Comparing GLM, GLMM, and GEE modeling approaches for catch rates of bycatch species: A case study of blue shark fisheries in the South Atlantic

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AbstractModeling and understanding the catch rate dynamics of marine species is extremely important for fisheries management and conservation. For oceanic highly migratory species in particular, usually only fishery‐dependent data are available which have limitations in the assumption of independence and if often zero‐inflated and/or overdispersed. We tested different modeling approaches applied to the case study of blue shark in the South Atlantic, by using generalized linear models (GLMs), generalized linear mixed models (GLMMs), and generalized estimating equations (GEEs), as well as different error distributions to deal with the presence of zeros in the data. We used fractional polynomials to deal with non‐linearity in some of the explanatory variables. Operational (set level) data collected by onboard fishery observers, covering 762 longline sets (1,014,527 hooks) over a 9‐year period (2008–2016), were used. One of the most important variables affecting catch rates is leader material, with increasing catches when wire leaders are used. Spatial and seasonal variables are also important, with higher catch rates expected toward temperate southern waters and eastern longitudes, particularly between July and September. Environmental variables, especially SST, also affect catches. There were no major differences in the parameters estimated with GLMs, GLMMs, or GEEs; however, the use of GLMMs or GEEs should be more appropriate due to fishery dependence in the data. Comparing those two approaches, GLMMs seem to perform better in terms of goodness‐of‐fit and model validation.