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

Area of Science:

• Ecology
• Evolutionary Biology
• Conservation Biology

Background:

• Quantifying individual heterogeneity in vital rates is essential for understanding open populations.
• Capture-recapture models often incorporate individual random effects using Bayesian frameworks and Markov chain Monte Carlo (MCMC) methods.
• These MCMC methods can be computationally intensive.

Purpose of the Study:

• To introduce Gauss-Hermite quadrature (GHQ) as an efficient numerical integration method for approximating capture-recapture models with individual random effects.
• To compare the performance of GHQ with MCMC simulations and finite mixture models.
• To demonstrate the utility of GHQ in population biology analyses.

Main Methods:

• Developed and applied the Gauss-Hermite quadrature (GHQ) approximation for capture-recapture mixed models (CR2Ms) with individual random effects.
• Compared GHQ with traditional Markov chain Monte Carlo (MCMC) simulations and finite mixture models.
• Utilized data from European Dippers and Sociable Weavers for model validation.

Main Results:

• Gauss-Hermite quadrature (GHQ) provides an efficient approximation for capture-recapture mixed models (CR2Ms) with individual random effects.
• GHQ was found to be computationally faster than Markov chain Monte Carlo (MCMC) simulations.
• The GHQ approach is implemented in the E-SURGE software package.

Conclusions:

• Gauss-Hermite quadrature (GHQ) is a viable and efficient alternative to MCMC for analyzing capture-recapture mixed models (CR2Ms).
• This method enhances the application of CR2Ms in population biology for conservation and evolutionary ecology.
• The E-SURGE program facilitates the implementation of these advanced statistical techniques.