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Plenary Address - 3:50-4:30 PM
Hierarchical mark-recapture models: A framework for inference about
demographic processes
Bill Link & Richard Barker
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The development of sophisticated mark-recapture models over the last four
decades has
provided fundamental tools for the study of wildlife populations, allowing
reliable inference about
population sizes and demographic rates based on clearly formulated models for
the sampling
processes. Mark-recapture models are now routinely described by large numbers
of parameters. These
large models provide the next challenge to wildlife modelers: the extraction
of signal from noise in
collections of parameters.
Pattern among parameters can be described by strong, deterministic relations
(as in
ultrastructural models) but is more flexibly and credibly modeled using
weaker, stochastic relations.
Trend in survival rates is not likely to be manifest by a sequence of values
falling precisely on a given
parametric curve; rather, if we could somehow know the true values, we might
anticipate a regression
relation between parameters and explanatory variables, in which true value =
signal plus noise.
Hierarchical models provide the appropriate framework for inference about
collections of
related parameters. Instead of regarding parameters as fixed but unknown
quantities, we regard them
as realizations of stochastic processes governed by hyperparameters. Inference
about demographic
processes is based on investigation of these hyperparameters.
We describe analysis of capture-recapture data from an open population based
on hierarchical
extensions of the Cormack-Jolly-Seber model. In addition to recaptures of
marked animals, we model
first captures of animals and losses on capture, allowing estimation of
survival and birth rates. We
present analyses for covariation between survival and birth rates. For
example, years that are poor for
survival may also be poor years for reproduction. In this case we would expect
the survival parameters
and birth rate parameters to be related.
The hierarchical approach that we describe provides the framework needed for
exploiting
structural relationships between parameters, improving individual estimates by
considering the
parameters in context of groups of related parameters. In addition it provides
a mechanism for
summarizing a large number of parameters in terms of hyperparameters that
characterize higher-order
distributions.
We believe that hierarchical models should represent an entirely natural mode
of thinking for
biologists. Were it possible for biologists to dispense with mark-recapture
estimation and instead
obtain exact values of parameters they would be unlikely to be satisfied with
the parameters as a
summary of the population processes that generated them. Instead we would
expect them to treat the
parameter values as data in some type of analysis.
Standard methods for analyzing mark-recapture data are poorly suited to
hierarchical modeling.
Analysis of deviance based on restricted models, as described by Lebreton et
al. (1992), can be used to
explore deterministic relationships between parameters. However, methods for
fitting random effects
models that allow for stochastic higher-order relationships between parameters
are relatively crude.
For example, the variance components procedure incorporated in program MARK
uses method of
moments, a procedure that can result in inadmissible estimates and that relies
on asymptotic sampling
properties for inference. We describe flat-prior Bayesian analyses using
Markov chain Monte Carlo as
a useful solution to these problems.
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Individual Papers
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4:30-4:55 PM
Components of population growth rate for white-winged scoters in
Saskatchewan
- Ray T. Alisauskas, Joshua J. Traylor, Cindy J. Swoboda, & F. Patrick
Kehoe
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There have been considerable declines in breeding range and abundance of
White-winged scoters (Melanitta fusca deglandi) in northwestern North
America.
Consequently, we began studying population biology of scoters in 2000 at
Redberry, Saskatchewan, Canada, where long-term had been done previously.
Krementz et al (1997) estimated apparent survival rates for this population
using capture-recapture of birds from 1975-1985. Since then, there have been
developments in the direct estimation of population growth rate using
reverse-time, capture-recapture of animals. We used the same capture histories
used by Krementz et al (1997) to directly estimate survival, seniority and
capture probabilities. Seniority probability is a parameter useful for
understanding the proportion of population growth rate composed of survival,
i.e., seniority = survival/population growth. Thus, if seniority and survival
probabilities are estimable, then population growth rate, lambda, can be
estimated
by substitution. Values of seniority approaching 1.0 suggest that there is
very little recruitment contributing to population growth rate. We used
Program Mark to compare 9 candidate models for estimating survival, seniority
and capture probabilities; the 9 models were combinations of different time
constraints (time-specific, time trend and time-invariant) imposed on each of
the three latent parameters. We then used model-averaging to derive a annual
estimates of each of the three latent parameters. Estimates of population
size, derived using estimates of capture probability, declined over the course
of the study. Calculation of population growth rate suggested that this
population was in decline (lambda = 0.78±0.02 SE) over the 11 years of
previous
investigation; because survival probability was constant, and seniority was
very close to one, the results further suggest that population declines were
the result of virtually no local recruitment (neither through immigration nor
local production of young). These historical findings provide context for
current local population dynamics of White-winged scoters at Redberry Lake
studied more recently (since 2000); they also have conservation implications
for scoters over their range in North America.
