Estimating demographic parameters from limited data:
life history of the endangered greater horseshoe bat
(the title may be changed after the outcome of the analysis…)
Michael Schaub1,3, Olivier Gimenez4, Antoine Sierro2,3, & Raphaël Arlettaz1,2,3
1. Zoological Institute – Conservation Biology, University of Bern,
Baltzerstrasse 6, CH–3012 Bern, Switzerland
2. Valais Bat Conservation Group, Nature Centre, CH–3970 Salgesch,
Switzerland
3. Swiss Ornithological Institute, CH–6204 Sempach, Switzerland
4. CEFE/CNRS, 1919 Route de Mende, F–34293 Montpellier Cedex 5, France
Running title: Population dynamics of greater horsheshoe bats
xx words (from abstract through to literature, inclusive)
Correspondence author:
Michael Schaub
Zoological Institute – Conservation Biology
University of Bern
Baltzerstrasse 6
CH–3012 Bern
Switzerland
Fax: +41 31 631 31 63
E-mail: michael.schaub@nat.unibe.ch
Abstract
1.
2. Synthesis and applications.
Abstract = words
Key words: Alps, Species conservation, integrated population model.
Introduction
In the face of the rapid global biodiversity loss, the declining-population
paradigm has become a central issue in conservation biology (Caughley). Its aim
is to identify reasons why a specific population is declining. There are several
possible approaches to identify reasons of population decline, the most popular
one is the demographic analysis (Norris). Central for a demographic analysis is
the estimation of demographic parameters (survival, reproduction, immigration,
emigration) and the exploration of the relationship between the variation of
these parameters and the variation of the population growth rate. This requires
that the strength of impact of a demographic rate on the population growth rate
is assessed by a sensitivity analysis (van Groenendeal). In a next step one has
then to identify by which factors those demographic parameters that are most
relevant for the variation of the population growth rate have been impacted.
Bats are declining globally (REF??), but very few detailed demographic
analyses have been performed so far. Even single demographic parameters are
poorly studied, as exemplified by a lack of estimates of survival rates obtained
with reliable statistical methods (exception are Sendor, Pryde, weitere?).
Population dynamics of bats is difficult to study for a number of reasons. The
most popular methods to assess whether a population is changing, is the count
of individuals that emerge from a nursery colony. Such colonies mostly consist of
reproducing females, but a fraction of males and non reproducing females are
often also present (REF). Because flying bats cannot be sexed and aged, their
fraction is unknown. If these fractions change over time, the count of bats
emerging at the roost do not reflect exclusively population changes.
Unfortunately, it is not possible to know whether the fraction has changed over
time. Another difficulty is the estimation of the fecundity. Fecundity is defined as
the number of offspring that is produced each year per adult female. In most bat
species females give birth to one offspring only per year, but most do not
reproduce each year (REF). Females that skip a breeding event are often not at
the nursery colony (REF), and thus the ratio of the count of the newborn to the
count of adult females present at the colony is not a reliable estimate of
fecundity. Furthermore, catching of bats and marking them is not popular
anymore, because catching may disturb them and ringing can cause injury at the
FLUGHAUT (Raphael: hier müssen noch eine Reihe von Zitaten eingesetzt
3
warden). Because basic demographic information is lacking for many bat species,
it is difficult to target conservation actions for them.
The recently developed integrated population models are new tools to the
conservationist toolbox that are likely to prove useful for bat demographic
monitoring. Such models have been applied so far to birds (Besbeas . Brooks)
and seals (Thompson). They combine the population census and demographic
data in a single model allowing estimating demographic parameters. Because the
population census contains also information about all demographic parameters of
the population under study, the estimates of the demographic parameters
become significantly more precise (Besbeas). Thus, there is the hope that such
models could be used to estimate demographic parameters, also if there are only
few demographic data available. However, the model needs to be adapted in
such a way that they account for the fact that not only one population segment
(e.g. adult females) is censused, but a combination from different segments.
The greater horseshoe bat (Rhinolophus ferrumequinum) is one of the
most threatened bat species of Central and Western Europe (REF). In
Switzerland it is red-listed (REF), with only two known relictual colonies, one in
eastern Switzerland (Graubünden), one in south western Switzerland (Valais).
Greater horseshoe bats gather in summer in large colonies for offspring rearing.
