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NCEAS WORKING GROUP REPORT
DYNAMICS OF LARGE MAMMALIAN HERBIVORES IN CHANGING ENVIRONMENTS:
ALTERNATIVE MODELLING APPROACHES
FIRST MEETING HELD AT NCEAS IN SANTA BARBARA, 11-23 NOVEMBER 2001
Thirteen members of the Herbivore Dynamics group participated in this first meeting, while five people
were unable to attend for various reasons. Although the meeting had originally been scheduled to span 14
days, most people were only able to attend for between 6 and 10 days.
The first three days involved presentations of our individual motivations for attending, and expectations
of the outcomes and products to be achieved. The final product could be a set of papers, a book, or a
research proposal, but no decision was reached at this stage. There were specific presentations on
alternative modelling approaches (Owen-Smith) and on formal model selection procedures (Hobbs).
Much discussion was generated, consolidating the shared vision and exciting prospects ahead. Outlines of
specific datasets were also presented, most notably the Kruger Park census records encompassing 11 or
more species in some spatio-temporal detail. Sub-sections were established to work on (1) climatic
influences on population time series, (2) effects of spatial heterogeneity and environmental context on
population stability, and (3) demographic processes. The conveners are Lundberg for climate and Hobbs
for space. Section 3 was subdivided between a segment relating dynamics to body mass as an aggregate
measure of resources (convenor - Illius), and one concerned with life history and demographic structure
(convenor - Coulson). This provisional subgrouping is open to anarchic interventions and interchanges
between groups.
Agreement was also reached on the shared database design. The templates for data format and detailed
instructions for entry can be found in the Data Instructions folder at the NCEAS website location
established for our group. Data assembled according to these instructions is to be sent initially to Gross,
who will serve as the data manager. He will check the entries for any problematic features before lodging
them at the website. Hobbs will assist by handling local weather data. The template for the weather data is
likewise at the website. Kendall will serve as the overall webmaster. Anything to be posted on the website
should be sent to him.
A proposal to NCEAS requesting support for a postdoctoral fellow affiliated to the herbivore group has
been drafted, and will be submitted following comments and further input from group members. Notably,
Per Lundberg will take up a sabbatical fellowship at NCEAS from September 2002, for a year, and will
help guide the work of the postdoc. The 2002 meeting has provisionally been scheduled for 12-22
November, encompassing 10 working days.. This period is a compromise among those participants who
have time constraints earlier, and those who have later constraints during December, and will be
confirmed after consultation.
The rapport developed and shared enthusiasm was a memorable feature of this first meeting. We recall
fondly the range of delightful restaurants in Santa Barbara, and the wine-tasting opportunities too briefly
sampled on our one afternoon away from computer screens. Specific achievements and directions
established by the sub-sections were as follows:
Climate
The time has passed when population ecology was concerned with purely deterministic dynamics and the
corresponding models. Both theory and data now show that a deeper understanding of population and
community processes can only be achieved if environmental variability is explicitly included in both
‘mechanistic’ and ‘statistical models’, i.e., in the theoretical toolbox as well as in the interpretation of
data. Also, the observed and predicted large-scale climatic changes challenge ecologists as to how we
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may understand the responses of different ecosystem components to those changes. Population responses
to environmental variability act at two (not mutually exclusive) levels. First, the short-term responses to
weather variability (and corresponding changes in trophic structure of the community in which the
population of concern is embedded) are manifested by changes population growth rate and increased or
decreased population fluctuations. Second, climatic changes may change both short-term population
growth rate, but also long-term population abundance and distribution, either directly or through changes
in resources, predators or habitat.
