Estimation of capture probabilities using generalized estimating equations and mixed effects approaches.

Area of Science:

• Ecology
• Wildlife Biology
• Statistical Modeling

Background:

• Capture-recapture studies are crucial for estimating wildlife population sizes.
• Modeling individual heterogeneity in capture probabilities presents significant challenges.
• Accounting for the correlation structure across capture occasions is essential.

Purpose of the Study:

• To propose and evaluate novel statistical approaches for estimating population size in closed capture-recapture models.
• To address the challenge of individual heterogeneity in capture probabilities.
• To compare the performance of generalized estimating equations (GEE) and generalized linear mixed modeling (GLMM) against existing methods.

Main Methods:

• Development of generalized estimating equations (GEE) and generalized linear mixed modeling (GLMM) frameworks.
• Application of these methods to model capture probabilities as a function of individual covariates.
• Utilizing quasi-likelihood and partial likelihood estimation techniques.
• Conducting simulation studies to assess estimator performance under various scenarios.

Main Results:

• The proposed quasi-likelihood approach based on GEE demonstrated lower standard errors (SE) for population size estimation compared to partial likelihood methods (GLM, GLMM).
• Estimator performance was robust when a large proportion of individuals were captured.
• In scenarios with low capture proportions, estimates became unstable, but the GEE approach still outperformed other methods.

Conclusions:

• GEE and GLMM provide effective frameworks for analyzing capture-recapture data with individual heterogeneity.
• The GEE approach offers a statistically advantageous method for estimating population size, particularly in terms of precision.
• Careful consideration of capture proportions is necessary for reliable population estimates in capture-recapture studies.