Studies from populations at the margin of the species distribution range in Great
Britain have shown that females start with reproduction at an age of 2 or 3
years, that mortality rate during the first year of life is 47%, that mortality of
adult females is in the range of 9-14%, and that the breeding frequency is about
0.9 (Ransome 1991, 1995). Moreover, Ransome (1989) suggest that population
dynamics is mainly driven by the variation of offspring production, which itself is
related to weather condition in spring. Yet, the estimates and conclusion of these
studies relies on the untested assumption that the fate of each bat is know with
certainty.
Our aims of this paper are fourfold. First, we demonstrate the flexibility
and power of integrated population models to estimate demographic parameters
from sparse data from a colony of greater horseshoe bats. This provides us with
basic information about the demography of this endangered species. Second, we
tested whether the demographic parameters had trends over time and estimated
the rate of change of the study population. This allowed us to identify roughly
whether a gradual change of a demographic parameter has resulted in a
4
population change, and to evaluate the current state of the very population.
Third, we calculated population growth rate elasticities (Ehrlen and van
Groenendael 1998) and generation time in order to identify how the population
could potentially be regulated. Fourth, we compare the rate of population change
obtained from the counts alone with the estimate from the population model and
discuss how the integrated population model can be used to conduct a
demographic monitoring of bats.
OLD PARTS OF INTRODUCTION
While such a demographic analysis is a powerful tool, it is difficult to apply
for many species because detailed demographic data are not available for them.
Even worse, data insufficiency is particularly frequent in declining or rare species
(Beissinger 2002), thus for species which have the highest conservation priority.
Data insufficiency for an endangered species may result from two reasons. First,
because of the rareness of the species the sample size is naturally low, and
second, to avoid the possible negative impact due to disturbance, researchers
hesitate to catch and mark individuals of endangered species, a prerequisite to
obtain most demographic data. Typically, knowledge about the development of
the population size is quite well known, but only few longitudinal data of
individuals (demographic data) are available. This is because population census
can be carried out without disturbing the animals, whereas this is usually not
true for obtaining longitudinal data. In such a situation, it is crucial to make most
efficient use of all available data.
Small populations of organisms are particularly vulnerable to extinction because
they potentially cumulate several handicaps such as genetic depression or risks
inherent to demographic stochasticity (REFS). Populations of endangered species
are often properly monitored, at least in the western world, with information on
demographic trend and reproductive output frequently available. Yet, under most
circumstances, conservationists ignore almost everything about the actual
population dynamic mechanisms beyond the observed trend and reproductive
output. For instance, a population can be stable but have an insufficient intrinsic
reproductive rate so as to compensate for mortality: only immigration ensures its
long-term survival. On the other hand a population can show signs of overall
5
decline but still function as a net exporter of recruits to other populations, for
instance when habitat alteration reduces local carrying capacity at population
range periphery but not within unaffected rich central habitat patches. The
metapopulation theory provides a conceptual framework to this kind of question:
is a population functioning as a source or as a sink, i.e. does it export more
recruits than it «needs», or, alternatively, does it «consume» more recruits than
it can produce (e.g. Hanski 1998, REFS)? Metapopulation models apply when the
fate of individuals within a given population is known. The emergence of more
and more sophisticated methods for analysing capture-recapture and sightingresighting datasets facilitates the unraveling of vital parameters such as local
recruitement, immigration vs permanent emigration, with the latter being
especially difficult to separate from mortality (REFS). These techniques are
becoming essential tools in modern conservation biology (REFS).
We show here how the combination of monitoring data on population size and
yearly reproductive output, coupled with a mark-recapture modelling, may lead
to identifying crucial demographic parameters for diagnosing the vitality of a
small population of the critically endangered Greater horseshoe bat (Rhinolophus
ferrumequinum).
Data and methods
Data sampling
We studied the greater horseshoe bat colony located in the attics of a XIIth
century Chapel (Vex; 46°XXN, 09°XXE). This colony is the only known in the
whole Valais (ODER give distance to the next known colony). This population was
discovered in 1988, just prior to the renovation of the building (1989-90) which
could be planned in compliance with the requirements for colony preservation
(Arlettaz, unpublished). With the exception of two years, we censused from 1986
onwards in every year the number of individuals emerging from the roost at
dusk, prior to the onset of parturition. During the first weeks after parturition,
visits to the attics after the emergence of subadult and adult bats – when young
were left unattended – enabled counting and ringing every freshly born cohort
since 1991 (260 newborns ringed in total). This way, adults were never disturbed
at the colony roost. In 2004 and 2005, short before parturition, which
corresponds to the period when the census were carried out and when the
6
population peaks (Ransome XX, own unpublished data), we captured, on one
single day and at daylight, the whole population present in the attics after
blocking the main flight entrance. Ring number, sex and physiological status of
the bats (n2004 = 54, n2005 = 52) were recorded. This massive capture had
implications neither on the number of bats eventually returning to the roost on
the following days nor on the number of newborns: indeed, 2004 and 2005
yielded an unequalled number of offspring. Because the ringing of the new born
bats stated in 1991 only, we considered for our analysis the period from 1991 to
2005, although in the year 1991 no population census was carried out.
