundaries was motivated solely by the
aim of establishing trends over five-year periods when survey effort was high, and longer periods
(of ten or twenty years) when survey effort was lower. Bootstrapping led to generally narrow
confidence intervals for the more numerous species but, given the importance of outliers for sika
deer at least (as determined by subsequent analyses, see Section 4.3.3), could have been
supplemented with jackknifing to generate confidence intervals even more robust to erroneous
data points.
These concerns aside, the trend analyses revealed some important patterns in the
trajectories of ungulate populations in SAZ. There were strong similarities between the trends of
95
Analysis of ungulate dynamics
several populations, suggesting that these populations respond to similar factors, and providing
additional support for the accuracy of density estimation, at least as a temporally-relative
measure. In particular, red deer and roe deer showed very similar trajectories in all three zones of
SAZ. In the oak-birch zone, their pronounced increases from the early 1960s to the early 1990s,
were followed by general declines over the next decade, most marked in the red deer population
of that zone. The same pattern was seen in wild boar in all zones of SAZ and is in contrast to the
almost exponential increase of sika deer in the oak-birch zone over the last decade of this data set.
These trends add weight to the developing picture of strong competition between sika and red
deer, which was further emphasised by the results of the time series analyses.
The most
disturbing pattern evident from the trend analyses, is the abrupt and widespread decline in wild
boar numbers over the last decade. Time-series analyses suggested that wild boar may be
negatively affected by recent reductions in effective protection within SAZ. Although boar are
among the rarest ungulates in SAZ, they are surprisingly frequently encountered, suggesting that
they will be highly vulnerable to opportunistic poachers. This situation is likely to be exacerbated
by the fact that boar are concentrated in the Oak-birch zone along the coast, closest to centres of
human population and most accessible to hunters.
4.4.3
Density dependence
The results of our tests for density dependence are important for several reasons. Perhaps the
most significant, is the development of a robust and relatively powerful approach to testing for
density dependence. Although we have not developed a formal inferential framework here,
additional work (P.A. Stephens, unpublished data) shows that the test could be substantially more
powerful than existing alternatives (e.g. see Shenk et al., 1998). Previous tests have tended to
consider only data sets consisting of a single annual estimate, but it seems likely that a large
proportion of long term data sets contain far more information about the structure of survey error
than this would imply. Our test is novel in permitting the structure of that error to be mapped on
96
Analysis of ungulate dynamics
to simulated data sets and, by using bootstrapping, to determine whether the error was sufficient
to have generated the observed properties of autoregression. The majority of existing tests show
an increase in power with increasing sample size (number of years) but the benefits of this are
undermined by the rapid increases in Type I error rates that also result (Shenk et al., 1998;
Vickery & Nudds, 1984). Crucially, there is no reason why our test should be vulnerable to such
increases in Type I error, rendering it increasingly useful with longer data sets. Several authors
have discussed the robustness of tests for density dependence in relation to the ratio of withinyear CV (coefficient of variation) to between-years CV (Forchhammer et al., 2002; Freckleton et
al., in prep.; Shenk et al., 1998). Generally, if within-year CV is small relative to between-years
CV, then census error is minor and tests for density dependence should be robust to census error
(Forchhammer et al., 2002). However, when samples are drawn from an intractable distribution
with a significant proportion of zeros, CV estimation is invalid; in these cases, bootstrapping
offers the only powerful method for assessing the consequences of error.
Overall, half of the populations examined showed some evidence for direct density
dependence using our bootstrapped test. That the other populations did not show such evidence
could arise either because density dependence in the species is relatively weak, or because their
populations are currently held at levels below where intraspecific competition depresses growth
rate. Several authors have noted that ungulates and other large mammals tend to exhibit ‘ramped’
transient dynamics, meaning that there is very little density regulation up to a relatively high
proportion of the potential carrying capacity of the environment, above which density acts
strongly to inhibit population growth (Fowler, 1981, 1987; McCullough, 1992). Interspecific
competition, in particular, can obscure the effects of direct density dependence and it is noticeable
that roe deer, which appear to experience negative impacts from red deer and sika deer in various
areas (Table 4.5), showed no sign of direct density dependence in any zone of SAZ. Sika deer
also showed no sign of direct density dependence. That this was the case is perhaps unsurprising,
given the nature of an expanding population that is new to the environment, and evidenced by the
97
Analysis of ungulate dynamics
near-exponential increase in sika deer numbers over the past decade. Until the last decade, the
species was rare and it exists presently only in the oak-birch zone, where it is still not abundant
(little more than 1 km-2 by the end of the study period). We predict, however, that as the
population continues to grow towards a density more like that of red deer in the oak-birch zone
(which have, at times, exceeded 6 to 7 km-2), direct density dependence will be detectable in this
population.
4.4.4
Time-series analysis
Our time series analyses represent the first formal attempts to assess a full range of parameters
that could affect the dynamics of ungulate populations within SAZ.
Proponents of model
selection theory place a strong emphasis on a priori model design, generally assuming that there
will be good prior reasons for the inclusion or rejection of certain parameters (e.g. Burnham &
Anderson, 2002). Unfortunately, reality is often different in that, of a large number of putative
influences, there is little reason to assume that one may be of greater importance than another.
Our study is an example of this situation: we had no strong reasons to select one particular
weather covariate, one human impact index or, indeed, one autoregressive order, over potential
alternatives. Similarly, although we could have minimised the number of competitive species
terms within candidate models, there is little to suggest that roe deer might compete more with
red deer than sika deer, for example. The consequence of these problems is that, even using our
strategy of permitting a maximum of one winter weather covariate and one human impact factor
in any one candidate model, large numbers of models were compared for each data set. AIC
provides a powerful means of balancing the conflicting goals of simplicity and goodness of fit
(Johnson & Omland, 2004; Stephens et al., 2005) and, using this in conjunction with a limit of
four parameters in any one model, we minimised the risks of substantial overfitting.
Nevertheless, the danger of overfitting remains because, with 20 or more parameters appearing in
the different candidate models (albeit never in the same one), it was highly probable that, even by
98
Analysis of ungulate dynamics
chance, one parameter or more would fit the data well (see Ginzburg & Jensen, 2004, for
example). This is not a problem unique to our study. Assessing a 25 year time series of mule
deer abundance, Peek et al. (2002) assessed models with up to seven covariates and an
autoregressive term, generating a very large number of models that could be fitted to the data.
More spectacularly, Lubow & Smith (2004) compared models with from 12 to 70 parameters to
explain a 23 year time series of data on the population dynamics of the Jackson elk herd, finding a
best-supported model with 25 parameters. This approach stands in contrast to the observation
that a model with 10 parameters could fit almost any 25 year time series (Ginzburg & Jensen,
2004). One way to overcome these problems, is to use model averaging (Burnham & Anderson,
2002). Using this technique, only parameters that consistently appear with the same sign in the
set of best models will appear to have a strong influence in the multi-model average.
Consequently, the remainder of our discussion is based on averaged models derived by this
process (Table 4.5).
Populations varied greatly in the degree to which selected models explained observed
dynamics. Given the many potential sources of error in converting track counts into annual
estimates of density, it is pleasing that biologically meaningful models described several
populations (including the sika deer population, four red deer populations and one roe deer
population) very well. Poorer model fits for musk deer, wild boar and some lower-density roe
deer populations may be a consequence of overwhelming observation error in the data on these
populations, which inhibits meaningful interpretation of the underlying processes. Low density,
substantial aggregative behaviour and, in the case of musk deer, limited information about their
movements, may well underlie the noise in these data sets. In most cases, more intensive study
would be required to generate data of a quality that would permit detailed analyses of the factors
affecting growth among these populations. Whether such intensive studies would be worthwhile
depends strongly on the goals of the Zapovednik monitoring system and, in particular, whether
time-series analysis is a priority. An alternative explanation for poorer model fits, is that the
99
Analysis of ungulate dynamics
dynamics of these species are too complex to be captured by the simplistic linear models we used
in our analyses.
As these were the first time-series analyses conducted using the data on
ungulates in SAZ, their findings may be viewed as preliminary. More detailed studies conducted
in the future could incorporate non-linearities (especially among weather variables, as discussed
in Section 4.3.4) and interactions among covariates.
We have commented on the detailed findings of our time-series analyses in Section 4.3.4.
Here, we comment more broadly on three important processes assessed in that section: lagged
density dependence, impacts of weather, and impacts of protection from human depredations.
Overall, density dependence, including lagged density dependent terms, emerged as an important
process for many populations, in keeping with many other studies of ungulates (see Table 4.1).
The positive effects of previous population sizes for growing populations are unsurprising. For
example, sika deer attain sexual maturity between months 16 and 18 after birth (Danilkin, 1995)
and, consequently, where reproductive potential is the limiting factor for population growth,
population at time t is likely to have less of a bearing on population growth from time t to t+1,
than population size at time t-1. That this emerged as the strongest example of lagged density
dependence, whilst other tests showed no support for the action of direct density dependence, is
compelling support for this explanation. By contrast, the musk deer population did not appear to
be increasing throughout the study period, and musk deer showed evidence of direct (Table 4.3)
as well as delayed (Table 4.5) density dependence. Alternative explanations for lagged density
dependence often invoke interactions with other trophic groups (Forchhammer et al., 2002; Post
et al., 2002; Stenseth et al., 1998), especially where there is strong coupling between trophic
groups (Bjornstad et al., 2001); delayed climatic effects (Forchhammer et al., 2001) including
carry-over effects from poor nutritional status of cohorts (Beckerman et al., 2002; Berryman,
1992); differential effects of density on age or sex classes (Gaillard et al., 1998; Mysterud et al.,
2002); and the impacts of territoriality (Erb et al., 2001). At present, it is hard to say which of
these is most likely to affect musk deer.
100
Analysis of ungulate dynamics
For most of the populations analysed, winter weather covariates typically had the
strongest effects of any of the weather covariates. In general, these effects were in the expected
directions but the apparent benefits of colder, snowier winters for wild boar before 1980 are
perplexing and may merit further consideration. In Section 3.3.1, we showed that wild boar are
the only species for which existing data show a strong influence of snow depth on daily travel.
The effect was most striking in the Korean pine-deciduous zone, where boar daily movement
distances were much greater in shallower snow. It seems likely that deep snow inhibits both boar
movement and boar foraging to a greater degree than it inhibits these behaviours in the deer
species. It would be surprising, therefore, if wild boar were positively affected by colder, snowier
winters. Negative effects of severe winters have been seen in studies of wild boar in other parts
of Russia (Markov, 1997) and Europe (Jedrzejewska et al., 1996). For all of these reasons, we
rejected the possibility of positive effects of winter severity, as most likely arising from spurious
regressions.
Finally, we noted above that human impact variables appeared in the averaged models for
many (over half) of the studied populations, including at least one model of each species.
Deriving indices that accurately reflect human impacts within the Zapovednik is complex and
there may be no way to quantify the exact level of illicit practices that are inevitably conducted in
a way to avoid detection.
Nevertheless, our analyses suggest that human impacts may be
important variables affecting the dynamics of all the ungulates of SAZ. Recent declines in
numbers of boar (possibly in response to reductions in anti-poaching measures) are disturbing and
point to the necessity of maintaining the high level of protection with which the Zapovednik
system is associated.
101
Appendix 4A
The following table summarises the variables used in global models for each population studied by time-series analysis (see further in Sections
4.2.4, 4.2.5, 4.2.6 and 4.3.4). General hypothesised effects are noted in the table, indicating where a variable is likely to have a positive effect (↑),
a negative effect (↓), or where it could affect changes in population size in either way (-). Typically, where models received good support but
included variables that did not conform to prior hypothesised effect directions, they were rejected (see further in Appendix 4B). No prior
hypotheses were made about the effects of lagged density dependence, as these depend on the stage of population development and other aspects
of the interaction of a species with its environment. Although the dominant effects of competitors are likely to be negative, other effects are
possible, especially for roe deer, for example, which can benefit from the presence of larger ungulates if this results in paths being kept open
through deep snow (Danilkin, 1995). Consequently, we did not automatically reject models that suggested positive interactions between species.
