Statistical models to standardize catch rates in the multi-species trawl fishery for Patagonian grenadier (Macruronus magellanicus) off Southern Chile

Changing targeting behavior of fishing fleets and zero-catch records of the target species are two characteristics common to many multi-species trawl fisheries. These features complicate analyses intended to produce indices of relative abundance from commercial catch rate data. Trawl catch rates of Patagonian grenadier caught off Southern Chile were used to calculate indices of relative abundance for this species. To allow for targeting behavior and zero catches, we first defined a subset of relevant tows combining a logistic regression on the species catch composition and knowledge about the persistence of Patagonian grenadier in the catches from the area where historically it has been more abundant. A standardization analysis was then conducted on this subset of the data using a generalized linear model (GLM) framework. Analysis of deviance tables and standard residuals GLM diagnostic plots were used for selecting the statistical models that best described the data. The candidate models tested were the delta-lognormal, delta-gamma, quasi-Poisson and compound Poisson. The models that best supported the Patagonian grenadier catch rate data were the delta-lognormal and compound Poisson models. Standardization models were then extended to generalized linear mixed models to include the vessel main effect and the significant interactions with the year effect as random effects. Estimations of the annual series of relative abundance were then obtained from the coefficients of the year effects of these models, both of which showed higher abundance for the years 2001--2008 than in previous years of the series.