Integrated population model
We model population dynamics of the greater horseshoe bat using an integrated
population model (Besbeas et al. 2002), which describes the system with two
linked processes: the state process and the observation process. The state
process describes the true, but unknown, state of the population at different
times and the observation process links the state of the population to the
observed part of the population during the surveys. The state process is
described by different demographic parameters (survival, fecundity), which is
estimated each with a separate probabilistic model. We use Bayesian methods to
fit this model. Bayesian integrated population models applied to animal
populations is a rather novel development (Buckland et al. 2004; Brooks, King,
and Morgan 2004; Maunder 2004; Thomas et al. 2005; Thompson, Lonergan,
and Duck 2005).
We start describing the model with the state process. We define four
different states (1 year females, adult females, 1 year males, adult males) and
monitor the individuals in each state prior to birth in each year. The transition
probabilities from state x in year t to state y in year t+1 is described by a
projection matrix that is parameterised with the demographic rates survival and
fecundity and with the sex ratio at birth. We assume that annual survival rate
during the first year of life is different from annual survival later, and that the
latter does not change anymore with age. Because most individuals do not start
to reproduce in their first year of life (Ransome 1990), we constructed a model
with 2 different age classes: individuals aged 1 year (subadults) and individuals
that are older than 1 year (adults). We assumed that all females start to
7
reproduce when they are 2 years old. We included both sexes in the model,
which finally looks like
 0
 N 1f 
 f
 f
 N a    a ,t
 0
 N 1m 

 m
 N a  t 1  0
sf t 1,ft
0
 af,t
0
(1  s ) f 
m
t 1,t
0
0
 am,t
0   N 1f 
 

0   N af 
0   N 1m 
 

 am,t  t  N am  t
(1),
where N xk ,t is the number of individuals of sex k in age class x in year t,  x,k t is
the annual local survival rate from year t to year t+1 of individuals of sex k and
age class x, f t is the number of offspring produced per adult female ( N af,t ) in
year t, and s t is the proportion of newborn females among all newborn in year t.
Superscripts m and f denote male and female, respectively, subscript 1 denotes
the first age class, subscript a the adult age class and t the year. Because the
model shall be stochastic, we describe the population change of each segment of
the population with Poisson and Binomial models. Specifically we model the
number of individuals in the first age class in year t+1 with Poisson models, by
N1f,t 1 ~ PoN af,t st f t1f  for females and by
N1m,t 1 ~ PoN am,t 1  st  f t1m  for males.
The number of adults in year t+1 is modelled with Binomial models, as
N af,t 1 ~ Bin N af,t  N1f,t ,af,t  for females and by
N am,t 1 ~ Bin N am,t  N1m,t ,am,t  for males.
Likelihood for estimation of local survival rates
The model contains demographic parameters that are estimated from capturerecapture data and from year- and sex-specific numbers of newborn. To estimate
local survival from individual capture-recapture data (u), we used the CormackJolly-Seber (CJS) model (Lebreton et al. 1992). The frequency of individual
encounter histories follows a multinomial distribution with the two parameters
local survival (  x,Kt ) and recapture ( p xK,t ) probability. The formulation of the
likelihood of this model is straightforward and described in many papers
(Lebreton, Burnham, Clobert, and Anderson 1992), and we renounce to repeat
8
this here. As we only have recaptures from the last two years, we fixed the
recapture probabilities for all but the last two years to zero.
Likelihood for estimation of fecundity
We counted in each year the number of newborn individuals of each sex. The
sex-specific number of newborn ( J k ) follows a Poisson distribution and depends
on the number of adult females and the sex-specific fecundity rates ( f k ). Thus,
the number of newborn males in year t is,
J tM ~ Po( N af,t f t m ) ,
and the number if newborn females in year t is,
J t f ~ Po( N af,t f t f ) .