Similarly, sika deer (which are essentially limited to the oak-birch zone) were included as potential factors in red deer and roe deer analyses after
1980, even in other zones. Some biologists believe that sika deer displace other deer from favoured habitats, so the effects in these other zones
may be complex. Finally, the dominant effects of human impact factors are also given. These effects may also vary between zones, especially
where, for example, increases in human pressure in more accessible areas drive populations into less accessible areas. Again, therefore, models
which did not conform to the hypothesised effects given here for human impact variables, were not automatically rejected.
Table 4A.1
Variables included in the time-series analyses for each population. Abbreviations for zone are: OB, oak-birch habitat; KD,
Korean pine-deciduous habitat; SF, spruce-fir habitat. Variable codes are as summarised in Table 4.4
Species
Red deer Red deer Red deer Red deer Red deer Red deer Roe deer Roe deer Roe deer Roe deer Sika deer
Zone
Period
OB
OB
KD
KD
SF
SF
OB
OB
KD
SF
OB
Pre-1980 Post-1980 Pre-1980 Post-1980 Pre-1980 Post-1980 Pre-1980 Post-1980 Post-1980 Post-1980 Post-1980
Musk
deer
KD
Full
Musk Wild boar Wild boar
deer
SF OB&KD OB&KD
Full Pre-1980 Post-1980
Variable
Nt
Nt-1
Nt-2
xt
xt-1
xt-2
Red
Roe
Sika
Rdnt
↓
-
↓
-
↓
↓
-
↓
-
↓
↓
-
↓
↓
↓
↓
Oak
Pine
AltMast
↑
Tig
Lynx
↓
↓
↓
↓
-
↑
↓
↓
-
↑
↑
↑
↑
↑
↓
↓
↓
↓
↓
↓
-
↓
-
↓
-
↓
↓
↓
↓
↓
↓
-
-
↑
↑
↓
↓
↓
↓
-
↓
-
↓
-
↓
↓
↑
↑
↑
↑
↑
↑
↑
↓
↓
↓
↑
↓
↓
↓
(Table continues …)
Species
Red deer Red deer Red deer Red deer Red deer Red deer Roe deer Roe deer Roe deer Roe deer Sika deer
Zone
Period
OB
OB
KD
KD
SF
SF
OB
OB
KD
SF
OB
Pre-1980 Post-1980 Pre-1980 Post-1980 Pre-1980 Post-1980 Pre-1980 Post-1980 Post-1980 Post-1980 Post-1980
Musk
deer
KD
Full
Musk Wild boar Wild boar
deer
SF OB&KD OB&KD
Full Pre-1980 Post-1980
Variable
WS
WT
WC
VT
VP
ST
SP
AT
WNPO
RP
IE
EP
↓
↑
↑
↓
↑
↓
↑
↑
↓
↑
↓
↑
↑
↓
↑
↓
↑
↑
↓
↑
↓
↑
↑
↓
↑
↓
↑
↑
↓
↑
↓
↓
↑
↓
↓
↑
↓
↓
↑
↓
↓
↑
↓
↓
↑
↓
↑
↑
↓
↑
↓
↑
↑
↓
↑
↓
↑
↑
↓
↑
↓
↑
↑
↓
↑
↓
↑
↑
↓
↑
↓
↑
↑
↓
↑
↓
↑
↑
↓
↑
↓
↓
↑
↓
↓
↑
↓
↓
↑
↓
↓
↑
↓
↓
↑
↓
↓
↑
↓
↑
↑
↓
↑
↓
↑
↑
↓
↑
↓
↓
↑
Appendix 4B
The following table summarises the best-supported models selected by time-series analysis for each population. The best-supported model (with
lowest AIC value) and those within two AIC units of it are shown. In two cases (roe deer in Korean pine-deciduous habitat, 1980-2002 and wild
boar in oak-birch and Korean pine-deciduous habitats, 1962-1979) no model in the top set (within two AIC units of the best model) made
biological sense (for reasons given in the Comments column). In these cases, the best biologically-supported model and those within two AIC
units of it are also shown.
Table 4B.1
Best-supported models selected by time-series analysis of each population. Some models were rejected from the confidence set
for reasons given in the Comments column
Model (number: structure)
AICc ΔAICc
wi
R2 Comments
n
K
01: dt = 0.06 + 0.18 Nt-1 + 0.33 Oak - 0.33 WS - 0.30 AT
17
6
-39.83
0.00
0.40
0.78
02: dt = 0.08 + 0.25 Oak - 0.29 WS - 0.19 AT
18
5
-39.52
0.31
0.35
0.64
03: dt = 0.12 - 0.66 Nt + 0.63 Nt-1 - 0.37 WS
17
5
-38.87
0.96
0.25
0.70
01: dt = - 0.00 - 0.53 Roe + 0.25 EP
20
4
-18.86
0.00
0.22
0.52
02: dt = - 0.00 - 0.28 Nt - 0.34 Roe
20
4
-18.58
0.27
0.19
0.51
03: dt = - 0.00 - 0.49 Roe
20
3
-17.82
1.04
0.13
0.41
04: dt = - 0.00 - 0.51 Roe - 0.21 ST
20
4
-17.76
1.10
0.13
0.49
05: dt = - 0.00 - 0.51 Roe - 0.21 Sika
20
4
-17.74
1.12
0.13
0.49
06: dt = - 0.00 - 0.20 Nt - 0.41 Roe + 0.18 EP
20
5
-17.31
1.54
0.10
0.56
07: dt = - 0.00 - 0.53 Roe - 0.15 ST + 0.20 EP
20
5
-17.07
1.78
0.09
0.55
01: dt = - 0.03 - 0.39 xt - 0.13 ST - 0.25 RP
16
5
-39.66
0.00
0.47
0.80
02: dt = - 0.03 - 0.39 xt - 0.13 AT - 0.28 RP
16
5
-38.90
0.76
0.32
0.79
03: dt = - 0.03 - 0.39 xt - 0.24 RP
16
4
-38.03
1.64
0.21
0.72
01: dt = 0.07 - 0.34 xt - 0.27 WS - 0.17 SP
22
5
-53.68
0.00
0.26
0.81
02: dt = 0.07 - 0.35 xt - 0.37 WS + 0.14 VP + 0.13 RP
22
6
-52.78
0.90
0.17
0.83 Possible spurious relationship with reports of poaching
03: dt = 0.07 - 0.37 xt + 0.08 Sika - 0.25 WS - 0.16 SP
22
6
-52.38
1.29
0.14
0.83
04: dt = 0.07 - 0.41 xt + 0.11 Roe - 0.26 WS - 0.15 SP
22
6
-52.05
1.62
0.12
0.83
05: dt = 0.07 - 0.35 xt - 0.29 WS + 0.07 VP - 0.14 SP
22
6
-52.01
1.67
0.11
0.83
06: dt = 0.07 - 0.36 xt - 0.26 WS - 0.16 SP - 0.07 EP
22
6
-51.76
1.92
0.10
0.83 Possible spurious relationship with efficacy of protection
07: dt = 0.07 - 0.34 xt - 0.27 WS - 0.06 ST - 0.18 SP
22
6
-51.74
1.94
0.10
0.83
Red deer, Oak-birch habitat, 1962-1979
Red deer, Oak-birch habitat, 1980-2002
Red deer, Korean pine-deciduous, 1962-1979
Red deer, Korean pine-deciduous, 1980-2002
(Table continues …)
Model (number: structure)
AICc ΔAICc
wi
R2 Comments
n
K
01: dt = - 0.25 + 0.60 WNPO - 0.71 RP
11
4
-7.05
0.00
0.52
0.79
02: dt = - 0.25 - 0.61 xt - 0.50 RP
11
4
-5.66
1.38
0.26
0.76
03: dt = - 0.25 - 0.72 xt + 0.46 VP
11
4
-5.33
1.72
0.22
0.75
01: dt = 0.19 - 0.71 xt + 0.32 Sika
19
4
-21.14
0.00
0.31
0.56
02: dt = 0.19 - 0.72 xt + 0.34 Sika + 0.18 ST
19
5
-20.47
0.67
0.22
0.61
03: dt = 0.19 - 0.49 xt
19
3
-20.13
1.01
0.19
0.45
04: dt = 0.19 - 0.68 xt + 0.27 Roe
19
4
-19.90
1.24
0.17
0.53 Possible spurious relationship with roe deer
05: dt = 0.19 - 0.80 xt + 0.40 Sika + 0.15 WNPO
19
5
-19.20
1.94
0.12
0.59
01: dt = 0.07 + 0.33 Oak - 0.43 WS - 0.25 VT + 0.24 ST
17
6
-15.20
0.00
0.15
0.64
02: dt = 0.07 + 0.34 Oak - 0.33 WS
17
4
-14.85
0.35
0.13
0.42
03: dt = 0.07 + 0.34 Oak - 0.36 WS + 0.23 ST
17
5
-14.82
0.38
0.13
0.53
04: dt = 0.07 + 0.33 Oak - 0.40 WS - 0.24 VT
17
5
-14.69
0.51
0.12
0.52
05: dt = 0.07 - 0.45 Nt + 0.30 Red + 0.37 WC - 0.32 VT
17
6
-14.05
1.15
0.09
0.62
06: dt = 0.07 + 0.22 Red + 0.39 Oak - 0.39 WS - 0.30 VT
17
6
-13.79
1.41
0.08
0.61
07: dt = 0.07 - 0.32 Nt + 0.33 WC
17
4
-13.49
1.71
0.06
0.37
08: dt = 0.07 - 0.42 Nt + 0.32 Red - 0.36 WS - 0.32 VT
17
6
-13.46
1.74
0.06
0.60
09: dt = 0.07 - 0.20 Nt-1 + 0.32 Oak - 0.35 WS + 0.30 ST
17
6
-13.43
1.77
0.06
0.60
10: dt = 0.07 - 0.20 Nt + 0.26 Oak - 0.36 WS + 0.25 ST
17
6
-13.34
1.87
0.06
0.60
11: dt = 0.07 - 0.32 Nt + 0.40 WC - 0.25 VT
17
5
-13.33
1.87
0.06
0.48
Red deer, Spruce-fir, 1962-1979
Red deer, Spruce-fir, 1980-2002
Roe deer, Oak-birch habitat, 1962-1979
(Table continues …)
Model (number: structure)
AICc ΔAICc
wi
R2 Comments
n
K
01: dt = - 0.01 - 0.40 Nt
22
3
-31.29
0.00
0.09
0.44
02: dt = - 0.01 - 0.41 Nt - 0.16 Nt-2 - 0.19 Oak + 0.19 EP
22
6
-31.09
0.20
0.08
0.63 Possible spurious relationship with oak mast
03: dt = - 0.01 - 0.43 Nt - 0.18 Oak + 0.19 EP
22
5
-31.03
0.26
0.08
0.57 Possible spurious relationship with oak mast
04: dt = - 0.01 - 0.38 Nt - 0.15 Nt-2
22
4
-31.00
0.29
0.08
0.50
05: dt = - 0.01 - 0.43 Nt + 0.13 EP
22
4
-30.40
0.89
0.06
0.49
06: dt = - 0.01 - 0.40 Nt - 0.12 Oak
22
4
-30.21
1.07
0.05
0.48 Possible spurious relationship with oak mast
07: dt = - 0.01 - 0.42 Nt - 0.12 ST
22
4
-30.20
1.08
0.05
0.48
08: dt = - 0.01 - 0.41 Nt - 0.15 Nt-2 + 0.13 EP
22
5
-30.03
1.26
0.05
0.55
09: dt = - 0.01 - 0.37 Nt - 0.15 Nt-2 - 0.13 Oak
22
5
-29.95
1.34
0.05
0.55 Possible spurious relationship with oak mast
10: dt = - 0.01 - 0.40 Nt - 0.19 Oak - 0.13 WS + 0.20 EP
22
6
-29.91
1.37
0.04
0.61 Possible spurious relationship with oak mast
11: dt = - 0.01 - 0.48 Nt - 0.17 Oak - 0.14 SP + 0.23 EP
22
6
-29.82
1.46
0.04
0.61 Possible spurious relationship with oak mast
12: dt = - 0.01 - 0.38 Nt - 0.11 WS
22
4
-29.80
1.49
0.04
0.47
13: dt = - 0.01 - 0.49 Nt - 0.16 SP + 0.18 EP
22
5
-29.77
1.52
0.04
0.54
14: dt = - 0.01 - 0.42 Nt - 0.11 Sika
22
4
-29.75
1.54
0.04
0.47
15: dt = - 0.01 - 0.42 Nt - 0.14 Sika - 0.16 Oak
22
5
-29.45
1.83
0.04
0.54 Possible spurious relationship with oak mast
