Indices for capturing spatial patterns and their evolution in time, with application to European hake (Merluccius merluccius) in the Bay of Biscay

A series of candidate statistical indices is used in an attempt to capture spatial patterns of fish populations from research survey data. To handle diffuse population limits, indices are designed not to depend on arbitrary delineation of the domain. They characterize the location (centre of gravity and spatial patches), the occupation of space (inertia, isotropy, positive area, spreading area, and equivalent area), statistical dispersion (Gini index and coefficient of variation of strictly positive densities), and microstructure. Collocation between different ages and years is summarized by a global index of collocation. Indices are estimated for hake from a bottom-trawl data series in the Bay of Biscay in autumn of 1987-2004. The study provides a detailed description of the spatial patterns of different hake age groups, age 3 appearing to be a turning point in these dynamics. Capturing spatial patterns through indices allows the comparison of surveyed populations and identification of trends and outliers in the time-series. Spatial indices are used in a multivariate approach to obtain an overview of the relationships between the different spatial indices characterizing the spatial behaviour of six age groups of hake, and to assess their persistence through time.