Reviewing and improving spatiotemporal modeling approaches for mackerel’s total annual egg production

Abstract

Since the late 1970s the international ICES mackerel egg survey takes place in the Northeast Atlantic to obtain an estimate of total annual egg production (TAEP), to assess the spawning stock biomass and to support the sustainable management of the mackerel stock. However, its standard calculation of TAEP has some shortcomings: egg production is estimated from arithmetic averages of individual observations regardless whether they are extreme, rarely observed values, and has shown difficulties coping with the spatial expansion of mackerel spawning observed since 2007 (increasing the number of interpolated estimates). Various previous modeling efforts attempted to map the habitat of spawning mackerel to obtain more accurate egg production estimates by using generalized additive models (GAMs). In this study, we review and improve these models by introducing new features: We model both the western and southern components of the mackerel stock with a Tweedie distribution and test more than 400 model forms, including new predictors (like population size) and complex covariate interactions. We select the best model with various metrics, including the score of a tenfold cross validation. Our results show that environmental variables should be included in the model as simple functional, unimodal terms. This leads to a model that is more similar to a generalized linear mixed model than the typical GAM with smoothers. Models including only smoothers performed worse as they have a poor skill to extrapolate beyond the sampled region. Additionally, accounting for the effect of population size on the spatial distribution of eggs was shown to be fundamental to better model performance.Graphical abstract