16: dt = - 0.01 - 0.43 Nt - 0.09 SP
22
4
-29.43
1.86
0.04
0.47
17: dt = - 0.01 - 0.42 Nt + 0.09 IE
22
4
-29.43
1.86
0.04
0.47 Possible spurious relationship with illegal entries
18: dt = - 0.01 - 0.45 Nt - 0.20 Oak + 0.12 VT + 0.22 EP
22
6
-29.41
1.87
0.03
0.60 Possible spurious relationship with oak mast
19: dt = - 0.01 - 0.39 Nt + 0.09 VP
22
4
-29.35
1.94
0.03
0.46
20: dt = - 0.01 - 0.40 Nt - 0.15 Nt-2 - 0.11 Sika
22
5
-29.29
2.00
0.03
0.53
Roe deer, Oak-birch habitat, 1980-2002
(Table continues …)
Model (number: structure)
AICc ΔAICc
wi
R2 Comments
n
K
01: dt = 0.13 - 0.66 xt - 0.32 Lynx - 0.42 WS + 0.26 RP
20
6
-31.46
0.00
0.64
0.87 Possible spurious relationship with reports of poaching
02: dt = 0.13 - 0.52 xt - 0.22 Pine - 0.34 Lynx - 0.44 WS
20
6
-30.26
1.19
0.36
0.86 Possible spurious relationship with pine mast
03: dt = 0.13 - 0.54 xt - 0.27 Lynx - 0.38 WS + 0.20 VT
20
6
-28.71
2.74
0.16
0.85
04: dt = 0.13 - 0.54 xt - 0.27 Lynx - 0.44 WS
20
5
-27.45
4.00
0.09
0.81
05: dt = 0.13 - 0.60 xt - 0.34 Lynx - 0.42 WS + 0.17 AT
20
6
-26.87
4.59
0.07
0.84
01: dt = 0.06 - 1.12 xt + 0.80 Red
16
4
0.07
0.00
0.15
0.35
02: dt = 0.06 - 1.04 xt + 0.72 Sika
16
4
0.15
0.08
0.14
0.34
03: dt = 0.06 - 0.43 xt
16
3
0.33
0.26
0.13
0.19
04: dt = 0.29 - 1.01 xt + 0.62 xt-2
13
4
0.82
0.75
0.10
0.46
05: dt = 0.06 - 1.53 xt + 1.13 Red + 0.39 AT
16
5
0.88
0.81
0.10
0.46
06: dt = 0.06 - 0.98 xt - 0.64 EP
16
4
1.02
0.95
0.09
0.31
07: dt = 0.06 - 0.52 xt - 0.34 IE
16
4
1.11
1.05
0.09
0.30
08: dt = 0.06 - 1.33 xt + 0.83 Sika + 0.37 RP
16
5
1.38
1.31
0.08
0.44 Possible spurious relationship with reports of poaching
09: dt = 0.06 - 1.11 xt + 0.89 Sika - 0.32 Pine
16
5
1.57
1.50
0.07
0.43 Possible spurious relationship with pine mast
10: dt = 0.06 - 1.04 xt + 0.64 Sika - 0.29 IE
16
5
1.91
1.85
0.06
0.42
16
6
-23.66
0.00
1.00
0.77
Roe deer, Korean pine-deciduous, 1980-2002
Roe deer, Spruce-fir, 1980-2002
Sika deer, Oak-birch habitat, 1980-2002
01: dt = 0.38 - 0.96 xt + 0.60 xt-1 - 0.30 Red + 0.24 ST
(Table continues …)
Model (number: structure)
AICc ΔAICc
wi
R2 Comments
n
K
01: dt = 0.04 - 0.68 Nt + 0.65 Nt-1 + 0.63 ST
22
5
-3.99
0.00
0.19
0.54
02: dt = - 0.01 - 0.43 Nt + 0.63 ST + 0.48 RP
23
5
-3.43
0.56
0.14
0.50 Possible spurious relationship with reports of poaching
03: dt = - 0.01 - 0.56 WC + 0.73 AT
23
4
-3.39
0.60
0.14
0.43
04: dt = - 0.10 - 0.40 Nt-2 + 0.48 VP + 0.54 ST + 0.61 RP
22
6
-2.47
1.52
0.09
0.58 Possible spurious relationship with reports of poaching
05: dt = 0.03 - 0.69 Nt + 0.49 Nt-1 + 0.62 ST + 0.27 RP
22
6
-2.41
1.58
0.08
0.58 Possible spurious relationship with reports of poaching
06: dt = - 0.07 + 0.03 Nt-2 - 0.59 WC + 0.79 AT
22
5
-2.28
1.71
0.08
0.50
07: dt = 0.04 - 0.78 Nt + 0.68 Nt-1 + 0.21 VT + 0.65 ST
22
6
-2.20
1.78
0.08
0.58
08: dt = 0.03 - 0.65 Nt + 0.60 Nt-1 + 0.20 Lynx + 0.64 ST
22
6
-2.08
1.91
0.07
0.57 Possible spurious relationship with lynx
09: dt = 0.06 + 0.92 Nt-1 + 0.69 ST + 0.88 EP
22
5
-2.01
1.98
0.07
0.50
10: dt = - 0.05 - 0.64 Nt + 0.32 Nt-2 + 0.59 ST + 0.50 RP
22
6
-1.99
2.00
0.07
0.57 Possible spurious relationship with reports of poaching
01: dt = 0.11 - 0.46 xt
36
3
-49.33
0.00
0.16
0.48
02: dt = 0.11 - 0.44 xt - 0.10 ST
36
4
-48.32
1.00
0.10
0.50
03: dt = 0.11 - 0.47 xt - 0.09 IE
36
4
-48.30
1.03
0.10
0.50
04: dt = 0.11 - 0.48 xt - 0.08 VT
36
4
-48.00
1.33
0.08
0.50
05: dt = 0.11 - 0.47 xt + 0.08 VP
36
4
-47.93
1.40
0.08
0.50
06: dt = 0.11 - 0.48 xt - 0.08 WS
36
4
-47.90
1.43
0.08
0.49
07: dt = 0.11 - 0.47 xt + 0.08 WC
36
4
-47.85
1.48
0.08
0.49
08: dt = 0.11 - 0.45 xt + 0.12 WC - 0.13 ST
36
5
-47.76
1.56
0.07
0.53
09: dt = 0.11 - 0.45 xt - 0.11 WS - 0.12 ST
36
5
-47.46
1.86
0.06
0.52
10: dt = 0.11 - 0.46 xt + 0.06 EP
36
4
-47.42
1.91
0.06
0.49
11: dt = 0.11 - 0.47 xt + 0.05 WT
36
4
-47.39
1.94
0.06
0.49
12: dt = 0.11 - 0.50 xt - 0.12 WS + 0.12 VP
36
5
-47.38
1.94
0.06
0.52
Musk deer, Korean pine-deciduous, 1962-2002
Musk deer, Spruce-fir, 1962-2002
(Table continues …)
Model (number: structure)
AICc ΔAICc
wi
R2 Comments
n
K
01: dt = - 0.08 + 0.34 xt-1 - 0.86 WC
13
4
-10.37
0.00
0.70
0.69 Possible spurious relationships with winter weather variables
02: dt = - 0.10 + 0.42 xt-1 + 0.24 Oak - 0.86 WC
13
5
-8.72
1.65
0.30
0.76 Possible spurious relationships with winter weather variables
03: dt = 0.12 - 0.40 xt + 0.37 WS
15
4
-8.03
2.34
0.22
0.57 Possible spurious relationships with winter weather variables
04: dt = 0.12 - 0.61 xt
15
3
-7.83
2.54
0.20
0.45
05: dt = - 0.10 + 0.38 xt-1 + 0.18 AltMast - 0.88 WC
13
5
-7.53
2.84
0.17
0.73 Possible spurious relationships with winter weather variables
06: dt = - 0.07 + 0.72 xt-1 - 0.38 Rdnt - 0.77 WC
11
5
-7.46
2.90
0.16
0.85 Possible spurious relationships with winter weather variables
07: dt = 0.12 + 0.60 WS
15
3
-7.41
2.96
0.16
0.44 Possible spurious relationships with winter weather variables
01: dt = - 0.07 - 0.48 xt + 0.32 WC + 0.38 EP
22
5
-12.52
0.00
0.29
0.50
02: dt = - 0.07 - 0.60 xt + 0.31 WT + 0.40 EP
22
5
-11.88
0.64
0.21
0.49
03: dt = - 0.07 - 0.67 xt + 0.24 AltMast + 0.33 WT + 0.33 EP
22
6
-11.08
1.44
0.14
0.55
04: dt = - 0.07 - 0.53 xt - 0.28 SP + 0.42 EP
22
5
-11.02
1.51
0.14
0.47
05: dt = - 0.07 - 0.74 xt + 0.29 AltMast + 0.37 AT + 0.45 EP
22
6
-10.63
1.89
0.11
0.54
06: dt = - 0.07 - 0.63 xt + 0.30 AT + 0.50 EP
22
5
-10.56
1.97
0.11
0.46
Wild boar, Oak-birch and Korean pine-deciduous habitats, 1962-1979
Wild boar, Oak-birch and Korean pine-deciduous habitats, 1980-2002
Analysis of ungulate dynamics
5. SURVEY PROTOCOL
5.1
Background
Although winter transect counts have been employed in SAZ for over four decades, a rigorous
analysis of the power of this approach to monitoring large ungulates, together with its associated
error, has not previously been conducted. Such an analysis is necessary to focus attention on the
aims and possibilities of the survey and, ultimately, to guide ongoing development of the survey
protocol. In this section, we present an analysis of the current survey design, with an emphasis on
two aspects of design: minimising zero counts and determining required total survey effort.
Following Hayward et al. (2002), we began by assessing the length of transect segments
required to reduce the proportion of zero counts (i.e. instances when no tracks of a given species
are recorded along an entire transect segment). The importance of zero counts depends on the
type of analysis to which the data are subject. However, for many analyses (particularly those
which rely on distributional assumptions) zeros can pose a significant hindrance.
This is
especially the case where it is desirable to conduct parametric statistical analyses that rely on
normality in data. Large numbers of zeros can substantially skew data away from normality and
cannot be transformed to a normal distribution. The result is that zero counts are problematic in
surveys, as they increase the need to amalgamate transect segments for meaningful analysis,
reducing the potential for finer-scale analysis. Secondly, we explored the relationship between
mean track encounter rate and the total length of transects (the “survey effort”) required annually
to approximate the mean track encounter rate. This allowed us to estimate the error associated
with estimates of the density of different species, as a function of annual survey effort. Finally,
we also conducted a power analysis to determine the amount of error in annual estimates that can
be tolerated, if abundance trends of given magnitude are to be detected. By combining this power
analysis with our estimates of the relationship between error and survey effort, we were able to
identify the survey effort required to detect trends for each of the ungulate species in SAZ.
