Sole egg distributions in space and time characterised by a geostatistical model and its estimation variance

Geostatistics is used to model the spatio-temporal variability in egg volumetric density measured by monitoring surveys performed on a major spawning ground of sole in the Bay of Biscay (France). An approximation formula is proposed for computing the estimation variance of the mean egg density estimated over space and time. The major structural feature is the time invariance in the spatial distribution of the relative density (density(x,t)/mean(t)). This leads to interpretation of the different samplings as different realisations of the same random function in space. Because of the timerepeated samplings at each station, drift (or trend) and residuals can be separated. The drift is defined as the spatial structural component that is constant over time. The spatio-temporal variability was described by a multiplicative model with two effects: a time effect corresponding to a proportionality to the spatial average at each time and a space effect corresponding to the time-invariant spatial distribution of the relative density. Residuals showed structure in space but not in time and no space–time interaction. Geostatistical aggregation curves were used to characterise invariance over time of the aggregation pattern, the drift was mapped using non-stationary IRF-k (Intrinsic Random Functions of order k) kriging and variograms and crossvariograms were used to study the structure in the residuals.