It is straightforward to calculate the overall fecundity rate ( f t ) and the
proportion of newborn females among all newborn ( s t ) from the sex-specific


fecundity rates as f t  f t m  f t f , and st  f t f / f t m  f t f .
The observation process
Our population census (counts of all bats leaving the roost) consists of
individuals from all four states, but with unequal proportions. From bat ecology
we know that all reproducing females and a variable fraction of males and nonreproducing females is present at nursery colonies. However, because flying bats
cannot be aged and sexed, we could not attribute them to the four states. Still,
to include these counts into the population model, we should know the
proportion of the four states, and we proceeded as follows to estimate them.
First we note that the recapture probability that we estimate with the CJS model
is composed of two parts, the probability that a bat is recaptured given presence
in the colony, and the probability to be present in the colony (Schaub et al.
2004). This is strictly true, if the probability to be present is random. Because we
captured all bats that were in the colony at time of capture, the true recapture
probability had been 1. Under the assumption that the probability to be present
at the colony was random, the estimated recapture rate (from the CJS model) is
equal to the probability to be in the colony. Because we only had such estimates
for each state from the last two years, we calculated the geometric mean of the
two values and considered these mean values to be the same over the complete
9
duration of the study. Specifically, the probability that an individual of age x and
sex k was present in the colony is calculated as  xk 
p xk, 2004 p xk, 2005 .
The population census in year t ( y t ) was then modelled with a Normal
distribution as,
yt ~ N ( 1f N1f,t   af N af,t   1m N1m,t   am N am,t , y2 ) ,
where the variance  y2 describes the census error.
The integrated model
The joint likelihood of this model is the production of the likelihood of each part.
The different model fragments (likelihoods for survival, fecundity, census) have
parameters in common, as illustrated graphically be the directed acyclic graph
(Fig. 1).
Olivier: est-ce que tu pourrais ecrire quelques phrases sur l’intégration (e.g.
comme en Brooks et al. 2004, p 518). Mais je ne suis pas sur s’il est vraiment
necessaire.
The strength of the integrated population model is that each model fragment
borrows information from other model fragments, resulting in higher precision of
parameter estimates and allowing to estimate otherwise inestimable parameters.
Candidate models, prior distributions and derived parameters
We were interested to test, whether survival and/or fecundity rates have
changed gradually over time. Thus, we take
logit xk,t    xk   xk year , and
log  f t k    k   k year ,
where year is a continuous variable. Furthermore, we included models in which
survival was not sex-specific, and we applied models where these demographic
rates were constant (  xk and/or  k set to 0). We used different combinations
resulting in a set of 15 candidate models. Included is also a more general model
with time-dependent parameters. We used the deviance information criterion
(DIC, (Spiegelhalter et al. 2002)) to rank these models according to their support
by the data.
10
Because a priori knowledge about demographic parameters in the greater
horseshoe bat is very limited, we choose uninformative priors for all parameters
we intend to estimate. Specifically, we used vague normal priors (N(0,1000)) for
the regression parameters (, , , ), vague beta priors ((1,1)) for the
recapture rates, and vague normal priors truncated to positive values for the
initial state-specific population sizes (N(10,10000) for N1k,1 , and N(20,10000) for
N ak,1 ).
Goodness-of-fit: Olivier: est-ce qu’il y a quelque chose ?
To calculate the posterior distributions of the parameters of interest, we used
Markov Chain Monte Carlo (MCMC) simulations implemented in program
WinBUGS (Spiegelhalter, Thomas, and Best 2004). Initial trials showed that
convergence occurred fast (after about 5000 iterations) as evidenced by the
Brooks – Rubin – Gelman diagnostics (Brooks and Gelman 1998). For the main
analysis we therefore run the MCMC algorithm for 1’100’000 iterations, discarded
the first 100’000 iterations as burn-in and thinned the remainder to one in every
tenth iteration. With this conservative approach we obtained stable results.
We calculated some derived parameters to characterise the population. The
annual growth rate t was calculated as the ratio of the number of adult females
in year t to the number of adult females in year t+1. The averaged population
growth rate over the study period was calculated as the geometric mean of all
year-specific values. The size of the complete population prior to birth is the sum
of all the member of the four states in that year. [evtl. Braucht es nicht ein
eigenes Kapitel, kann auch direct in die Resultate einfliessen.]