112
Analysis of ungulate dynamics
5.2
Methods
5.2.1
Zero counts and the length of transect segments
To assess the relationship between transect segment length and the probability with which zero
tracks were encountered, we relied on the results of our simulations (Section 3.2.6). These
showed that the probability with which zero, one or more unique movement paths are
encountered along a transect can be predicted using a Poisson probability distribution of the form:
P(Y ) 
(   D  S ) Y  (   DS )
e
Y!
(5.1)
where Y is the number of unique paths encountered, D is the density of animals making tracks, S
is transect segment length and  is the mean rate at which animal paths are encountered when
S = 1 km and D = 1 km-2. Using this equation, it is possible to predict transect segment lengths
required to keep the proportion of zeros below some threshold, again as a function of density. We
did this for each species and, where appropriate (as dictated by the findings in Section 3.3.1),
combinations of relevant conditions (see estimates of  in Table 3.6).
5.2.2
Survey effort and associated error
To determine the relationship between survey effort and uncertainties in density estimation, we
assessed the field data. Specifically, we examined how increases in field data sample sizes led to
increases in the accuracy with which the mean encounter rate was approximated. To do this, we
used areas and years for which the most data had been collected (i.e. those years in which at least
50 transects had been conducted). By re-sampling with replacement, we effectively bootstrapped
the mean track encounter rates on these samples but, rather than being interested in achieving a
consistent mean, we were interested in the total length of samples required in order to provide a
good approximation of the mean. For example, 51 transects were conducted in Korean pinedeciduous habitat in 1967. Fig. 5.1 shows ten bootstraps of the mean encounter rate of red deer,
113
Analysis of ungulate dynamics
obtained by sequentially adding random transects to a sample. It is apparent that even with very
large samples (as much as 3,000 km of transects) there remains some variation in the mean
encounter rate. However, it is also evident that while variation initially declines rapidly as total
survey length increases, that decline soon becomes very gradual. In the case illustrated (red deer
with a mean encounter rate of approximately 1.44 km-1), increases in survey effort beyond
approximately 500 km bring very little gain in terms of a more accurate approximation of the
mean.
4.0
Mean encounter rate (km-1)
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
500
1000
1500
2000
2500
3000
Sample effort (km)
Figure 5.1.
Ten bootstraps (black lines) of the relationship between sample effort (kms of
transect) and precision of mean encounter rate. The actual mean for the sample is illustrated by
the red line.
One way to summarise the increase in accuracy as sample size increases, is to assess the
relationship between coefficient of variation (CV; the ratio of standard deviation of estimates to
the mean estimate) and sample effort (Hayward et al., 2002). To do this, we derived 100
bootstraps as detailed above, for each case where at least 50 transects had been conducted in one
of the three major habitats during any biological year. Mean CV was calculated for each category
of known mean encounter rate (categories were designated to the nearest 0.2 km-1) and each
114
Analysis of ungulate dynamics
category of sample effort (designated to the nearest 20 km), over all bootstrap samples within
those categories.
5.2.3
Power analyses and required survey effort
The amount of survey effort required annually depends on the specific aims of the survey. For
example, if the aim of the survey is to detect trends in ungulate abundance, then the magnitude of
trends that should be detected, the period over which they should be detected, and the area within
which they should be detected (i.e. at the level of the drainage basin, the habitat zone, or the
entire reserve), will all affect the required survey effort. As the detection of trends is a common
aim of vertebrate monitoring (Thompson et al., 1998), we decided to analyse power with respect
to that aim. We assumed that there would be limited utility in trying to detect trends in ungulate
abundance within individual drainages, as populations will likely move among drainages
(especially the smaller basins) in response to temporal heterogeneity in resources. However, as
most ungulate populations occur in only one or two of the three major habitat zones in SAZ, it
seems likely that detection of abundance trends at the level of the habitat zone will be useful.
Short term trends (i.e. those lasting a few years) may result from normal fluctuations in the
environment, such as from a series of poor mast crop years. However, if only long term trends
are deemed to be of interest, there is a danger that substantial changes in abundance could be well
underway before they are detected. As a compromise, we assumed that it would be useful to
detect trends in abundance over periods of five years.
Our analysis assumed that trend will be examined using regression methods by testing for
a significant slope coefficient based on a t-test of the null hypothesis that slope is zero
(Gerrodette, 1987; Thompson et al., 1998).
Although other statistical approaches could be
employed, we based our analysis on this method because its applicability for monitoring
vertebrate populations has been thoroughly assessed in recent literature (see review in Thompson
et al., 1998). We used Monte Carlo simulations to determine how CV of density estimates and
115
Analysis of ungulate dynamics
alpha (probability of a Type I error) influenced power. Specifically, we generated 300,000
simulations of track indices over a 5-year monitoring horizon to estimate power to detect an
annual change in density estimates of -10%, or -20%. The analyses assumed that declines were
of the exact magnitude tested (10% or 20% per annum) but that measurements of abundance were
subject to error dictated by the sampling CV. Thus, our simulations included observation error
(inaccuracies in estimation) but no process error (inaccuracies in the actual population trend).
5.3
Results
5.3.1
Zero counts and the length of transect segments
We assessed the transect segment lengths required to produce certain proportions of zero counts.
The results of this analysis are summarised in Fig. 5.2. Clearly, target transect lengths are highly
dependent on three factors: the daily movement behaviour of the species, its local population
density and the acceptable proportion of zero counts. In general, however, it appears that for low
density species (in the order of 0.5 km-2), a low proportion of zero counts will only be achieved
by creating long transect segments, typically of 7 to 10 km, or even longer. By contrast, for
moderate densities (of 1 to 2 km-2), transects of 3 to 6 km should be sufficient, whilst with
ungulate densities of over 2 km-2 zero counts should be rare even with transect segments of 3 km
or less (Fig. 5.2). Given equal densities, zero counts are most problematic for roe deer in late
winter, as these have the shortest daily travel distances of the species considered. However, as
this species is one of the more abundant, zero counts should generally pose less of a problem.
5.3.2
Survey effort and associated error
Relationships between CV of estimates and survey effort (total km y-1) were generated for each
species in each of the three main habitat zones in which they occur. Results were all qualitatively
similar but some sample results are illustrated in Fig. 5.3. In general, bootstrapping demonstrated
the expectation that CVs were lower for higher mean encounter rates. The qualitative similarities
116
Analysis of ungulate dynamics
117
Analysis of ungulate dynamics
10
Required transect segment length (km)
(a)
10
(b)
8
8
6
6
4
4
4
2
2
2
0
0
1
2
3
4
5
0
0
10
1
2
3
4
5
10
(e)
8
8
6
4
4
4
2
2
2
0
1
2
3
4
5
1
2
3
4
5
10
(h)
8
8
6
4
4
4
2
2
2
0
1
2
3
4
5
4
5
0
1
2
3
4
5
0
1
2
3
4
5
8
6
0
3
10
(i)
6
0
2
0
0
10
1
8
6
0
0
10
(f)
6
0
(g)
8
6
0
(d)
10
(c)
0
0
1
2
3
4
5
-2
Density of tracks in the environment (km )
Figure 5.2.
Transect lengths required to produce less than 50% zeros (bottom line in each
panel), 25% zeros (middle lines) and 10% zeros (top lines) for: (a) red deer in early winter; (b)
red deer in late winter; (c) roe deer in early winter; (d) roe deer in late winter; (e) sika deer; (f)
wild boar in oak-birch habitat, early winter; (g) wild boar in oak-birch habitat, late winter; (h)
wild boar in Korean pine-deciduous or spruce-fir habitat, early winter; (i) wild boar in Korean
pine-deciduous or spruce-fir habitat, late winter.
between results allow us to make some general recommendations across species, habitats and
densities. Specifically, it appears that CV in mean encounter rate declines very rapidly as survey
effort is increased up to 250 km y-1 and that significant gains are made up to approximately 500
km y-1. Increasing the survey effort beyond 500 km y-1 appears to bring marginal improvement in
accuracy in most cases (especially those where encounter rate is high), however, whilst in other
cases (e.g. moose in areas of low density), significant improvements would only be made through
substantial increases in survey effort (such as increasing the survey by a further 500 to 1,000 km
y-1). This issue can be examined in more detail using a power analysis, as shown in the next
section.
118
Analysis of ungulate dynamics
Coefficient of variation in mean encounter rate
(a)
2.0
2.0
(d)
1.6
1.6
1.2
1.2
0.8
0.8
0.4
0.4
0.0
0.0
0
500
1000
1500
2000
2500
3000
0
500
1000
1500
2000
2500
3000
0
500
1000
1500
2000
2500
3000
0
500
1000
1500
2000
2500
3000
2.0
2.0
(b)
(e)
1.6
1.6
1.2
1.2
0.8
0.8
0.4
0.4
0.0
0.0
0
500
1000
1500
2000
2500
3000
2.0
2.0
(c)
(f)
1.6
1.6
1.2
1.2
0.8
0.8
0.4
0.4
0.0
0.0
0
500
1000
1500
2000
2500
3000
Survey effort (km y-1)
Figure 5.3.
Sample relationships between encounter rate CV and survey effort: (a) red deer
in Korean pine-deciduous habitat (dashed lines show encounter rate categories: 0.5, 1.3 and 2.1
km-1, top to bottom); (b) red deer in oak-birch (top to bottom: 0.3, 2.7, 4.7 km-1); (c) wild boar in
oak-birch (top to bottom: 0.1, 0.9, 1.9 km-1); (d) roe deer in oak-birch (top to bottom: 0.1, 1.7, 3.5
km-1); (e) sika deer in oak-birch (top to bottom: 0.1, 0.9, 1.9 km-1); (f) moose in spruce-fir (top to
bottom: 0.1, 0.3 km-1).
5.3.3
Power analyses and required survey effort
The relationship between power to detect a trend and CV of density estimates is shown in Fig.
5.4. Clearly, larger CVs in density estimates can be tolerated where it is only necessary to detect
more pronounced trends, and where the existence of trends will be accepted on the basis of
119
Analysis of ungulate dynamics
1.0
(a)
0.8
0.6
0.4
α = 0.25
α = 0.20
0.2
Power to detect trend
α = 0.10
α = 0.05
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.0
(b)
0.8
0.6
0.4
α = 0.25
α = 0.20
0.2
α = 0.10
α = 0.05
0.0
0.0
0.2
0.4
0.6
0.8
1.0
CV of density estimates
Figure 5.4.
Relationship between power to detect trends in abundance and CV of density
estimates: (a) 10% annual decline over 5 years; (b) 20% annual decline over 5 years. Solid lines
show relationships for given α levels. Broken horizontal lines show points yielding 80% power,
whilst broken vertical lines show acceptable CVs of density estimates associated with 80%
power, for each α level.
120
Analysis of ungulate dynamics
weaker evidence (higher α). Broken lines in Fig. 5.4 show threshold values of CV that can be
tolerated whilst still achieving 80% power to detect trends.
These depend on the α level
employed but CVs are in the order of 10 to 20% for detection of a 10% annual decline, and 20 to
40% for detection of a 20% annual decline, given the range of α levels assessed (0.05 ≤ α ≤ 0.25).
Determining the amount of survey effort required annually to achieve tolerable CVs in
density estimates is complex, as this depends on the density of the surveyed species. As a general
guide, we derived recommendations based on track encounter rates in the habitat zone in which
each species is most common, but designed to reflect the encounter rate experienced in relatively
poor years (i.e. years of relatively low abundance in relation to recent records).
These
recommendations are summarised in Table 5.1, which should also clarify our approach.
