Transitive geostatistics to characterise spatial aggregations with diffuse limits : an application on mackerel ichtyoplankton

Abstract In the context of the analysis of mackerel ichtyoplankton, and more generally of populations with diffuse limits (e.g. pelagic fish), we present a methodology that avoids the problem of the delineation of the area of presence. The principle, which leads to the concept of Individual Based Statistics, is to give each sample a weight proportional to its density, i.e., proportional to the number of individuals it represents. A level and an index of aggregation are proposed to characterise statistically population with diffuse limits, while the inertia of locations and the transitive covariogram can be used as spatial characteristics. In particular, a superposition of structural components with different scales can be described on the covariogram. In the Northeast Atlantic, during the spawning seasons 1986, 1989, 1992 and 1995, the inertia of the population of stage I mackerel eggs is remarkably stable despite inter- and intra-annual variations of the total abundance. The spatial structures, as described by the covariograms, are made of two components: a small range component (nugget effect) and a long range exponential component. The stability of the inertia is essentially due to the stability of the long range. On the other hand, the observed variations of the index of aggregation are essentially due to the variations of the short range component. A comparison between newly spawn eggs and stage V eggs (last stage before hatching) is also made and interpreted in terms of diffusion and mortality rates.