Application of Generalized Linear Models and Generalized Estimation Equations to model at-haulback mortality of blue sharks captured in a pelagic longline fishery in the Atlantic Ocean

Abstract

At-haulback mortality of blue shark (Prionace glauca) captured by the Portuguese pelagic longline fish- ery targeting swordfish in the Atlantic was modeled. Data was collected by onboard fishery observers that monitored 762 fishing sets (1 005 486 hooks) and recorded information on 26 383 blue sharks. The sample size distribution ranged from 40 to 305 cm fork length, with 13.3% of the specimens captured dead at-haulback. Data modeling was carried out with Generalized Linear Models (GLM) and Gener- alized Estimation Equations (GEE), given the fishery-dependent source of the data. The explanatory variables influencing blue shark mortality rates were year, specimen size, fishing location, sex, season and branch line material. Model diagnostics and validation were performed with residual analysis, the Hosmer–Lemeshow test, a receiver operating characteristic (ROC) curve, and a 10-fold cross validation procedure. One important conclusion of this study was that blue shark sizes are important predictors for estimating at-haulback mortality rates, with the probabilities of dying at-haulback decreasing with increasing specimen sizes. The effect in terms of odds-ratios are non-linear, with the changing odds- ratios of surviving higher for the smaller sharks (as sharks grow in size) and then stabilizing as sharks reach larger sizes. The models presented in this study seem valid for predicting blue shark at-haulback mortality in this fishery, and can be used by fisheries management organizations for assessing the efficacy of management and conservation initiatives for the species in the future.