Elasticity analysis
Using the estimated demographic parameters, we constructed a female-based
matrix projection model. This model is identical to the model shown in eq (1),
except that only the females are considered. We applied the methods outlined in
detail in Caswell (2001) to calculate from this matrix the lower level population
growth rate elasticities and the generation time. These calculated we performed
with the software ULM (Legendre).
11
Results
The number of individuals that we counted each year increased over time from
27 in the year 1992 to 59 in the year 2005 and the number of newborn increased
from 11 in year 1991 to 32 in year 2005 (Fig. 2).
Model selection revealed that the simplest model with survival and
fecundity rates that are constant across time and no sex-dependence in survival
rates had the strongest support (Table 1). However, the difference in DIC to the
next best candidate models was small, and thus there remains considerable
uncertainty about the structure of the best model. The models which were
closest to the most parsimonious one contained sex effects on survival and a
linear trend in fecundity.
The estimated demographic rates show that the greater horseshoe bat is a
long-lived species with average adult survival higher than 0.9 (Table 2). The
fecundity rate was rather low with about 70% of all adult females that reproduce
in a season. The sex ratio of the newborn was slightly skewed to the females, but
the skew was not significantly different from an even sex ratio (the 95% credible
interval contains 0.5, Table 2). As expected, the proportion of individuals that
were present at the roost was lowest in adult males and highest in adult females.
The proportion of first year males that were present at the colony was lower than
that of first year females, but the difference was not significantly different
(overlapping credible intervals, Table 2).
All estimated demographic parameters of males had larger standard
deviations than the corresponding parameters of females (Table 2). This was also
apparent for the sex-specific first year survival rates from the second best
model: the standard deviation for the males (0.145) was twice as large as the
standard deviation of the females (0.071) although the means were almost
identical (males: 0.512, females: 0.500).
The estimated population sizes of the four states were increasing over time
(Fig. 3). The estimates of the adult males were again rather imprecise, reflecting
the small amount of information in our data about adult males. The number of
first year males in the first study year was also badly estimated, yet it is difficult
to know why this occurred (Olivier: as-tu une idée?). We calculated the size of
12
the total population, i.e. the sum of adult and first year males and females. The
size of the complete population increased from 78 individuals (SD: 25) in the
year 1992 to 96 individuals (SD: 14) in the year 2005. The estimated size of the
population in the year 1992 is not very reliable, because the number of adult
males is overestimated at the beginning of the study (Fig. 3). If we consider that
the number of adult males is the same as the number of adult females (this can
reasonable be assumed because there was no difference in survival between the
sexes), then the whole population would have increased from 47 to 93
individuals between 1992 and 2005.
The mean annual population growth rate calculated as the geometric mean
of the year-specific population growth rates of the adult females indicated
positive population growth (1.051, SD: 0.015, 95% credible interval: 1.023 –
1.082). The annual population growth rates varied between 0.998 (SD: 0.079)
and 1.092 (SD: 0.073). The mean population growth rate obtained by the counts
was higher (1.062), and the variation between years was larger (Fig. 4).
The generation time (mean age of mothers at child birth) was 9.49 years,
indicating again that the greater horseshoe bat is a long-lived species. As can be
expected for a long-lived species, the population growth rate elasticities were
largest for adult survival, and lowest for first year survival (Table 2). Thus,
population growth rate is much more affected by the same relative change of
adult survival, than by the same change of fecundity or sex ratio, and even less
by the same change in juvenile survival.
Discussion
The integrated population model applied to a sparse and complicated data set of
an endangered bat species has proven to be suitable to estimate demographic
rates, to estimate the size of the population and to conduct some tests regarding
the variation of these demographic rates. We found that the greater horseshoe
bat colony at Vex is increasing by about 5% each year, that the species is longlived with an adult survival rate of about 90% and that females reproduce
successfully in about 2 out of 3 years.
Integrated population models are very flexible tools that can be adapted to
a variety of sampling situations. The advantage of this framework is that it allows
modelling of biological plausible population processes and estimation of key
biological parameters, while at the same time explicitly recognizing the
13
uncertainties involved in the data collection (Thomas et al. 2004). Critical is of
course that the biological processes are well captured in the model. The most
critical part in our model was the assumption that the temporary emigration was
random (i.e. the probability to be present at the colony is independent on
whether the bat has been present one year before). This assumption was
necessary to be able to use the recapture probabilities as indication of presence
of the different population states. As non-reproducing females are often not
present at the colony and reproduction is likely to have costs (REF), it is possible
that temporary absence at the colony depends on the reproductive success in the
previous year, and is thus a first order Markov process. If at least four years with
recapture data would have been available, it would be possible to test whether
temporary emigration is random and to obtain better estimates thereof (Schaub
et al. 2004). Another assumption that we had to make refers to the age of first
reproduction. We assumed two years, while we know from the literature that
some individuals of this species reproduced for the first time only when they
were three or more years old (Ransome 1995). We constructed a modified model
in which we assumed that all individuals start to reproduce when three years old
only, but this model was clearly worse than the best one (DIC = 28.96).
