Evaluation of fixed- and random-effects models and multistage estimation procedures in statistical population reconstruction

Abstract

Statistical population reconstruction (SPR) using hunter-supplied, age-at-harvest data provides a flexible framework for estimating population parameters and trends over large geographic areas. Early development of the technique assumed natural survival and the vulnerability coefficients that translate hunter effort into harvest mortality are constant over time. We developed random-effects models that relaxed these assumptions to produce more realistic models for cohort analysis. We compared the statistical performance of fixed-effects and random-effects models and the relative benefits of single-stage and 2-stage estimators of abundance with Monte Carlo simulation studies. In single-stage analyses, initial cohort abundance is estimated directly within the likelihood model. In 2-stage analyses, survival and harvest probabilities are estimated using likelihood conditional on total cohort harvest. Annual abundances are then estimated outside the likelihood using Horvitz–Thompson type estimators. Our simulation results indicate random-effects models conditional on total cohort harvest have low bias and yield asymptotic 95% confidence intervals that have near nominal coverage. The other estimation procedures produced confidence intervals for annual abundance that had far-from-nominal coverage. Our new random-effects, 2-stage model is illustrated using 18 years of age-at-harvest data from an elk (Cervus elaphus) herd in the Lower Peninsula of Michigan. Results indicate the multistage estimation process incorporating random effects provides accurate abundance estimates and confidence interval coverage, and we recommend its use. © 2013 The Wildlife Society.