Dealing with overdispersed count data in applied ecology

Abstract

Summary 1. The ability to identify key ecological processes is important when solving applied problems. Increasingly, ecologists are adopting Akaike's information criterion (AIC) as a metric to help them assess and select among multiple process-based ecological models. Surprisingly, however, it is still unclear how best to incorporate AIC into the selection process in order to address the trade-off between maximizing the probability of retaining the most parsimonious model while minimizing the number of models retained. 2. Ecological count data are often observed to be overdispersed with respect to best-fitting models. Overdispersion is problematic when performing an AIC analysis, as it can result in selection of overly complex models which can lead to poor ecological inference. This paper describes and illustrates two approaches that deal effectively with overdispersion. The first approach involves modelling the causes of overdispersion implicitly using compound probability distributions. The second approach ignores the causes of overdispersion and uses quasi-AIC (QAIC) as a metric for model parsimony. 3. Simulations and a novel method that identifies the most parsimonious model are used to demonstrate the utility of the two overdispersion approaches within the context of two ecological examples. The first example addresses binomial data obtained from a study of fish survival (as related to habitat structure) and the second example addresses Poisson data obtained from a study of flower visitation by nectarivores. 4. Applying either overdispersion approach reduces the chance of selecting overly complex models, and both approaches result in very similar ecological inference. In addition, inference can be made more reliable by incorporating model nesting into the selection process (i.e. identifying which models are special cases of others), as it reduces the number of models selected without significantly reducing the probability of retaining the most parsimonious models. 5. Synthesis and applications. When data are overdispersed, inference can be improved by either modelling the causes of overdispersion or applying QAIC as a metric for model parsimony. Inference can also be improved by adopting a model filtering procedure based on how models are nested. The general simulation approach presented in this paper for identifying the most parsimonious model, as defined by information theory, should help to improve our understanding of the reliability of model selection when using AIC, and help the development of better selection rules.