Certainly the age of first reproduction is not the same in all individuals, and a
more realistic model would include a parameter that estimates the age-specific
proportion of first time breeders. Such a model, was however, unrealistic with
our data, but if more recapture events were carried out, this would become an
option.
The estimates of the demographic parameters and the population sizes
were more precise for females, than for males. This reflects that fact that our
data contain much less information about the males than about the females.
Indeed, most adult males do not occur at the nursery colony, thus they are
neither included in the population census nor in the recapture data. The
imprecise estimates of the male parameters also prevented the detection of
possible sex-specific differences. We would have expected the local survival rates
of the juvenile males to be lower than that of the females, because of male
biased dispersal in mammals (REF). We expect the precision of the male
estimates and the power to detect sex-specific differences to increase when
monitoring is continued.
14
The estimated survival rates of greater horseshoe bats are similar to the
ad hoc estimates given by Ransome (1991). Reliable estimates of survival rates
in other bat species are scarce: in most species adult survival is in the range
between 0.6 and 0.8 (Sendor and Simon 2003, Pryde et al. , own. unbub. data
WEITERE REF). It has been recognized a long time ago that bats are relatively
long-lived compared to other mammals of the same size (REF). Within the
groups of bats, there exists different life-histories, and likely there is also a cline
from relatively short-lived to relatively long-lived species, as found in other
groups
of
vertebrates
(Saether
and
Bakke
2001).
Although
the
basic
demographic information of many other bat species must be known to conclude
anything, we believe that the greater horseshoe bat is at the long-lived end of
this continuum. This is also exemplified by the long live span of single
individuals: we recaptured an individual in 2005 that was marked as adult in year
1983, thus it was at least 23 years old. Ransome (1995) reported a female that
was 29 years old.
Comparison of fecundity is difficult because again this estimate is lacking
in many studies. Ransome (1995) got higher estimates 0.9, than we had.
Ransome (1995) estimated fecundity in a different way, he calculated the ratio of
females that had signs of reproduction to all females captured. Yet, if nonreproducing females do not use the roost where captures are carried out, this
estimate is biased high.
[Raphael: is there any other literature that provide
estimates of fecundity? ]. Fecundity in bats is difficult to estimate precisely, we
think that the integrated population models offer a promising avenue. The key
feature of the integrated population to estimate fecundity is that it can estimate
the size of the female population, being often different than the counts. Yet, the
estimate is still rather imprecise in our model.
We have found no trends in the demographic rates over time. Yet, models
in which adult survival and in particular fecundity were changing gradually, were
not very far from the best model. In both of these models the parameters were
increasing slightly over time. A possible increase of fecundity may be due to
better thermoregulatory condition in the attic after the installation of an artificial
heating and with increasing colony size. However, the limits of using sparse data
is again that fine patterns are difficult to grasp.
15
Elasticity – long lived species – what can we expect for population dynamics?
(see findings in other studies on long-lived individuals)
Future monitoring – counts must be close
Extensive sampling with low disturbance possible (e.g. capture not every year:
expense: some things cannot be tested, evaluated (as above)).
Generalities
juv. Survival in the range of the others
-
“extensive” monitoring to not disturb the animals. With IPM it
-
is possible to estimate the demographic parameters and to understand the
population functions. It could be used as monitoring.
The data samples need to be independent, this was here the
-
case, because we used two different data sampling techniques.
Yet, in our case, it is doubtful whether this will improve our
-
system. This is because the bats only have one small entrance hole to the
church, and the sight to this hole is perfect. Thus, we can reasonable
assume that are count are very close to a perfect one. Yet, in other
situations, this may be an option, and including different sub-model into
the integrated population model is straightforward in the Bayesian
context.
-
Why did the population increase?
-
Possible emigration? At the time there is just the possibility to
compare
our
results
with
those
from
Ransome
to
infer
possible
emigration.
