Modelling the variability in fish spatial distributions over time with empirical orthogonal functions: anchovy in the Bay of Biscay

Characterizing the space–time variability in spatial distributions as well as understanding its drivers is basic to designing robust spatial management plans. As a prerequisite, we analyse here how this variability relates to population dynamics in conjunction with environmental conditions. For that, spatio-temporal statistical approaches are needed but seldom used in fisheries science. To fill this gap, we showcase the usefulness of the method of empirical orthogonal functions (EOFs). Guidelines are given to apply the method on a series of gridded maps as derived from fisheries survey dataseries that now span over decades. The method is applied to the series, 2000–2012, of the spatial distributions of European anchovy in the Bay of Biscay at spawning time. Across the series, the EOF decomposition allowed to identify three main types of spatial distributions. One type corresponded to an extended distribution, another to a restricted distribution in core areas, and the third to a very coastal distribution. The coastal spawning distribution corresponded to a low population growth rate as it was never followed by a large recruitment in the subsequent year. We did not attempt to explain the spatial patterns per se but the drivers of change from one type of distribution to another. Stock size and fish size as well as bottom temperature and water column stratification were the covariates that controlled the variability in the spatial distributions over time. Further, the spatial distribution at spawning time related to recruitment in the following year, meaning that variability in the spatial distribution of spawning affected population dynamics. The typology of maps based on EOF decomposition summarized this spatial variability into spatial spawning configurations, which may serve spatial planning.

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