Individual heterogeneity in studies on marked animals using numerical integration: capture-recapture mixed models

In conservation and evolutionary ecology, quantifying and accounting for individual heterogeneity in vital rates of open populations is of particular interest. Individual random effects have been used in capture-recapture models, adopting a Bayesian framework with Markov chain Monte Carlo (MCMC) to carry out estimation and inference. As an alternative, we show how numerical integration via the Gauss-Hermite quadrature (GHQ) can be efficiently used to approximate the capture-recapture model likelihood with individual random effects. We compare the performance of the two approaches (MCMC vs. GHQ) and finite mixture models using two examples, including data on European Dippers and Sociable Weavers. Besides relying on standard statistical tools, GHQ was found to be faster than MCMC simulations. Our approach is implemented in program E-SURGE. Overall, capture recapture mixed models (CR2Ms), implemented either via a GHQ approximation or MCMC simulations, have potential important applications in population biology.