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Natural and anthropogenic effects on the early life stages of European anchovy in one of its essential fish habitats, the Guadalquivir estuary

Some models (eg. water mass I) showed autocorrelation in the residuals. To assess the importance of violating this regression assumption we created five alternative models or submodels (Figure S1). Each of the models accounted for this problem in a different way: (i) alternative model 1 included ‘month’ as a temporal factor, (ii) sub-model 2 included the response variable (anchovy abundance) as an explanatory term lagged by one month, (iii) in sub-model 3 the trigonometric functions sin(2πt/12) and cos(2πt/12) were added as covariates, where t is the monthly index (Stenseth et al. 2006), (iv) model 4 used ‘month’ again, but this time entered with cubic spline basis, and finally (v) model 5 formulation incorporated an autoregressive term in a mixed model framework (GAMM) (Wood 2006, Hefley et al. 2017). All sub-models showed non-correlated residuals (Figure S2) and therefore corrected for the lack of independence. Some of the sub-models (models 1 and 3, for example) did not retained some of the covariates (freshwater discharges and M. slabberi) while models 2, 4 and 5 kept practically the same structure. All things considered we can conclude that autocorrelation, when present, does not affect the main results.