This group’s first attempt has been to characterize the dynamics of a set of large herbivore species
across different environments. Some initial data sets available to the working group have been analyzed
by applying basic system identification and time series tools. System identification allows us to build
mathematical models of dynamic systems based on measured data. We have identified the lag structure of
both a set of both temperate and tropical species, and estimated the direct and lagged influence of one
common environmental variable (rainfall) on the rate of change of those populations. The lag structure
identification also allows us to determine the stability properties of the populations analyzed. As a first
step, we applied (log-) linear autoregressive techniques. This will be extended by non-linear response
surface analyses. Various model selection criteria were used to evaluate the competing models. A
summary outline of these preliminary findings has been lodged at the website.
The continuation of this work will include 1) refined model selection procedures in order to
characterize the dynamics of large herbivores across environments and taxa, 2) identification of the
environmental (weather) variables most strongly influencing the dynamics, 3) building models to forecast
changes in population fluctuations and abundance under various climate change scenarios.
The system identification will be crucial to analyses of how spatial structure of the environment and how
stage structure of the populations influence the dynamics of large herbivores. Therefore, the work of the
three sub-sections is necessarily intertwined.
Space
The interplay between spatial and temporal heterogeneity in shaping the trajectories of large herbivore
populations was addressed, and the following key questions and activities identified.
1) Spatial heterogeneity mollifies the effects of temporal variability on large herbivore population
dynamics. Variation in space creates alternatives for large herbivores. Animals can choose
among these alternatives during periods of resource scarcity and, in so doing, they are able to
moderate the effects of diminished resource supply. Examples of this kind of effect include
topographically induced spatial variation in plant phenology in temperate and tropical systems.
This idea leads to the predictions shown in Figure 1 (appended).
2) Spatial heterogeneity enhances the performance of large herbivore populations. We expect a
positive relationship between large herbivore biomass density (e.g, kg/km2) and rainfall amount.
Some of the residuals in this regression can be explained by measures of spatial heterogeneity
(Figure 2).
3) The biomass density of large herbivore populations adjusted for effects of aboveground net
primary production (ANPP) will be positively related to size of conservation areas and/or
measures of their spatial heterogeneity (Figure 3).
4) Mobility increases the range of habitat area that animals can exploit. As a result, the ability to
migrate should increase the spatial heterogeneity experienced by large herbivores. This increase,
in turn, will dampen the effects of temporal heterogeneity on population growth rates.
A database structure was identified that will be populated with population data, climate data, and
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spatial data to test question 1-2, while a database on conservation areas in Africa will address
question 3. Data on migratory and non-migratory populations of the same species in East Africa will
address prediction 4.
Demography - mass
Two important influences on consumer-resource dynamics are intra-specific competition for food
and environmental variability. Both of these can cause variation in food intake by herbivores, and so
affect the rate and direction of change in population size. Intra-specific competition is usually
indexed by population density, but this is an inaccurate representation of per capita food supply
because environmental variability causes appreciable variability in primary production, much of
which is independent of herbivore population density. It would be preferable, therefore, to identify a
variable that more closely matches per capita food intake. We chose to examine whether juvenile or
yearling body mass, being directly related to food intake, would serve to overcome this deficiency.
Annual variation in lamb and yearling body mass in bighorn sheep was found to explain much more
variation in reproductive performance than could density. In addition, yearling mass appears able to
capture both direct and delayed effects of changes in population density on recruitment. Similar,
though less striking, results were found for two other closely-studied species, Soay sheep and
mountain goats. We anticipate that this approach will allow us to separate more clearly in other
herbivore species the effects of climate and inter-specific competition on food intake. Because data
on juvenile and yearling mass are often available for harvested populations, our approach can have
immediate applications in wildlife management.
Demography - life history
Two objectives were identified.
1) Quantifying the impact of a range of age structures on the dynamics of populations
Studies of marked individuals from ungulate populations have crudely identified a potentially strong
influence of fluctuating age structure on population dynamics. The age structure can fluctuate
independently of total population size. We will identify the influence of age structure on dynamics,
using matrix methods.