-
First study on bats  promising approach to estimate
fecundity (which is difficult in bats)
-
Difficult is also that the composition of bats that we see (use
for monitoring) is unknown. Here, we can estimate them.
-
What ever is chosen for the males (a priori), it had no impact
on the female parameters. The female parameters is not sensitive to prior
16
choices, this is different in males. More data on males would be necessary
to adequately estimate the male parameters.
-
Probability to be present: based on the counts or on the
captures alone we would not have been able to estimate that, only the
fraction of ad males among all bats that are present, but not the fraction
of all ad males among all ad males
-
Evtl. Size of the superpopulation: not sure whether this is an
important estimate, but it may be interesting.
-
This is a very-longlived mammal: compare with survival
estimates of other mammals.
-
Further extensions: multiple age classes for survival and
recapture rates – needs more recapture events
-
Consequences: what can we expect reagreding the population
dynamics (long-lived species).
Acknowledgements
We thank first the local authorities who provided free access to the bat roost, in
particular the community and parish of Vex. The Conservation Service of the
State of Valais as well as the Federal Environment Office funded the restauration
of a bat friendly church.
17
Table 1. Modelling results of different integrated population models of greater
horseshoe bats from the Vex colony (1991-2005). The model parameters are the
age-specific survival rates ( 1 : juveniles, a : adults) and fecundity rate (f). The
other parameters in the models, the state-specific populations sizes and the
recapture rates, were in all models time- and sex-specific. The notation (T) refers
to a linear time trend of the specific parameter, (t) to year-specific rates, (s)
refers to sex specific rates, and (.) denotes constancy. Given are the model
deviance, the model complexity (pD), and the difference of the deviance
information criterion between the best and the current model. Models are ranked
according to their support by the data, the best supported model being at the
top.
Model
Deviance
pD
DIC
1 (.), a (.), f (.)
320.19
24.81
0.00
1 ( s), a (.), f (.)
320.74
25.37
1.10
1 (.), a (.), f (T )
320.78
25.54
1.30
1 (.), a ( s), f (.)
320.84
25.54
1.37
1 (.), a (T ), f (.)
321.06
25.80
1.86
1 (.), a (s), f (T )
321.37
26.53
2.89
1 (T ), a (.), f (.)
320.97
27.13
3.09
1 ( s), a ( s), f (.)
321.63
26.56
3.18
1 (.), a (T ), f (T )
321.55
26.72
3.26
1 ( s), a (.), f (T )
321.58
26.80
3.37
1 (T ), a (T ), f (.)
321.70
27.51
4.20
1 (T ), a (.), f (T )
321.56
28.05
4.61
1 ( s), a ( s), f (T )
322.25
27.67
4.91
1 (T ), a (T ), f (T )
322.45
28.82
6.26
1 (t ), a (t ), f (t )
271.44
728.99
655.42
18
Table 2. Posterior mean, standard deviation (SD) and limits of the 95% credible
intervals (lower, upper) of the parameters estimated with the most parsimonious
model ( 1 (.), a (.), f (.) ), and population growth rate elasticities of the demographic
parameters.
Estimates
Mean
SD
Lower
Upper
Elasticity
Juvenile survival ( 1 )
0.491
0.063
0.375
0.622
0.0189
Adult survival (  a )
0.909
0.020
0.868
0.945
0.8709
Fecundity ( f )
0.692
0.114
0.513
0.956
0.1291
Proportion of newborn females ( s )
0.540
0.032
0.477
0.600
0.1291
Presence of first year females (  1f )
0.821
0.105
0.576
0.973
-
Presence of adult females (  af )
0.919
0.042
0.822
0.981
-
Presence of first year males (  1m )
0.673
0.140
0.390
0.925
-
Presence of adult males (  am )
0.278
0.092
0.129
0.487
-
Census variance (  2 )
25.44
15.75
7.96
65.49
-
19
Fig. 1. Directed acyclic graph (DAG) of the model used in this paper.
Parameters to be estimated are represented by circles, the data by
rectangles. Arrows represent dependences between nodes. To simplify the
graph, the four states are represented by one node N. Node notations: u:
capture-recapture data, y: census data, Jm: number of male newborn, Jf:
number of female newborn, s: sex ratio at birth, f: fecundity rate, : local
survival rates (different sex and age classes), p: recapture rate (different
sex and age classes), N: population size, 2: variance of the census.