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4:55-5:20 PM
Statistical Aspects of using genetic markers for individual identification in
capture-recapture studies - Paul Lukacs & Ken Burnham
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We describe analysis issues in which genetic markers differ from bird ringing
in applicability for use in capture-recapture studies. Identification of
individual birds based on genetic markers, often mircosatellites, involves
some uncertainty. The amount of uncertainty depends on many factors including
the number of loci used in the genetic analysis, number of alleles per locus,
allele frequencies, degree of relatedness of individuals, etc. The
uncertainty can be quantified based on the probability of two genotypes being
identical (matching) given they belong to different individuals. Given the
match probabilities, all possible capture histories and their probability of
occurrence can be determined. We present a likelihood based method for the
analysis of capture-recapture data using genetic markers as individual
identification which incorporates potential uncertainty in identification.
The capture histories and their associated probabilities of occurrence are
then used in the capture-recapture analysis to estimate parameters such as
population size or survival. This method also applies to situations where
physical marks of birds are only partially read.
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5:20-5:45 PM
Occupancy as a surrogate for abundance estimation - Darryl MacKenzie & Jim
Nichols
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In many monitoring programmes it may be prohibitively expensive to estimate the actual
abundance of a bird species in a defined area, particularly at large spatial scales, or
where birds occur at very low densities. Often it may be appropriate to consider the
proportion of area occupied by the species as an alternative state variable. However,
as with abundance estimation, issues of detectability must be taken into account in
order to make accurate inferences: the non-detection of the species does not imply the
species in genuinely absent. Here we review some recent modelling developments that
permit unbiased estimation of the proportion of area occupied, colonization and local
extinction probabilities; allow for unequal sampling effort; and enable covariate
information on sampling locations to be incorporated. We also describe how these models
could be extended to incorporate information from marked individuals, which would enable
finer questions of population dynamics (such as turnover rate of nest sites by specific
breeding pairs) to be addressed.
We believe these models may be very applicable to a wide range of bird species, and may
also be useful for investigating questions about habitat quality. For example, the
species is more likely to have higher local extinction probabilities, or higher turnover
rates of specific breeding pairs, in poor quality habitats.
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5:45-6:10 PM
Modeling population dynamics with ringing, age ratio, and breeding population
sample surveys
- Mark Otto
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We modeled mid-continent North American mallard population dynamics while
accounting for the sampling error in each of the demographic time series. We
used survey sample estimates and covariances from all vital statistics:
hunting and non-hunting survival from the USGS Bird Banding Laboratory's
ringing data, reproduction indexed by the ratio of juveniles to adults in the
USFWS Harvest Survey Section's parts collection survey, and breeding
population data from the USFWS May aerial waterfowl breeding ground survey.
Modeling all surveys with their sampling error simultaneously was a
multivariate approach in which all the component demograpic series were
treated equally to obtain the best estimates of the population process over
time.
The model was a two-level hierarchical mixed effects model. The secondary
level used a Leslie-matrix population model to combine the series and
nonstationary signal extraction to obtain true value. The true values were
compromises between the population dynamics and the survey estimates. The
moethod change less precise survey estimates to minimize the differernces
between the breeding population true values and their predictions, given past
data.
The primary hierarchical level consisted of random effects, the survey sample
estimates and their covariances. The ringing data estimates had a multinomial
sampling distribution where the hunting and non-hunting survival rates varied
over time. The reproduction and breeding population estimates had normal
sampling distributions with known and fixed variance estimates. Having data
from all vital statistics exposed inconsistencies among the series and allowed
us to estimate biases.
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