Bayesian Methods for Analyzing Movements in Heterogeneous Landscapes From Mark–recapture Data

Abstract

Spatially referenced mark-recapture data are becoming increasingly available, but the analysis of such data has remained difficult for a variety of reasons. One of the fundamental problems is that it is difficult to disentangle inherent movement behavior from sampling artifacts. For example, in a typical study design, short distances are sampled more frequently than long distances. Here we present a modeling-based alternative that combines a diffusion-based process model with an observation model to infer the inherent movement behavior of the species from the data. The movement model is based on classifying the landscape into a number of habitat types, and assuming habitat-specific diffusion and mortality parameters, and habitat selection at edges between the habitat types. As the problem is computationally highly intensive, we provide software that implements adaptive Bayesian methods for effective sampling of the posterior distribution. We illustrate the modeling framework by analyzing individual mark-recapture data on the Glanville fritillary butterfly (Melitaea cinxia), and by comparing our results with earlier ones derived from the same data using a purely statistical approach. We use simulated data to perform an analysis of statistical power, examining how accuracy in parameter estimates depends on the amount of data and on the study design. Obtaining precise estimates for movement rates and habitat preferences turns out to be especially challenging, as these parameters can be highly correlated in the posterior density. We show that the parameter estimates can be considerably improved by alternative study designs, such as releasing some of the individuals into the unsuitable matrix, or spending part of the recapture effort in the matrix.

A general discrete‐time modeling framework for animal movement using multistate random walks

“…Ovaskainen et al (2008) and Johnson et al (2008) provided important first steps in accessible software by creating DISPERSE and the R package CRAWL to perform the complicated computations that the models, respectively, require. Despite its relative mathematical simplicity, the large number of parameters and latent variables inherent to our modeling framework also make implementation a computational challenge.…”

Variables associated with detection probability, detection latency, and behavioral responses of Golden-winged Warblers (Vermivora chrysoptera)

“…For computational efficiency we use the same M for each block j, where M is the average posterior (co)variance of l j within blocks and is updated each iteration of the burn-in period Haario et al (2001). The scalar m is chosen using the method of Ovaskainen et al (2008) so that the proportion of successful jumps is optimal, with a rate of 0.44 when l j is a scalar declining to 0.23 when l j is high dimensional (Gelman, Carlin, Stern, and Rubin 2004).…”

“…Latent variables whose residuals are non-independent are sampled in blocks using Metropolis-Hastings updates and an efficient proposal distribution is determined during the burn-in phase using adaptive methods (Haario, Saksman, and Tamminen 2001;Ovaskainen, Rekola, Meyke, and Arjas 2008). The parameters of the mixed model (β and u) follow a multivariate normal distribution and can be Gibbs sampled in a single block using the method of Garcia-Cortes and Sorensen (2001).…”

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“…While the problem of sampling the full distribution of dispersal distances can be addressed through appropriate study design and analysis, environmental heterogeneity presents a greater challenge to robust estimation of survival and dispersal (Ovaskainen et al 2008). As dispersal is an emergent phenomenon reflecting interactions between an organism and its environment, a kernel generated from CMR data may only be truly meaningful within the conditions occurring in the sampled area (Schneider 2003).…”