5.4
Discussion
Our analyses have demonstrated that the adequacy of survey effort is contingent on several
factors, some of which can be controlled by survey design criteria. In this way, our results
highlight the importance of setting clear objectives to guide winter transect counts in SAZ. At
present, these objectives are not widely known or clearly stated. One possible reason for this, is
that the purpose of the winter transect count is far broader than simply collecting data on
ungulates.
Nevertheless, monitoring will become most effective when clear objectives are
defined for SAZ, so that the survey can be designed to meet all of those objectives adequately. In
the absence of precise objectives, we can make only general recommendations related to common
goals of ungulate monitoring (but see further in Section 7). Hence, the results of our analyses
should be revisited following a rigorous exercise to set specific objectives for winter track counts
in SAZ.
In the absence of clear objectives and associated decisions regarding spatial and temporal
scales of interest, habitats of interest, necessary precision, and priorities regarding species of
interest, we can outline several broad conclusions from our analysis. First, our results suggest
121
Analysis of ungulate dynamics
122
Analysis of ungulate dynamics
Table 5.1
Recommended annual survey effort based on the assumed goal of detecting
change in the dominant habitat zone during periods of relatively low abundance.
Parameter
RE
RO
Species
SD
MU
Main habitat zone
Mean annual encounter rates (tracks km-1) in that habitat
since 1990:
Minimum
Maximum
Approximate lower quartile
OB
OB
OB
1.65
6.31
2.39
1.40
3.55
1.80
Approximate survey effort (km y-1) required to detect trend
at lower quartile of encounter rate:
to achieve 10% CV
to achieve 20% CV
to achieve 30% CV
to achieve 40% CV
400
90
40
20
720
200
100
60
MOa
WB
SF
SF
OB
0.27
2.63
0.55
0.48
3.52
1.32
0.00
0.09
0.00
0.16
2.08
0.33
2100
500
230
130
600
150
70
40
1500
360
160
90
a
It is unlikely that trends in moose abundance could be detected over 5 years, given their very low
abundance at present. Consequently, required survey effort for moose was not calculated.
that CVs of 20% or less should be achievable for all species except moose, by conducting no
more than 500 km of transects each year, in each habitat zone. This figure may appear high.
However, if we assume that sika deer will continue to increase in abundance, then it seems likely
that less effort will be required. As an approximate guideline, 250 to 350 km per year in each
habitat zone should be adequate to detect declines of 10% per annum with 80% probability for
most species, assuming an α level of 0.20. From Fig. 5.3, it is evident that for most scenarios,
increases in total survey effort above this range will bring only incremental improvements in
accuracy and, consequently, will only be necessary to answer questions that demand high levels
of precision. Interestingly, it is common practice for managers of hunting leases in the Russian
Federation to aim for approximately 250 km of representative transects when surveying game
(D.G. Pikunov, pers. comm.). In recent years, the target of 250 to 350 km of transects per year
has been achieved consistently for the oak-birch and Korean pine-deciduous areas, although the
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Analysis of ungulate dynamics
spruce-fir area has frequently dropped below the target. Whether further effort should be invested
in the spruce-fir area depends on the ultimate goals of the ungulate survey.
The incidence of transects producing zero results is another issue that depends on the
ultimate aim of the track surveys. For many statistical purposes, a low incidence of zeros is
desirable. In that case, individual transects of 6 to 10 km should ensure that relatively few zeros
are recorded for most species, although this result is confounded by highly aggregative behaviour
(a problem that survey design cannot overcome). The average length of a transect segment (that
part of a transect within a given habitat type) is currently just over 3 km. Small increases in the
lengths of these could substantially decrease the proportion of zeros for several species.
Unfortunately, required transect lengths are greatly affected by the density of the species
surveyed and for some species (e.g. wild boar in some areas), only very long transect segments
would ensure that zero counts are rarely recorded. Geographic conditions (the spatial extent of
habitat patches) may also limit transect lengths. Finally, efforts to achieve desired survey length
should keep in mind other principles of sampling, such as maintaining dispersion of sample
locations and implementing some level of randomisation in placement of transects.
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Analysis of ungulate dynamics
6. TIGER-PREY RELATIONSHIPS
6.1
Background
A central motivation for this study of the long-term dynamics of ungulates in SAZ was the
importance of ungulates as prey for Amur tigers. In this section, we concentrate on that predatorprey relationship, by assessing the prey requirements of tigers and the potential impact of tigers
on prey. Field data on kill rates and prey preferences from the Amur tiger project are currently
being analysed (Goodrich and Miquelle, unpublished data). These will allow more detailed
analyses of prey requirements and should also permit more precise predictions of the impacts on
different prey species. In this section, however, we restrict ourselves to theoretical predictions of
intake and impact, using published data on the allometry of metabolic rates, and simple modelling
approaches to estimate likely impacts.
There are three principal approaches to estimating the prey requirements of predators.
Although currently unavailable (as discussed above) and difficult to collect, field data on kill rates
provide the best source of data specific to a given system. A second approach uses empiricallybased allometric relationships between body mass and metabolic rate, together with estimates of
assimilation efficiency, to predict the amount of meat that a predator must consume to meet its
daily requirements. Finally, data from similar systems can be used to provide general estimates
of actual kill rates or quantities consumed. Here, we use both of the latter sources to estimate
likely intake rates of Amur tigers.
Estimating the likely impact of large predators on prey is far more complex and
controversial than estimating prey requirements (Eberhardt, 1997, 1998; Eberhardt et al., 2003;
Eberhardt & Peterson, 1999; Messier, 1991, 1994) but is correspondingly more important for
understanding system dynamics and for developing management plans.
The challenge of
predicting predator impacts results from several factors. First, few systems are simple enough to
permit the analysis of the effects of a single predator on a single prey. In particular, human
125
Analysis of ungulate dynamics
exploitation of both predators and (largely ungulate) prey is often a confounding factor (Eberhardt
et al., 2003).
Secondly, and perhaps most importantly, an understanding of the impact of
predation relative to other effects on prey population growth, requires age specific information on
mortality and reproduction, together with information on the status of stressors other than
predation (for example, forage condition, climate and social interactions).
Simpler systems could be assessed through modelling interactions but this can also be
complicated by the fact that carnivorous mammals often show some form of social regulation,
such that territory sizes are rarely a straightforward response to prey availability. For the wolf at
least, Fuller (1989) provided evidence that territories may expand, contract, disappear, or be
established in response to changes in prey availability or distribution, but the rate at which these
changes occur is unclear. Such complexities in the relationship between predator and prey
densities can confound attempts to model the impacts of predators on prey.
In this section, we use two modelling approaches to examine the possible impacts of
tigers on their prey in SAZ. First, we use an energetic balance model that assumes that densities
of tigers and their prey will tend towards long-term equilibria determined by the productivity of
the prey and the numerical response of the tigers. Secondly, we use a simulation model that
permits the inclusion of stochasticity in prey availability. For the reasons detailed above, this
approach requires certain assumptions about the territorial responses of tigers to prey density. For
both methods, we consider a single prey system, using red deer as the primary prey species (due
to their dominance in the tiger diet, Miquelle et al., 1996). However, our results should also be
applicable to a multi-prey-species system.
6.2
Methods
6.2.1
Estimating the requirements of tigers
Energy requirements of tigers were first calculated on the basis of field metabolic rates (FMR),
themselves based on body mass. Approximate mean body masses of Amur tigers were taken
126
Analysis of ungulate dynamics
from field data and were: females, 120kg; males, 180kg. The most comprehensive assessments of
FMR across a range of taxa are those conducted by Nagy and colleagues (1987; 1994; 1999).
Overall for 79 species of mammals, Nagy et al. (1999) estimated the relationship between body
mass (M, in grams) and FMR (in kJday-1) as:
FMR = 4.82 M 0.734
(6.1)
Although sample size was much smaller, Nagy et al. (1999) also estimated the relationship from
data on seven species of Carnivora, as:
FMR = 1.67 M 0.869
(6.2)
To convert these estimates of energy use into estimates of required consumption, it is also
necessary to know the energy content of meat, the typical meat content of prey, and the
assimilation efficiency of predators. Estimates of the energy content of ungulate meat vary (e.g.
7.9MJkg-1, Davison et al. 1978; 5.2MJkg-1, Gorman et al. 1998), as do estimates of assimilation
efficiency by carnivores. We used an intermediate figure of 6.5MJkg-1 and, accounting for a
potential loss in the urine, we used an approximation of 85% utilisation of ungulate meat
(Davison et al., 1978; Gorman et al., 1998; Litvaitis & Mautz, 1976) . We also assumed that 90%
of juvenile (up to 6 months) live weight and 75% of the live weight of older animals (over 6
months) was consumed (e.g. Ackerman et al., 1986; Fuller, 1989; Glowacinski & Profus, 1997;
Hornocker, 1970). Finally, to convert estimates of requirements into an estimate of actual
numbers of animals consumed also requires estimates of the body mass of prey species. Average
masses of ungulates common in the Sikhote-Alin area are given in Table 6.1. Estimates of
consumption rates of wild tigers are also available from the literature (Sunquist et al., 1999) and
we used these for comparison with predictions from allometric relationships (equations 6.1 and
6.2).
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Analysis of ungulate dynamics
Table 6.1
Ungulate body masses
Species
red deer
roe deer
sika deer
wild boar
6.2.2
Mean mass (kg) and (sample size)
males
females
224
43
117
144
(9)
(2)
(5)
(7)
149 (12)
30 (1)
73 (12)
131 (5)
Source
Bromley & Kucherenko (1983)
A. Myslenkov, unpublished data
Bromley & Kucherenko (1983)
Bromley & Kucherenko (1983)
Estimating the impacts of tigers
We used two modelling techniques to estimate potential impacts. For the first of these, we
compared the relationship between prey productivity and prey density, with that between predator
requirements and predator density. These are linked by empirically-based relationships between
predator density and prey density (hereafter, “numerical responses”), permitting the point of
equilibrium to be estimated. Consequently, we termed this the “energy balance” approach. Four
steps are required to construct this model: estimation of the tiger numerical response; estimation
of prey productivity curves; estimation of tiger requirement curves; and comparison of
productivity and requirements, in order to estimate equilibria. As stated previously, the model
was designed using data on red deer, as these are the principle prey of tigers in SAZ.
Data on the tiger numerical response were collated from thirteen field studies of
(primarily Bengal) tigers. It has been suggested that some wild carnivores show Type I (i.e.
linear) numerical responses to prey availability (e.g. wolves, Canis lupus, Eberhardt, 1997;
Eberhardt & Peterson, 1999). However, given the strong territoriality and social intolerance of
tigers (Smith et al., 1987), a Type II (or asymptotic) numerical response may be expected. To
determine which type of response best explained the data, we fitted two different linear (Type I)
responses and two asymptotic (Type II) responses, and compared their explanatory power using
AICc (see Section 3.2.1) and R2. The linear models included an ordinary least squares fit and a
least squares bisector (LSB, e.g. Ricker, 1973). The LSB model may be used where it is
128
Analysis of ungulate dynamics
explicitly acknowledged that both axes (in this case, estimates of prey density and estimates of
tiger density) may be subject to similar levels of error. To obtain an LSB fit, least squares
regression is used to regress each axis on the other (i.e. tiger density on prey density and prey
density on tiger density) and the LSB model is the bisector of these two regressions. The
asymptotic models were two commonly used variants that allow a range of speeds of progression
to the asymptote. These were an inverse curve of the form y = a + b / x and a Michaelis-Menton
curve of the form y = ax / (b + x), where a and b are constants in both cases.
Next, we estimated the relationship between deer density and productivity, allowing for
habitats with a range of carrying capacities (in the absence of predation) of from 2 to 20 km-2.
