Towards built-in capture–recapture mixed models in program E-SURGE

Abstract

We consider the first steps towards implementing capture–recapture mixed models (CR2Ms) in program E-SURGE. The main issue when estimating the parameters of mixed models is that integrals associated with the random effects distributions need to be dealt with. Rather than using a Bayesian approach with Markov chain Monte Carlo and in line with Gimenez and Choquet (Ecology 91:951–957, 2010), we show that a frequentist approach using numerical integration can be tractable when independent clusters of individuals can be identified. In this case, the maximum likelihood approach is time-efficient because the dimension of the integral for the likelihood is small. This allows us to integrate the likelihood by an efficient and appropriate quadrature method with a procedure for error control. Building on program E-SURGE (Choquet et al. in Modeling demographic processes in marked populations, volume 3 of Springer series: environmental and ecological statistics. Springer, Dunedin, 2009b), we extend the GEMACO language (Choquet in Can J Stat 36:43–57, 2008) to incorporate random effects in a large set of capture–recapture models, including multievent models (Pradel in Biometrics 61:442–447, 2005). To illustrate the flexible implementation of CR2Ms in E-SURGE, we consider two real examples, one with an individual random effect and one with group random effects. Future developments and limitations are also discussed.