20
Fig. 2 Yearly population counts (census) of greater horseshoe bats at
emergence of the roost in Vex (in 1991 and 2001 no census was carried
out) and the total number of newborn in each year.
21
Fig. 3. Posterior distribution of the three main demographic parameters
juvenile survival rate, adult survival rate and fecundity.
22
Fig. 4. Estimated population size of greater horseshoe bat colony in Vex
stratified according to sexes and age classes. The bars are the posterior
mean and the vertical lines represent the limits of the 95% credible
intervals.
23
Fig. 5. Annual population growth rates estimated with the raw counts
(counts) and with the integrated population model (IP model). The point
from the IP model are posterior means, the vertical lines show the limits
of the 95% credible interval.
24
Fig. 4. Density plots of the demographic parameters based on the best
model.  Perhaps to be shown in an appendix
25
Appendix
- evt. BUGS code
-
Density plots of all estimated quantities
-
26
Literature Cited (not full yet)
Beissinger S. R. 2002. Population viability analysis: past, present, future. Pages 5-17 in SR
Beissinger, editor. Population Viability Analysis. The University of Chicago Press, Chicago.
Ref Type: Book Chapter
Besbeas P., S. N. Freeman, B. J. T. Morgan, and E. A. Catchpole. 2002. Integrating markrecapture-recovery and census data to estimate animal abundance and demographic
parameters. Biometrics, 58:540-547.
Ref Type: Journal
Brooks, S. P. and Gelman, A. Alternative methods for monitoring convergence of iterative
simulations. Journal of Computational and Graphical Statistics 7, 434-455. 1998.
Ref Type: Journal (Full)
Brooks S. P., R. King, and B. J. T. Morgan. 2004. A Bayesian approach to combining animal
abundance and demographic data. Animal Biodiversity and Conservation, 27.1:515-529.
Ref Type: Journal
Buckland S. T., K. B. Newman, L. Thomas, and N. B. Koesters. 2004. State-space models for
the dynamics of wild animal populations. Ecological Modelling, 171:157-175.
Ref Type: Journal
Ehrlen J. and J. van Groenendael. 1998. Direct perturbation analysis for better conservation.
Conservation Biology, 12:470-474.
Ref Type: Journal
Lebreton J. D., K. P. Burnham, J. Clobert, and D. R. Anderson. 1992. Modeling survival and
testing biological hypothesis using marked animals: a unified approach with case studies.
Ecological Monographs, 62:67-118.
Ref Type: Journal
Maunder M. N. 2004. Population viability analysis based on combining Bayesian, integrated,
and hierarchical analyses. Acta Oecologica, 26:85-94.
Ref Type: Journal
Pryde M. A., C. F. J. O'Donnell, and R. Barker. 2005. Factors influencing survival and longterm population viability of New Zealand long-tailed bats (Chalinolobus tuberculatus):
27
Implications for conservation. Biological Conservation, 126:175-185.
Ref Type: Journal
Royle J. A. 2004. N-mixture models for estimating population size from spatially replicated
counts. Biometrics, 60:108-115.
Ref Type: Journal
Schaub M., O. Gimenez, B. R. Schmidt, and R. Pradel. 2004. Estimating survival and
temporary emigration in the multistate capture-recapture framework. Ecology, 85:2107-2113.
Ref Type: Journal
Sendor T. and M. Simon. 2003. Population dynamics of the pipistrelle bat: effects of sex, age
and winter weather on seasonal survival. Journal of Animal Ecology, 72:308-320.
Ref Type: Journal
Spiegelhalter, D., Thomas, A., and Best, N. G. WinBUGS User Manual, Version 1.4. [1.4.].
2004. Cambridge, MCR Biostatistics Unit.
Ref Type: Computer Program
Spiegelhalter D. J., N. G. Best, B. P. Carlin, and A. van der Linde. 2002. Bayesian measure of
model complexity and fit. Journal of The Royal Statistical Society Series B, 64:583-639.
Ref Type: Journal
Thomas, L., Buckland, S. T., Newman, K. B., and Harwood, J. A unified framework for
modelling wildlife population dynamics. Australian and New Zealand Journal of Statistics
47[1], 19-34. 2005.
Ref Type: Journal (Full)
Thompson D., M. Lonergan, and C. Duck. 2005. Population dynamics of harbour seals Phoca
vitulina in England: monitoring growth and catastrophic declines. Journal of Applied
Ecology, 42:638-648.
Ref Type: Journal
28