Demographic parameters for red deer (e.g. Clutton-Brock et al., 1982; Houston, 1982) suggested
an approximate mean population growth rate of r = 0.3 in the absence of density constraints.
Density dependence in large ungulates is typically of a nonlinear or ramped form, with a plateau
of relatively constant growth and a ramp of density dependent decline in growth (Fowler, 1981,
1987; McCullough, 1992). Consequently, density dependence was assumed to act only above a
threshold at 0.6K, where K is the ‘carrying capacity’ of the environment. Beyond that point, we
assumed that mean potential population growth declined linearly from r = 0.3 to r = 0, at K. Due
to the low productivity of the system, we also assessed predator-prey equilibria where maximum
potential population growth of the prey population was r = 0.25. We assumed that an adult
female represents a red deer of approximately typical weight and, therefore, that the production of
1 km-2 red deer raised to adulthood each year would represent biomass production of
approximately 150 kg km-2 y-1; we combined this with predicted growth rates to produce biomass
production curves. As this simple model did not account for gender of tigers, we used the
estimate of daily consumption from Sunquist et al. (1999), in combination with the numerical
response, to determine how tiger off-take would vary with prey density. Clearly, this approach
assumes that the sex ratio remains constant throughout the range of prey densities considered.
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Analysis of ungulate dynamics
For the simulation model, we generated a simple population simulation of red deer
occupying 5,000 km2 of the Russian far East. Prey dynamics were essentially a stochastic version
of those used in the energy balance model, with density dependence acting negatively and linearly
on mean population growth above 0.6 K. Environmental stochasticity was incorporated by
drawing an “environmental condition” parameter from a uniform distribution. The impact of
environmental stochasticity was varied to achieve two scenarios: a moderately stochastic scenario
(population coefficient of variation, CV = 0.15) and a highly stochastic scenario (CV = 0.40).
Parameters used for tigers are summarized in Table 6.2. Predator dynamics were linked to
prey availability through energetic constraints on survival and reproduction. Because estimation
of functional responses is problematic (Marshal & Boutin, 1999), energetic constraints were
modelled using a simple depletion approach (Sutherland, 1996). Specifically, we assumed that
during each time step, tigers could remove all required prey (red deer) from the environment
down to some critical threshold density (below which predation is no longer energetically viable).
Tiger consumption rates were the same as those used for the equilibrium model. Tigers that could
not obtain their requirements during any time step were assumed to die or disperse. Social
tolerance, reproductive behaviour, dispersal behaviour and presence of transient animals were all
modelled on the basis of empirical data (e.g. Kerley et al., 2003, Goodrich, unpubl. data) (see also
Miquelle et al., 2005).
6.3
Results
6.3.1
Requirements of tigers
Energetic requirements were calculated according to the two allometric relationships given in
equations 6.1 and 6.2. Estimates of meat consumption were also taken from Sunquist et al.
(1999). These were converted into estimates of daily kill rates, as shown in Table 6.3. Clearly,
the Sunquist et al. (1999) estimate is approximate, given that it is an estimate for tigers in general,
130
Analysis of ungulate dynamics
Table 1. Life-history parameters used in the tiger-prey simulation model
Parameter
Survival
Maximum age
Background survival rate1
Fecundity and birth
Age at first reproduction
Annual probability of female
reproduction
Mean (± SD) litter size2
Sex ratio at birth (males per offspring)
Value
25
0.95 (females > 1yr)
0.90 (males > 1yr)
0.75 (cubs < 1yr)
Sources
(Danilkin, 1995)
(Kerley et al., 2003)
4 yrs
(Danilkin, 1995; Kerley et al., 2003)
0.553
(Kerley et al., 2003)
2.38 (± 1.15)
0.41
(Danilkin, 1995; Kerley et al., 2003)
(Kerley et al., 2003)
1
Background survival rates reflect mortality from causes other than food limitation. The figures
used were selected to reflect mortality in the absence of anthropogenic causes. Survival rates are
expressed as annual equivalents.
2
Litter sizes in the model were drawn from normal distributions described by these parameters
but were reduced if food was limiting.
3
The territories of male and female tigers are known to overlap. However, it was assumed that
one male could mate with no more than three females in any one year.
and is not broken down by gender. However, it is reassuring that for both genders, that estimate
falls within the range of estimates from the two allometric approaches. Consequently, the two
allometric approaches were used as low and high estimates for each gender. Simplifying the diet
to its three dominant components (which together represent approximately 93% of prey eaten),
equivalent numbers of ungulate prey killed annually were derived from those estimates (Table
6.4). These show that a male tiger may be expected to kill between 14 and 25 red deer annually,
together with 2 to 4 sika deer and 6 to 11 wild boar. A female tiger may be expected to kill
between 10 and 18 red deer, 2 or 3 sika deer and 4 to 8 wild boar annually. Obviously, these
figures are highly approximate and will depend on the relative availability of prey within a tiger’s
range, pregnancy or the presence of cubs and, potentially, on individual differences in prey
preferences. Nevertheless, as an approximate guide to the frequency of kills and potential impact
on prey populations, they are informative. Intermediate values suggest that male tigers should
131
Analysis of ungulate dynamics
kill approximately every 11 or 12 days, whilst solitary females should kill once every 16 to 17
days. Obviously, if a high number of young prey are taken, kill frequencies will be rather higher.
Table 6.3
Estimated daily kill rates by tigers
Estimated
FMR (MJ d-1)
Equivalent
meat at 6.5MJ
kg-1 (kg d-1)
Kill requirement, given 85%
assimilation efficiency and 25%
wastage of carcass (kg d-1)
Basis for estimate
Gender
Nagy et al. (1999)
(all mammals)
Male
34.7
5.3
8.4
Female
Male
25.8
61.6
4.0
9.5
6.2
14.9
Female
Not
specified
43.3
6.7
5.5
10.5
8.7
Nagy et al. (1999)
(Carnivora)
Sunquist et al. (1999)
Table 6.4
Estimated annual predation by tigers
Total killed
annually (kg)
Prey
Species
Scaled proportion of
diet1
Nagy et al. (1999)
(all mammals)
red deer
sika deer
wild boar
0.69
0.05
0.26
2104
164
789
1562
122
586
14
2
6
10
2
4
Nagy et al. (1999)
(Carnivora)
red deer
sika deer
wild boar
0.69
0.05
0.26
3734
292
1400
2625
205
984
25
4
11
18
3
8
Basis for estimate
1
2
Male
tiger
Female
tiger
Approximate
equivalent number of
prey2
Male
Female
tiger
tiger
Represents the relative proportions of each prey type in the diet if no other prey were taken.
Based on female prey masses.
6.3.2
Estimated impacts of tigers
Results of the energy balance model are shown in Fig. 6.1. The poor fit of Type I numerical
response models is evident from Fig. 6.1a. A Type II numerical response model appears more
132
Analysis of ungulate dynamics
likely from Fig 6.2b and this was confirmed by a comparison using AICc and other diagnostics,
which provided the best support for the two asymptotic models and suggested that the MichaelisMenton model was best supported by observed data (Table 6.5). Given the small difference in
the AICc values of the three best-supported models, model averaging (as discussed in Section
4.3.4) could be used to derive predictions of the tiger numerical response. However, owing to the
frequency with which Michaelis-Menton curves can be used to describe natural phenomena, as
well as to the similarities between the average model and the Michaelis-Menton function (P.A.
Stephens, unpublished data), we chose to use the fitted Michaelis-Menton function as our model.
Table 6.5
Comparison of tiger numerical response models
Model
Form
K
AICc
Δi
wi
R2
Least squares linear
LSB
Inverse
Michaelis-Menton
y = ax + b
y = ax + b
y=a+b/x
y = ax / (b + x)
2
2
2
2
-33.21
-30.94
-33.76
-34.66
1.45
3.72
0.90
0.00
0.21
0.07
0.28
0.44
0.333
0.003
0.395
0.484
Fig. 6.1c shows an example of how the energy balance model works. Production and
demand curves are contrasted and, where they meet is assumed to be the predator-prey
equilibrium. This is intuitive as, if the prey population drops below the equilibrium, the predator
population will also reduce, such that production outstrips demand and the system returns to the
equilibrium point. Similarly, should fluctuations take the prey population above the equilibrium,
the predator population would increase, increasing demand, and pressuring the system back
toward equilibrium. Using this approach, we solved equilibria for a range of initial prey carrying
capacities, under two scenarios of prey population growth rate (average maximum growth rate, r
= 0.30 and r = 0.25) (Fig. 6.1d). Predictions are similar and show that the highest reductions in
prey population are likely when prey are relatively scarce. Increasing prey density leads to a
reduction in the impact of tigers, due to the tiger’s Type II numerical response (a likely result of
133
Analysis of ungulate dynamics
social constraints on tiger density, rather than constraints of prey availability). If we assume
(very approximately) that prey densities in the more productive areas of SAZ are currently in the
order of 1000 kg km-2 (equivalent in biomass terms to approximately 6 to 7 red deer km-2), then
the results of the equilibrium model suggest that, in the absence of tiger predation, prey biomass
could be closer to 1200 to 1350 kg km-2.
The results of the simulation model of tiger predation are shown in Fig. 6.2. Using
existing estimates of prey biomass and tiger density, we derived territory size of tigers based on
the assumption that each territory of an adult resident tigress contains 3.3 tigers (a female, a third
of a male, 1-3 cubs or a young daughter; and one transient) (Fig. 6.2a). Using the predicted
territory sizes, simulation models of predation suggested that the proportion by which prey
populations were reduced below K by tigers was typically in the range of 18-25% and never
exceeded 30% (Fig. 6.2b). Tiger impact on prey decreased with higher prey density due to
constraints on tiger density imposed by territoriality (see Fig. 6.2a), except when stochasticity
was high. In this case, tigers were better able to limit prey when initial prey abundance was high,
as this reduced the possibility of prey becoming so scarce that tigers could not hunt effectively.
6.4
Discussion
Estimating the impact of large mammalian predators on prey is a problematic and contentious
issue (Eberhardt et al., 2003; Messier, 1994; Van Ballenberghe & Ballard, 1994). Our analyses
have illustrated a number of the complexities involved in such analyses but, nevertheless, have
provided a number of useful and informative results. Among these are estimates of the likely
number of kills made by individual tigers, an examination of the tiger’s type of numerical
response, together with fitting of explanatory models, and estimation of the likely effect of tiger
predation on prey populations.
134
Analysis of ungulate dynamics
Tiger density (km-2)
0.20
(a)
(a)
C
A
0.15
B
0.10
0.05
0.00
0
2000
4000
6000
8000
Prey density (kg km-2)
Tiger density (km-2)
0.20
(b)
(b)
0.15
0.10
0.05
0.00
0
2000
4000
6000
8000
Prey density (kg km-2)
Production or
requirements (kg km-2)
200
(c)
(c)
B
100
A
0
-100
0
1
2
3
4
5
0.40
Proportional reduction
below carrying capacity
6
Deer density (km-2)
0.30
(d)
(d)
A
0.20
B
0.10
0.00
0
2
4
6
8
10
12
14
16
18
20
Deer carrying capacity in the absence of predation (km-2)
Figure 6.1.
The energy balance model: (a) Tiger numerical response (A, regression of tiger
density on prey density; B, regression of prey density on tiger density; C, least squares bisector;
open circles show empirical data); (b) Michaelis-Menton fit to tiger numerical response;
(c) sample production (A) and requirement (B) curves when deer carrying capacity K = 5 km-2;
(d) predicted impact of tiger predation on prey population size, as a function of prey carrying
capacity in the absence of predation (A, deer maximum population growth, r = 0.25; B, r = 0.3).
See text for further details.
