Mark-recapture under individual heterogeneity and misidentification and Bayesian Clustering of Animal Abundance Trends For Inference and Dimension Reduction

Speaker: Brett McClintock and Devin Johnson ( NOAA Seattle)

Abstract

Link et al. (2010; Biometrics) recently developed a novel approach for the analysis of mark-recapture data when individual identification errors occur (e.g., due to observer or genotyping errors). However, their methodology does not allow for individual variation in parameters, such as detection probability or survival. Here we develop misidentification models for mark-recapture data that can simultaneously account for temporal variation, behavioral effects, and individual heterogeneity in parameters. Our approach can also be used to accommodate individual heterogeneity in the probability of misidentification, which often arises when mark (or DNA sample) quality differs among individuals. Using Bayesian analysis methods, we present Markov chain Monte Carlo algorithms for fitting our models. Using closed population abundance models for illustration, we re-visit a DNA capture-recapture population study of black bears in Michigan, USA and find evidence of misidentification due to genotyping error, as well as temporal, behavioral, and individual variation in detection probability. We also estimate a salamander population of known size from laboratory experiments evaluating the effectiveness of a marking technique commonly used for amphibians and fish. Our model was able to reliably estimate the size of this population and provided evidence of individual heterogeneity in misidentification probability that is attributable to variable mark quality. Our approach is more computationally demanding than previously proposed methods, but it provides the flexibility necessary for a much broader suite of models to be explored while properly accounting for uncertainty introduced by misidentification.

Devin Johnson:
We consider a model-based clustering approach to examining abundance trends in a metapopulation. When examining trends for an animal population with management goals in mind one is often interested in those segments of the population that behave similarly to one another with respect to abundance. Our proposed trend analysis incorporates a clustering method that is an extension of the classic Chinese Restaurant Process, and the associated Dirichlet process prior, which allows for inclusion of distance covariates between sites. This approach has two main benefits: (1) nonparametric spatial association of trends and (2) reduced dimension of the spatio-temporal trend process. We present a transdimensional Gibbs sampler for making Bayesian inference that is efficient in the sense that all of the full conditionals can be directly sampled from save one. To demonstrate the proposed method we examine long term trends in northern fur seal pup production at nineteen rookeries in the Pribilof Islands, Alaska. There was strong evidence that clustering of similar year-to-year deviation from linear trends was associated with whether rookeries were located on the same island. Clustering of local linear trends did not seem to be strongly associated with any of the distance covariates. In the fur seal trends analysis an overwhelming proportion of the MCMC iterations produced a 73–79% reduction in the dimension of the spatio-temporal trend process, depending on the number of cluster groups.