Model selection and multimodel inference for standardizing catch rates of bycatch species: a case study of oceanic whitetip shark in the Hawaii-based longline fishery

One key issue for standardizing catch per unit effort (CPUE) of bycatch species is how to model observations of zero catch per fishing operation. Typically, the fraction of zero catches is high, and catch counts may be overdispersed. In this study, we develop a model selection and multimodel inference approach to standardize CPUE in a case study of oceanic whitetip shark (Carcharhinus longimanus) bycatch in the Hawaii-based pelagic longline fishery. Alternative hypotheses for shark catch per longline set were characterized by the variance to mean ratio of the count distribution. Zero-inflated and non-inflated Poisson, negative binomial, and delta-gamma models were fit to fishery observer data using stepwise variable selection. Alternative hypotheses were compared using multimodel inference. Results from the best-fitting zero-inflated negative binomial model showed that standardized CPUE of oceanic whitetip sharks decreased by about 90% during 1995-2010 because of increased zero catch sets and decreased CPUE on sets with positive catch. Our model selection approach provides an objective way to address the question of how to treat zero catches when analyzing bycatch CPUE.