Model selection with overdispersed distance sampling data

Abstract

AbstractDistance sampling (DS) is a widely used framework for estimating animal abundance.DSmodels assume that observations of distances to animals are independent. Non‐independent observations introduce overdispersion, causing model selection criteria such asAICorAICcto favour overly complex models, with adverse effects on accuracy and precision.We describe, and evaluate via simulation and with real data, estimators of an overdispersion factor (), and associated adjusted model selection criteria (QAIC) for use with overdispersedDSdata. In other contexts, a single value ofis calculated from the “global” model, that is the most highly parameterised model in the candidate set, and used to calculateQAICfor all models in the set; the resultingQAICvalues, and associated ΔQAICvalues andQAICweights, are comparable across the entire set. Candidate models of theDSdetection function include models with different general forms (e.g. half‐normal, hazard rate, uniform), so it may not be possible to identify a single global model. We therefore propose a two‐step model selection procedure by whichQAICis used to select among models with the same general form, and then a goodness‐of‐fit statistic is used to select among models with different forms. A drawback of this approach is thatQAICvalues are not comparable across all models in the candidate set.Relative toAIC,QAICand the two‐step model selection procedure avoided overfitting and improved the accuracy and precision of densities estimated from simulated data. When applied to six real datasets, adjusted criteria and procedures selected either the same model asAICor a model that yielded a more accurate density estimate in five cases, and a model that yielded a less accurate estimate in one case.ManyDSsurveys yield overdispersed data, including cue counting surveys of songbirds and cetaceans, surveys of social species including primates, and camera‐trapping surveys. Methods that adjust for overdispersion during the model selection stage ofDSanalyses therefore address a conspicuous gap in theDSanalytical framework as applied to species of conservation concern.