Geometry of Species Distributions: Null Models of Biodiversity Patterns

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Global IP Fellows Meeting

David Storch
Research Fellow and Vice-Director, Center for Theoretical Study, and Assistant Professor, Department of Ecology, Charles University, Prague, Czech Republic
Geometry of Species Distributions: Null Models of Biodiversity Patterns
The ubiquity of general macroecological patterns of species abundance, distribution, and diversity indicates a role of very general ecological principles, universal across different taxa and different ecosystems. Two approaches trying to derive those patterns from simple first principles have recently emerged: (1) theories of metacommunity dynamics (exemplified by Hubbel´s neutral theory of biodiversity) and (2) geometric approaches based on rules generating particular spatial structures of species distributions. Indeed, many patterns, such as the increase of species richness with area (species-area relationship), the relationship between regional and local species richness, species spatial turnover, or the positive relationship between species range size and its local abundance, are tightly related to the patterns of spatial distributions of individual species. Species spatial distributions are always aggregated at many scales of resolution, and the pattern of aggregation has been described to be close to self-similar or fractal. It has been shown that knowledge of quantitative properties of these structures is sufficient for predicting spatial scaling of species richness and turnover. It has not been clear, however, from where these spatial structures arise. I will show that such structures, and thus most spatial macroecological patterns, are predicted using a simple geometric model assuming random hierarchical spatial aggregation, which we call “generalized fractal model”. This null model has quite straightforward biological interpretation in terms of hierarchy of habitat patches, each of them being randomly nested within more broadly defined habitats. Without any ad-hoc parameterization, it predicts observed spatial scaling of species richness and distribution, the slope and shape of the species-area relationship, and even the observed species-abundance distributions (i.e. the prevalence of rare species). Moreover, I will demonstrate that that simple considerations concerning the scaling of probability of species occurrences lead to a quite accurate prediction of observed spatial variation of species richness within the global scale.