Making better use of productivity data: A simulation study evaluating traditional and alternative estimation methods

Survey counts of juveniles is a common and important component of productivity estimation for imperiled wildlife species. However, the choice of analytical methods may lead to biased estimates for this important vital rate. For some wildlife groups, including raptors, traditional analytical methods often fail to account for variability in detection probabilities, potentially leading to an underestimation of productivity. For group living species, correlated behavior violates the assumption of independent detection in models that account for variable detection, potentially overestimating productivity. To test the effect of ignoring variable detection or correlated behavior when modeling raptor productivity, we simulated data under various scenarios by varying detection probabilities, sample sizes, mean counts, and correlation in detection probabilities. We evaluated the performance of four modeling approaches for estimating productivity: linear model of mean counts, Poisson model of maximum counts, an N-mixture model with a binomial detection model, and an N-mixture model with a beta-binomial detection model. Our simulation results showed that models ignoring imperfect detection generally underestimated productivity. When detection probabilities were correlated, N-mixture models with a binomial detection model severely overestimated productivity in common survey scenarios. In contrast, N-mixture models employing a beta-binomial detection model exhibited reduced bias and accurately estimated productivity across varying levels of correlation in detection probabilities. We also conducted two case studies using data for two raptor species. Results from these case studies exhibited similar patterns to our simulation study. Accounting for both variable detection and group behavior will improve productivity estimates for many species of management interest.