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

Abstract

Modeling 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. K E Y W O R D Scatch per unit effort, generalized estimating equations, generalized linear mixed models, generalized linear models, longline fisheries, pelagic sharks, statistical models S U PP O RTI N G I N FO R M ATI O NAdditional supporting information may be found online in the Supporting Information section.How to cite this article: Coelho R, Infante P, Santos MN.Comparing GLM, GLMM, and GEE modeling approaches for catch rates of bycatch species: A case study of blue shark fisheries in the South Atlantic. Fish Oceanogr. 2020;29:169-184. https ://doi.

Large-Scale Sheep Losses to Wolves (Canis lupus) in Germany Are Related to the Expansion of the Wolf Population but Not to Increasing Wolf Numbers

“…As the response variable was a count statistic, we checked for Poisson distribution and found it to be inappropriate due to overdispersion (Kolmogorov-Smirnov Z = 5.804, p < 0.001, mean = 98.99, variance = 16,978.32). Therefore, we applied a Generalized Linear Mixed Model (GLMM) with negative binomial distribution and log link (Koper and Manseau, 2009;Coelho et al, 2020). We ran an array of models with the main effects of one, two and three predictors in order to keep the most parsimonious models, avoid overfitting and foster interpretability of models (Chatterjee and Simonoff, 2013).…”

“…The precision of the best GLMM models was estimated by plotting 99% confidence intervals of predicted values and overlapping them with original values of the number of sheep killed by wolves. These models were validated by 10-fold crossvalidation and the accuracy of their predictions was estimated by calculation of mean root-mean-square error (RMSE) ± standard error (SE) from 10 random training/test sub-samples (Coelho et al, 2020;Khorozyan, 2020). SE was used as a measure of variation throughout the study.…”

The Effect of Fishery Management on the Yield of the Critically Endangered European Eel Anguilla anguilla in Mesotrophic Rivers and Streams in Central Europe

“…Fixed factors in the first two models were: (1) angling effort, (2) the size (median body weight) of stocked eels, (3) the stocking intensity of elvers, (4) the stocking intensity of yellow eels, (5) fish biomass, (6) nutrient intake, (7) water discharge, (8) otter population density, (9) cormorant population density, (10) the yield of non-regulated fishes, (11) the yield of regulated fishes, (12) the biomass of eels, (13) the number of river obstacles, and ( 14) the bank to surface ratio. Fishing site was added as a random factor to exclude the effect of individual fishing sites on yield and because the individual fishing sites (river and stream stretches) were connected, allowing the stocked fish to migrate between the fishing sites [37]. The mathematical equation for the models was: Yield ~Angling effort + Size of stocked eels + Stocking intensity of elver eels + Stocking intensity of yellow eels + Fish biomass + Nutrient intake + Water discharge + Otter population density + Cormorant population density + Yield of nonregulated fishes + Yield of regulated fishes + Biomass of eels + River obstacles + Bank to surface ratio + (1|fishing site).…”

Temporal and regional variation in catch across an extensive coastal recreational fishery: Exploring the utility of survey methods to guide and assess spatio-temporal management initiatives

“…Using the glmer.nb() command in the lme4 package [56], generalized linear mixed-effects models (GLMMs) assuming a negative binomial distribution were utilised to examine the influence of the factors zone (levels: North Coast, Mid-North Coast, Hunter, Sydney, Mid-South Coast and South Coast; Fig 1) and season (levels: Winter, Spring, Summer and Autumn) on the expanded number of kept and released individuals of a given species [57,58]. Since the primary sampling units in the study were randomly selected households and there was a possibility of some selected households catching a given species in more than one level of the factors zone and season, an inherent property of this survey data is that repeated catches across zones or seasons within a single household may be more similar to each other than catches in other households.…”

“…where C represents the kept or released catch; β 0 the vertical intercept; β 1 and β 2 the regression coefficients for the independent parameters zone (x 1,ij ) and season (x 2,ij ) respectively; β 3 the regression coefficient for the interaction term between zone and season; a j represents a random variable; and, ε ij represents the errors term [58,61]. Models were initially fitted assuming both a Poisson or negative binomial distribution family.…”