Most previous examination of age structures using matrix models has assumed that the population is
at the stable age structure. For ungulate populations this is rarely the case. However, the age
structure may be an important component of population dynamics, because individuals in different
age categories can respond to density and climatic variation in contrasting ways. The relative
influence of age structure on the dynamics of populations compared to density-dependent and independent processes may vary as a function of life history trait values of a species (longevity, age
at first breeding, rate of twinning) and of the ecosystem in which the species is embedded (predation
/ no predation, temperate / tropical).
We will use methods that allow us to estimate how a range of age structures affects lambda. The
method is analytical and is based on work by Caswell (2001) and Fox and Gurevich (2000). The
methods estimate the sensitivities of matrix elements for a given age structure. The impact of the
matrix element on lambda can be identified by multiplying the sensitivities by standard deviation of
the matrix element. These methods have not previously applied to any animal populations.
We will represent our results by plotting the impact of each vital rate on lambda across a range of
age structures. As the age structure of a population is systematically varied, we may observe a
systematic change in the influence of each vital rate on the population growth rate.
To meet our objective we need a transition matrix consisting of the mean values of each vital rate,
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and a matrix of the standard deviations of the vital rates. The matrices will contain recruitment and
survival functions of yearlings, prime-aged adults and senescent adults. We currently have matrices
from approximately 10 studies and plan to add another 10 studies.
2) Exploring how selection on morphometric, phenotypic or genetic traits varies with lambda
We will do this by extending the methods of van Tienderen (2000) to non-stable age structures,
which will entail estimating sensitivities of vital rates for each year of a time series, via the
construction of a transition matrix. Using regression methods, we will identify the association
between variation in a trait (e.g. birth date) and each matrix element. For example, we would
explore the association between birth date and calf-yearling survival using logistic regression. These
functional relationships can be combined with sensitivities through the use of elastograms to identify
selection on each trait. If we are able to identify fluctuating selection pressures (that are correlated
with density-dependent or -independent processes) this would identify an ecological mechanism for
maintaining additive genetic variation within populations. This second objective requires detailed
data both on vital rates and on trait values. We currently have four populations that we could apply
these methods to, and are currently trying to identify further systems. The MATLAB code that is
being developed for objective 1 will be modified to allow us to address objective 2.
Database establishment
A basic product generated by the group is a database of herbivore population dynamics that will
facilitate broad-scale comparisons across species or environments. Group members agreed to
contribute the datasets to which they had access, subject to the stipulation that the database only be
accessible to group members and only for shared activities within the group. Where there was
multiple ownership of data, agreements would need to be negotiated before the data could appear in
publications.
The database will initially be set up in Excel, and then transferred to a relational database. Full
instructions for entering data will be circulated to all members, and also posted at the group website.
John Gross will be the database manager, assisted by Stephen Cox from NCEAS. John will initially
receive and pre-process all data using SAS code that will identify obvious errors and omissions,
before transferring the data to Stephen to archive.
The database that is being contributed by various group members will potentially encompass more
than 100 species/location datasets. Additional ungulate population data could potentially be obtained
from publications or government agencies or collaborators.
Report compiled by Norman Owen-Smith
2001-11-21
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Figure 1. Predictions made by spatial heterogeneity hypothesis. The leftmost panel shows that population trajectories are
grouped into categories of high and low spatial heterogeneity should show divergence in the effects of temporal
heterogeneity (x-axis) on population growth rate (y-axis). In particular, high spatial heterogeneity should allow higher
growth rates at a given level of temporal heterogeneity. The right two panels show that we expect that residual variation in
population growth rates should be explained by variation in normalized difference vegetation index data representing
heterogeneity in vegetation.
2)
Figure 3. We expect that biomass density will increase as
the size of conservation areas increases and as measures of
their spatial heterogeneity increase (e.g., the CV on NDVI,
the number of clustered NDVI patches.
Figure 2. We expect a positive relationship between
measures of the spatial heterogeneity and the
residuals of the relationship between biomass density
and average rainfall.
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