Fast and flexible Bayesian Jolly Seber models and application to populations with transients

Abstract

AbstractJolly Seber (JS) models are an appealing class of capture-recapture models for modeling open populations because they allow for inferences about an array of population parameters, including abundance, survival, and recruitment. Multiple formulations of JS models have been developed and include both maximum likelihood and Bayesian approaches. Bayesian approaches offer greater flexibility; however, they are often extremely slow when applied to moderate to large populations because the latent states of all observed individuals, as well as any potential unobserved individuals (parameter-expanded data augmentation), must be simulated at each time step.JS model implementations can be sped up dramatically through marginalization, whereby the conditional likelihoods of states are tracked for unique capture histories, rather than the simulated states of all individuals. Here we describe a marginalized implementation of a multistate JS model and compare its performance to that of an implementation using simulated discrete states. We fit models to data generated under two scenarios, one in which no data was missing and another in which 25% of data was randomly removed. To illustrate how marginalization can accommodate more complex models and datasets, we describe a modified version of the model for application to populations with transients and fit the model to simulated data and to data collected on Kentucky Warblers (Geothlypis formosa) as part of the Monitoring Avian Productivity and Survivorship (MAPS) program.Both the discrete latent state and marginalized JS model implementations performed similarly with respect to bias and coverage; however, the marginalized implementation was roughly 1,000 times faster when no data were missing and 100 times faster when 25% of data was missing. The marginalized model accommodating transients also converged quickly and a more complex version of the model applied to the larger multi-site Kentucky Warbler data set yielded useful estimates of most parameters within a reasonable time frame (hours).Gains in efficiency provided by marginalization shown here should stimulate additional study and development of this useful class of models and provide new opportunities for real-world applications to large complex data sets.