Statistiques spatiales avec applications à l'écologie et à l'économie

Abstract : For ecology scientists, spatial statistics are a set of tools allowing characterization of the structure of a point set, for instance a map of trees in a forest plot. This structure is defined implicitly as a departure from complete spatial randomness (CSR), the result of a Poisson point process. Inhomogeneity of the process and non-independence of points are its causes. As they cannot be disentangled by analyzing the data, so-called "spatial concentration" or "aggregation" (evenness due to repulsion also exists but is actually rare) usually concerns non-independence while intensity is assumed as known. The literature of point processes and measures of spatial structures is reviewed to clarify concepts and choices. The purpose of this thesis was to produce methodological enhancements. Its main results are: * A test for the most used statistic, Ripley's K function, against the null hypothesis of CSR. It can replace Monte-Carlo simulations used until now in the literature. * An extension of K to inhomogeneous processes, within a typology of available statistics (absolute, relative and topographic measures). When data is available as number of objects per zones (say a number of tree in each forest plot) rather than their exact position, information theory is used to define a general framework allowing to characterize spatial structure (of species) and diversity (of plots) as two aspects of a single measure of inequality. This framework is applied to Shannon's index of biodiversity to derive a self-sufficient definition of beta diversity, its calculation independently from the difference between gamma and alpha diversity, and a statistical test of significance against the null hypothesis that plots are samples of the same community. The way is paved for other applications to measures of diversity and spatial structures. As a conclusion, it appears clear that pattern characterization tools are a first step to deal with ecological questionings. Their development is still a matter of research. Yet, they are far from sufficient to address ecological processes as point processes ignore the temporal aspect of object locations.
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Submitted on : Friday, November 26, 2010 - 2:13:12 PM
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Eric Marcon. Statistiques spatiales avec applications à l'écologie et à l'économie. Biodiversité et Ecologie. AgroParisTech, 2010. Français. ⟨NNT : 2010AGPT0075⟩. ⟨pastel-00540327⟩

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