Investigating patchiness of spatially organized ecosystems using field and simulated data

Abstract

Individuals of a population are rarely spatially homogeneously distributed. In most ecosystems, individuals present a certain degree of clustering, meaning that they are more often close to each other than by chance, forming patches of individuals1. Changes in external conditions (such as climate changes or human land use changes) might induce a spatial reorganization of the individuals. Particularly, some systems, called critical systems, are well-known to develop a characteristic spatial organization when close to a dramatic shift in state, that can involve important changes in population abundance and species diversity2. Classical examples are wind-disturbed tropical forests3, fire-disturbed forest4 and intertidal mussel beds5. In these systems, near the critical point of transition to complete extinction, the patch size distribution of tree or mussel cover exhibits a power law behaviour3,6. Here, we present a technique that provides a way of characterizing the spatial organization of patchy systems, and to investigate if there are fundamental changes in this spatial organization when conditions change. The protocol we propose can be applied to spatially organized real systems or to spatially explicit lattice model systems, and we expose the protocol for these two cases. The protocol consists in estimating the patch size distribution, i.e. the number of patches of individuals as a function of their size. The patch size distribution can be described by a mathematical law (e.g. a line, or a polynomial on a logarithm scale). When external conditions change, this law might change as well. Statistical tests allow the selection of the model that describes best the patch size distribution. In the case of Mediterranean arid ecosystems, we found that the patch size distribution of vegetation is characterized by a power law, and that this distribution deviates from a power law when external conditions deteriorate towards desertification7. The different steps of the protocol are summarized in a scheme (Fig. 1). Note that investigating the patch size distribution is only one of the possible ways of characterizing the spatial organization of a system. This methodology can be applied to any patchy system, and we expect similar results than ours in ecosystems subjected to stressful conditions (e.g. harsh environments such as alpine systems, salt marshes, intertidal habitats) where local positive interactions operate.