135
Analysis of ungulate dynamics
600
(a)
Territory size (km2)
500
400
300
200
100
0
0
1000
2000
3000
4000
5000
6000
7000
8000
Prey biomass density (kg km-2)
0.50
Proportion by which population is
reduced by tiger predation
(b)
0.40
0.30
C
B
0.20
A
0.10
0.00
0
1
2
3
4
5
6
7
8
9
10
-2
Red deer carrying capacity in the absence of predation (km )
Figure 6.2.
Tiger-prey simulation models: (a) Empirically derived relationship between
territory size and prey availability (based on 3.3 tigers per territory). Territory Area,
A = 22270 B–0.7764, F11 = 42.5, p < 0.001. (b) predicted impact of tiger predation on prey
population size, as a function of prey carrying capacity in the absence of predation (A, no
environmental stochasticity; B, moderate stochasticity (prey population coefficient of variation,
CV = 0.15); C, high stochasticity (CV = 0.35)).
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Analysis of ungulate dynamics
Our estimates of the annual kill rate of tigers are quite varied (Table 6.3), owing to
substantial differences in the two allometric predictions of FMR given by Nagy et al. (1999).
Given the estimates of intake rate from Sunquist et al. (1999), it seems likely that kill rates will be
towards the low end of our predictions (Table 6.4), and that Nagy et al.’s (1999) allometric
relationship based on carnivores rather over-estimates the requirements of tigers. This could be
due to the low sample size available for predicting the allometry of carnivore requirements but,
also, could arise because at least two of the larger Carnivora assessed by Nagy et al. (1999), are
wolves and African wild dogs (Lycaon pictus). We have speculated elsewhere (Miquelle et al.,
2005) that in contrast to tigers, social, cursorial hunters have very much higher than expected
energy requirements. This seems to fit with available evidence on the intake rates (Gorman et al.,
1998) and densities (Carbone & Gittleman, 2002) of social, cursorial carnivores, and may explain
why Nagy et al.’s (1999) allometric relationship for energy requirements leads to over-estimates
for tigers. It will be useful to compare our estimates to field data on kill rates, when these are
available. Should it be possible to parameterise matrix models of population growth for other
prey species in SAZ, our estimates will also permit a more detailed investigation of the likely
impact of tiger predation on individual species.
Our analysis of the tiger numerical response provides strong evidence of a Type II form,
presumably owing to regulation by social constraints when prey densities are higher, rather than
prey availability. The two asymptotic models examined were evidently better supported than
simpler, Type I models and, the complexities of estimating the underlying data notwithstanding,
the Michaelis-Menton model provided a surprisingly good fit to the data (R2 = 0.48).
The precise predictions of the models of tiger impact on prey populations are sensitive to
a number of underlying assumptions, including the potential growth rate of the prey population,
the variation in territory size with prey availability, and the nature of stochasticity experienced by
the prey population. Nevertheless, the two methods both predicted that within the range of
densities seen in SAZ, it is likely that tiger predation could be reducing prey populations by about
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Analysis of ungulate dynamics
20 to 30% below their expected size in the absence of predation. This impact is substantially
lower than has been estimated for other carnivores, especially for wolves (Eberhardt et al., 2003;
Miquelle et al., 2005; Van Ballenberghe & Ballard, 1994). That all of our modelled scenarios
suggested that tiger impacts would be reduced at higher prey densities accords with estimates
from the high ungulate biomass systems of the Indian subcontinent, where off-take has been
estimated at less than 10% (Schaller, 1967; Stoen & Wegge, 1996). In particular, our energy
balance model, which predicted 10% depletion when K = 20 km-2 deer (equivalent to a prey
biomass density of 3000kg km-2), is in close agreement with these estimates.
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Analysis of ungulate dynamics
7. GENERAL DISCUSSION
Our study was driven by three principal motivations: (i) the importance of gaining accurate
knowledge regarding densities of ungulates in SAZ and the utility of the survey protocol; (ii) the
broader contribution that our analyses can make to the field of estimating animal population
density from indirect sign; and (iii) the importance of understanding ungulate dynamics in SAZ,
in order to inform management of the Amur tiger. We divided our approach into five interrelated objectives and we have presented each, with an associated discussion, in the previous
sections. Our aim in this section is to bring together our main findings in light of these three
original motivations, and provide some specific recommendations for continued monitoring of
ungulates in SAZ.
7.1
Ungulate densities and the utility of the survey protocol
In Section 3, we provided support for the extensive work already existing in Russian literature
that, by comparison to other approaches, the FMP equation represents an easily applied and
accurate method for translating track encounter rates into estimates of density. An advantage of
our work is the use of a non-parametric bootstrapping method to generate confidence intervals
about density estimates derived using the FMP. Given reliable data on track encounter rates and
suitable, accurate estimates of daily travel distances, ungulate densities (with appropriate
confidence intervals) can be identified fairly accurately.
Two questions arise from this
investigation: how reliable are the underlying data (and, hence, how accurate are our mean
estimates) and how can the ranges be narrowed (giving greater precision of estimates)?
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Analysis of ungulate dynamics
7.1.1
Accuracy of data
Considering the issue of accuracy, two lines of evidence give us confidence in the quality of the
underlying data. First, fieldworkers must differentiate recent tracks from tracks over 24 hours old
– a classification certain to have some error. However, comparisons of fieldworker estimates of
tracks made in the last 24 hours, with counts made of tracks known to have been made on the
same day (which can be differentiated with a much higher level of accuracy) show high
correlations (Miquelle and Aramilev unpubl.). Second, accurate density estimates depend on
whether survey routes are representative of the survey area. Again, our analyses of different
approaches to post-stratification of the data (see Sections 3.2.4 and 3.3.2) provide indications that
the coverage provided by survey routes within SAZ is indeed highly representative. In particular,
although small numbers of data points can be affected by the type of stratification used
(encouraging the use of relatively broad scale and strictly objective stratification approaches), the
majority of data points are unaffected, regardless of whether the data are unstratified, or are
stratified by drainage basin or forest formation (see Fig. 3.3). This suggests that survey routes
within each drainage or forest type are generally in proportion to their area.
In spite of the foregoing observations, there remain many ways in which the accuracy of
mean estimates can be improved. Here, we focus on four important issues.
Independent validation of ungulate densities. Independent validation of density estimates
is essential if we are to have real confidence in the track count approach. Therefore, it is
necessary to collect data by some other method, in order to generate independent estimates of
density. In Section 1.1 we referred briefly to some of the problems involved with alternative
methods of censusing ungulates in SAZ. However, both aerial counts (Myslenkov & Voloshina,
2005) and direct observation combined with distance sampling (Zaumyslova, 2005) have been
used in SAZ. Aerial counts, combined with development of a sightability model (which requires
capture and marking individuals of each of the key ungulate species) (Samuel et al., 1987) would
provide an expensive but effective approach for validation of the track count method. Training
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Analysis of ungulate dynamics
forest guards and scientific staff of the reserve to collect distance sampling data could also
provide a means of verification for the WTC data in those areas where patrols are regular and
scientific investigations are conducted (i.e., where adequate sampling is possible). Although
these suggested methods need not be conducted regularly (data from a very few years would
probably be sufficient to indicate the accuracy of the WTC), in the years when they were
conducted, all would require a considerable increase in the manpower devoted to surveying. This
is unavoidable.
Representative surveys and bias reduction. A second issue affecting data quality is the
placement of survey routes and, in particular, whether routes are representative of the distribution
of habitats within SAZ. Ideally, survey design would include randomly placed transects to
estimate ungulate densities. Clearly the existing transect system is largely confined to more
accessible areas at lower altitude and in valley bottoms, thus raising the question of bias in survey
results. Our comparisons of different types of stratification provide support for the representative
layout of survey routes, but only in relation to the total area directly surveyed by those routes.
Whether these routes are representative of SAZ as a whole, could be determined in two ways.
First, GIS could be used to assess whether certain landscape features and habitats are over- or
under-represented in surveys. Under-represented features could then be surveyed to determine
whether they support very different ungulate densities to those in surveyed areas, thus revealing
whether survey route placement is a source of bias. A second approach would compare density
estimates from the current survey routes to estimates derived from similar levels of survey effort
along randomised transects. Either test for bias need be conducted for only a few years in order
to give an indication of the quality of current WTC practices. However, tests would require a
substantial increase in resources dedicated to surveying during those years. Whether that is
worthwhile, strongly depends on the purpose of surveying within the Zapovednik. If surveys are
designed to generate accurate estimates of ungulate abundance then additional effort, aimed at
reducing bias by surveying under-represented areas, is likely to be important.
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Analysis of ungulate dynamics
Improved estimates of ungulate daily travel distances. A third, related issue, provides an
alternative to the use of randomised transects. If density estimates are to be derived using the
FMP formula, as we suggest, then increasing the precision of density estimates (even when used
as a relative measure between years) depends on the availability of good estimates of 24-hour
movement data for each species. Gathering additional data on animal movements will have two
benefits. First, it will permit an improved understanding of the relationship between animal
movements and environmental conditions (including habitat, snow depth, time of year, mast crop,
etc.). As we discussed in Section 3, this is extremely important for generating good estimates of
density, whether absolute or relative (among habitats or years). Without a large library of travel
distances from different conditions, it will be extremely difficult to identify relationships between
environmental factors and movement distances. Collecting movement data using telemetry in a
variety of areas within SAZ could have further benefits. In particular, analysing mapped data on
animal movements may allow estimation of the relative use of different areas and habitat types
among species. This will have important implications for the stratification of survey effort and
will provide an alternative to conducting large numbers of randomised survey routes, through
potentially difficult terrain.
Dealing with multiple track crossings (“nabrods”).
A fourth issue affecting both
accuracy and precision of density estimates is that of multiple crossings, where tracks are so
confused that fieldworkers have been unable to discern the number of animals that have made
them.
These instances are recorded as “nabrods”.
Although only about 2% of all track
encounters are nabrods, for highly grouped species (such as wild boar and sika deer) these may
account for 10% or more of animal tracks. To convert track data into estimates of animal
abundance, either relative or absolute, it is essential that these records of “nabrod” be converted to
some value.
Consequently, interpretation of these records will significantly affect density
estimates and their accuracy. In this study, we converted data based on estimates of average
group size for each species. However, we believe that accuracy could be greatly increased if
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Analysis of ungulate dynamics
fieldworkers made the extra effort to record actual values instead of simply “nabrod.” We
recommend that fieldworkers on winter transects follow a protocol of going around nabrods in
ever increasing circles until they are able to derive an estimate of animal number. Although there
will be error in such estimates, the error is less than an estimate based on mean group size.
Therefore, in future surveys, we recommend that fieldworkers be trained in reporting track
number to the best of their ability, to avoid all records of nabrods.
7.1.2
Precision of estimates
The second major aspect of the survey protocol that was considered in this study is that of
precision. The survey effort required to increase precision is the explicit focus of Section 5. In
that section we showed that, for the more abundant species, current levels of survey effort (in
terms of kilometres surveyed per year) are sufficient to detect declines of 10% per year with 80%
probability, assuming an α level of 0.20 and five years of decline. For less abundant species, it is
unlikely that accurate data could be obtained. However, here we consider two ways that the other
species could be surveyed more precisely, so that smaller trends could be detected more easily.
Habitat zones and stratification. Throughout this study, we have followed the existing
system of classifying SAZ into three broad habitat zones and typically performing analyses for
each zone separately. There is some evidence, however, that substantial differences exist within
different parts of the oak-birch zone, and that this zone might reasonably be further divided. In
particular, Figs. 2.1 and 2.2 suggest that the four coastal oak-birch drainages (Abrek,
Blagodatnoe, Khuntami and Inokov) differ substantially from the three inland oak-birch drainages
(Lianovaya, Kuruma and Kunaleyka), with the former dominated by oak forests, whilst
birch/aspen forests predominate in the latter. For most of the ungulates, analyses of encounter
rates within these drainage basins do not show clear differences between the two sets of
drainages. However, sika deer show a marked tendency to aggregate in the coastal drainages, and
other species show similar, though subtler, differences. It is likely that, in the future, a four zone
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Analysis of ungulate dynamics
system of analysis would be more informative for interpreting the survey data. Should this
zoning system be implemented for survey purposes, it may be that further stratification of survey
data by drainage basin will become unnecessary, thereby obviating the complications that this
additional step introduces to data analysis. Emerging methods which combine survey data with
habitat variables to develop associations between density and habitat type also promise to
improve understanding of variance and, potentially, to increase precision. We recommend that
the relevance of these methods (e.g. Hedley & Buckland, 2004) to SAZ should be considered.
