A generalized mixed effects model of abundance for mark-resight data when sampling is without replacement

Abstract

In recent years, the mark-resight method for estimating abundance when the number of marked individuals is known has become increasingly popular. By using field-readable bands that may be resighted from a distance, these techniques can be applied to many species, and are particularly useful for relatively small, closed populations. However, due to the different assumptions and general rigidity of the available estimators, researchers must often commit to a particular model without rigorous quantitative justification for model selection based on the data. Here we introduce a nonlinear logit-normal mixed effects model addressing this need for a more generalized framework. Similar to models available for mark-recapture studies, the estimator allows a wide variety of sampling conditions to be parameterized efficiently under a robust sampling design. Resighting rates may be modeled simply or with more complexity by including fixed temporal and random individual heterogeneity effects. Using information theory, the model(s) best supported by the data may be selected from the candidate models proposed. Under this generalized framework, we hope the uncertainty associated with mark-resight model selection will be reduced substantially. We compare our model to other mark-resight abundance estimators when applied to mainland New Zealand robin (Petroica australis) data recently collected in Eglinton Valley, Fiordland National Park and summarize its performance in simulation experiments.