Plenary Address - 3:50-4:30 PM

Hierarchical mark-recapture models: A framework for inference about demographic processes

Bill Link & Richard Barker

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.

Individual Papers

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

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.

4:55-5:20 PM

Statistical Aspects of using genetic markers for individual identification in capture-recapture studies - Paul Lukacs & Ken Burnham

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.

5:20-5:45 PM

Occupancy as a surrogate for abundance estimation - Darryl MacKenzie & Jim Nichols

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.

5:45-6:10 PM

Modeling population dynamics with ringing, age ratio, and breeding population sample surveys - Mark Otto

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.