Appropriate survey effort. In Russia, there is a tendency to think of sampling effort in
terms of percentage of the area sampled. Biologists often refer to the 10% rule in sampling,
which suggests that sampling 10% of the study area is usually adequate. In this report, we do not
comment on what proportion of the area is sampled but, instead, consider only the absolute
number of kilometres surveyed.
There are two reasons for this.
First, determining what
proportion of an area is surveyed by counting tracks along 1 km of transect is far from
straightforward, requiring an estimate of perpendicular movement of animals relative to the
survey line. This will vary among species and between different environmental conditions
(depending on how these affect movement). Consequently, surveying 10% of an area will require
different amounts of total survey effort depending on the species studied, habitat traversed and
time of year. As a result, it is often easier to talk about survey effort in terms of the objective
measure of kilometres travelled. Secondly, when it is possible to determine the kilometres of
survey route required to survey 10% of an area, it does not automatically follow that this is an
adequate level of survey effort.
The abundance of the species and its spatial distribution
(clumped or not) both significantly influence the adequacy of a survey. Most important, however,
adequacy depends on the goals of the survey and can only be determined if the questions to be
answered by the survey are clearly established at the outset.
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Analysis of ungulate dynamics
7.2
Estimating animal density from sign
In Section 1.1, we discussed the importance of methods to estimate densities of animals indirectly
from their sign. As we noted there, a very wide array of methods for estimating densities from
sign is available but the field remains highly contentious (e.g. Carbone et al., 2001; Carbone et
al., 2002; Jennelle et al., 2002; Sadlier et al., 2004; Webbon et al., 2004). Two problems are
common to many approaches to estimating abundance from sign. These include the difficulties of
quantifying variance in estimates and, commonly, a lack of calibration of the relationship between
sign abundance and animal abundance. Our study can provide improvements in both areas. First,
the FMP formula has, hitherto, been little known outside Russia and we have found no instances
of similar methods being applied within the English-language ecological literature. Our talk at
the Society for Conservation Biology international conference in New York, August 2004,
generated considerable interest in the FMP formula, together with a recognition of its application
to other methods based on randomised encounters (particularly that of camera trapping). In many
wildlife studies, data on animal movements are collected in addition to attempts to estimate
abundance. When such data are available, the FMP formula presents a further method by which
densities may be estimated, providing the opportunity for checking density estimates against
those produced by an alternative method. The emphasis that we place on using nonparametric
bootstrapping to generate confidence intervals from transect data is also important for many
studies in which estimates of density are made from multiple samples. Most formal methods for
estimating the variance associated with density estimates rely on parametric methods which, in
turn, rely on tractable distributions and relatively large sample sizes (e.g. Buckland et al., 1993).
In practice, many wildlife studies, especially those of species occurring at low density, generate
data which meet neither of those requirements. In these cases, as in our study, the use of
nonparametric bootstrapping is likely to be invaluable for quantifying error.
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Analysis of ungulate dynamics
7.3
Ungulate dynamics and tiger conservation
The third major motivation for this study was the importance of understanding ungulate dynamics
in SAZ, and their relation to Amur tigers. Our analyses have shown that, by comparison with
other parts of the geographic range of tigers, SAZ (and, by extension, the Russian Far East) has
extremely low densities of prey, highlighting the vital importance of protecting existing prey
populations. Moreover, whilst the ungulates of SAZ have tended to increase over the course of
the monitoring period reported here, recent years have seen disturbing evidence of a downturn,
especially for red deer and wild boar, the two key prey species of the tiger (Fig. 4.6). The reasons
for this decline are unclear but the evidence suggests that predation by tigers is not a primary
factor driving these changes. For the red deer, several lines of evidence developed in the
preceding chapters suggest that warmer temperatures and recent increases in numbers of sika deer
may be leading to reduced numbers of red deer in the coastal basins and increases in the sprucefir zone. Given (i) the tiger’s evident adaptability to different prey complexes throughout its
range (Sunquist et al., 1999), and (ii) the dominance of sika deer in Lazovski Zapovednik, where
tigers are present at densities at least as high as SAZ, the potential for a gradual replacement of
red deer by sika deer in SAZ is cause for limited concern (at least, from the perspective of tiger
prey availability). The apparent decline of wild boar is more disturbing. Given that our results
indicate the tigers limit at least some prey species to a much lesser extent than other carnivores,
and that there is no evidence that tigers regulate prey numbers, it is important to consider the
other factors that are impacting prey numbers. For instance, the temporal analyses suggest that
the decline in wild boar numbers may be associated with reduced efficacy of protection within
SAZ.
Hence, changes in management approaches to reduce impacts of humans in the
Zapovednik (and specifically to reduce poaching) may result in positive responses of prey
populations.
It is perhaps disappointing that our time-series analyses (Section 4) did not provide a
clearer picture of the factors driving the dynamics of each species. As we noted there, however,
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Analysis of ungulate dynamics
our analyses are the first of their kind for this system and our findings must, as a result, be viewed
as preliminary. There is considerable opportunity for studying each species in more detail (for
example, assessing the role of nonlinear interactions with variables) but whether this will produce
greater insights into the dynamics of species is currently unclear. One limitation on the type of
time-series analyses we used is the need for accurate data on population densities. We have
discussed methods by which accuracy may be improved but, again, whether implementing those
methods is worthwhile depends on the goals of the monitoring programme.
Clearly, if
informative analysis of the dynamics of individual species is a stated goal of the monitoring
programme, then improving accuracy of density estimates must become a key aim of developing
the WTC protocol.
More broadly, our work on ungulate dynamics leads to questions on the goals and design
of the Zapovednik system. Most of the species studied showed evidence of the importance of
climatic factors affecting their dynamics. In keeping with global trends, a warming trend is
visible even from a cursory look at Fig. 4.3 g,i. Changing temperatures will have impacts on
many species that SAZ currently protects, and may already be having an impact on some of the
species studied in this report (red deer, sika deer and moose). Protected area networks that
function within a context of shifting wildlife distributions will be of considerable importance if
current trends accelerate.
Finally, it is also clear that a fixed system of monitoring will provide much more detailed
information on relatively common species, whilst even the detection of trends among rarer
species can be difficult, given limited resources and manpower. Clearly, if conserving those rarer
species is an important aspect of Zapovednik policy, management systems must be in place to
identify and prioritise species of concern, diverting resources towards their study where
necessary.
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Analysis of ungulate dynamics
7.4
Specific recommendations
Our work has suggested a variety of improvements that could be made to the monitoring work
conducted in SAZ. The goals of monitoring within the Zapovednik system are not for us to
designate. However, we suggest goals and make recommendations that we believe will better
define and enhance the ungulate monitoring conducted in SAZ.

Review strategies for protecting ungulates. Ungulates are at very low densities in SAZ
relative to other systems across Asia that support tigers. There is some evidence of
declining ungulate densities in recent years and this may be linked to the level of
protection that they receive. It is essential to safeguard and enhance these remaining prey
populations, in order to promote the stability of the tiger population.

Use a four-zone classification of SAZ for ungulate monitoring. As discussed elsewhere,
these zones would include the coastal zone (dominated by oak forests), the inner-coastal
zone (dominated by birch-aspen forests), the central zone (dominated by Korean pinedeciduous forests) and the montane zone (dominated by spruce-fir forests).

Define an overall goal for monitoring ungulates. This should specify whether monitoring
will produce only an index of relative abundance, or estimates of absolute abundance
also. It should also specify the units of interest (both species and zones) and whether
trend detection is important. If trend detection is important, the magnitude of trends and
the time periods over which these should be detected must also be defined. As an
example, we suggest that the goal be defined as follows: Ungulate monitoring in SAZ will
provide estimates of the absolute abundance in winter of ungulates in the four major
habitat zones. At least 1000 km of surveys will be conducted annually, distributed
equally over the four zones. The aim of this will be to give the maximum power to detect
trends in numbers of the more abundant species in the habitats most important to that
species.
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Analysis of ungulate dynamics

Recognise limitations and adapt to priorities and changing conditions. It is vital that the
limitations of the monitoring be recognised including, in particular, that density estimates
are associated with considerable uncertainty, and that species at lower abundance, with
shorter daily travel distances and with highly clumped behaviour will be subject to
greater uncertainty, such that trends are harder to detect with confidence. The monitoring
protocol should also be adaptable to changing priorities and to changes in conditions
(such as increasing or decreasing densities of certain species) . This adaptability may
require a core monitoring program to assure the integrity of a long-term data base,
alongside sampling that is more flexible in response to recognised monitoring needs.

Validate the relationships between track counts and density estimates. Independent
estimates of density must be generated using alternative methods, in order to indicate
how accurately density is estimated by current methodologies.
Field data for an
independent estimate of density would be collected for a limited number of years to
achieve validation but not become part of the long-term monitoring work. In particular,
we recommend the use of distance sampling or aerial surveys combined with the
development of sightability models.

Assess bias in transect network. Assess bias in the transect network using GIS analyses
of survey route placement and by comparing results of randomly placed transects to the
existing network within a number of basins of the reserve. If a significant bias is
detected, there are two alternatives to address this bias: (i) if the bias is stable and
predictable across all areas and all conditions, apply a simple correction factor; (ii) if the
bias is not stable and is difficult or impossible to predict, relocate transects to
approximate a random sampling effort.

Improve data base on daily travel distances. Daily travel distances must be collected for
each species during the time frame in which surveys are conducted, as there is evidence
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Analysis of ungulate dynamics
that travel distance drops in late winter (Sections 3 and 4). Data on travel distances must
also be collected across the range of environmental parameters that are likely to affect
movements.

Collect data on the numbers of animals that made each set of tracks encountered. To
collect data not only on the number of sets of tracks of each species encountered on
transects but, also, on the number of these that were made by single animals or groups of
various sizes, is likely to be awkward, especially from the point of view of data storage.
Nonetheless, our analyses showed that size of the travelling group may be important in
dictating the travel distance of some species. Consequently, collecting such data will be
helpful for improving the accuracy of density estimates. The data could also be useful for
determining group size distributions, which will have important implications for error
calculations and other aspects of understanding demography of the studied species.

Eliminate the recording of “nabrods“. Eliminate records of “nabrod” in SABZ the data
set by training all observers to circle nabrods and report actual numbers of tracks to the
best of their ability.
7.5
Concluding remarks
In conclusion, this has been an extremely beneficial collaboration between all four organisations
involved. The exchange of ideas and integration of scientific literatures that has resulted is an
important outcome that is easy to overlook. Using the data from SAZ to develop a new approach
to detecting density dependence in time-series of ecological data, and propagating the use of the
FMP formula outside Russia have been two developments of substantial significance. Despite the
intensity, consistency and rigour with which WTC data have been collected in SAZ, our analyses
were often limited by the quality of the underlying data. Analyses cannot improve the data
retrospectively and there is no substitute for increased intensity of survey effort (and expense) for
accurately estimating the densities of species within an area. However, whether such increases in
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Analysis of ungulate dynamics
effort and expense are necessary depends critically on the goals of the Zapovednik monitoring
programme.
It is vital that these goals are clearly defined, in order that resources can be
allocated, and surveys designed, accordingly.
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Analysis of ungulate dynamics
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