Éditeur(s) : HAL CCSD
Résumé : 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.
Les statistiques spatiales sont pour les écologues un ensemble d'outils permettant de caractériser la structure d'un semis de points, par exemple une carte représentant des emplacements des arbres dans une parcelle de forêt. Cette structure est définie implicitement comme un écart à semis complètement aléatoire, résultat d'un processus de Poisson. L'hétérogénéité du processus ponctuel dont le semis de points est une réalisation et la non-indépendance des points en sont les causes indiscernables, ce qui amène généralement à supposer l'intensité du processus connu et nommer " concentration spatiale " ou " agrégation " (la régularité spatiale est possible, mais rare en pratique) la non-indépendance. Une revue de la littérature des processus ponctuels et des mesures de structures spatiales est fournie pour clarifier les concepts et les choix. L'objectif de ce travail de thèse était de produire des améliorations méthodologiques. Ses résultats principaux sont : * L'établissement d'un test pour la principale statistique utilisée, la fonction K de Ripley, permettant de s'affranchir de la méthode de Monte-Carlo utilisée dans la littérature pour rejeter l'hypothèse nulle d'un processus complètement aléatoire. * L'extension de K aux processus hétérogènes, dans le cadre d'une typologie claire des statistiques (absolues, relatives, topographiques). Lorsque la position exacte des objets n'est pas connue, mais que des effectifs par zone sont disponibles (par exemple des nombres d'arbres par parcelle), la théorie de l'information est utilisée pour définir un cadre général permettant de caractériser la structure spatiale (des espèces dans les parcelles) et la diversité (des parcelles, en termes d'espèces) comme deux aspects d'une même mesure d'inégalité. Ce cadre est appliqué à l'indice de biodiversité de Shannon pour définir clairement la mesure de diversité bêta, son calcul direct indépendamment de la différence entre diversités gamma et alpha, et fournir un test statistique de non nullité. La voie est ouverte pour l'application à d'autres mesures de diversité et de structure spatiale. En conclusion, il semble clair que ces outils de caractérisation sont un premier pas pour traiter les questions écologiques, leur développement étant toujours du domaine de la recherche. Ils sont cependant très insuffisants pour répondre à des questions liées aux processus écologiques, assez éloignés des processus ponctuels qui ignorent l'aspect temporel de l'installation des objets.
https://pastel.archives-ouvertes.fr/pastel-00540327

NNT : 2010AGPT0075
pastel-00540327
https://pastel.archives-ouvertes.fr/pastel-00540327
https://pastel.archives-ouvertes.fr/pastel-00540327/document
https://pastel.archives-ouvertes.fr/pastel-00540327/file/13_Marcon2010.pdf

Éditeur(s) : HAL CCSD Elsevier
Résumé : Analyses of tree diversity and community composition in tropical rain forests are usually based either on general herbarium data or on a restricted number of botanical plots. Despite their high taxonomic accuracy, both types of data are difficult to extrapolate to landscape scales. Meanwhile, forestry surveys provide quantitative occurrence data on large areas, and are thus increasingly used for landscape-scale analyses of tree diversity. However, the reliability of these approaches has been challenged because of the ambiguity of the common (vernacular) names used by foresters and the complexity of tree taxonomy in those hyper-diverse communities.We developed and tested a novel approach to evaluate taxonomic reliability of forestry surveys and to propagate the resulting uncertainty in the estimates of several diversity indicators (alpha and beta entropy, Fisher-alpha and Sørensen similarity). Our approach is based on Monte-Carlo processes that simulate communities by taking into account the expected accuracy and reliability of common names. We tested this method in French Guiana, on 9 one-hectare plots (4279 trees – DBH ⩾ 10 cm) for which both common names and standardized taxonomic determinations were available. We then applied our method of community simulation on large forestry inventories (560 ha) at the landscape scale and compared the diversity indices obtained for 10 sites with those computed from precise botanical determination situated at the same localities.We found that taxonomic reliability of forestry inventories varied from 22% (species level) to 83% (family level) in this Amazonian region. Indices computed directly with raw forestry data resulted in incorrect values, except for Gini–Simpson beta-diversity. On the contrary, our correction method provides more accurate diversity estimates, highly correlated with botanical measurements, for almost all diversity indices at both regional and local scales. We obtained a robust ranking of sites consistent with those shown by botanical inventories.These results show that (i) forestry inventories represent a significant part of taxonomic information, (ii) the relative diversity of regional sites can be successfully ranked using forestry inventory data using our method and (iii) forestry inventories can valuably contribute to the detection of large-scale diversity patterns when biases are well-controlled and corrected.The tools we developed as R-functions are available in supplementary material and can be adapted with local parameters to be used for forest management and conservation issues in other regional contexts
ISSN: 0378-1127

hal-01204219
https://hal.archives-ouvertes.fr/hal-01204219
DOI : 10.1016/j.foreco.2014.05.045
PRODINRA : 286554

Éditeur(s) : HAL CCSD EDP Sciences
Résumé : International audience
Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness corresponding to a homogeneous Poisson point process. We first compute the exact first and second moment of the Ripley K-statistic under the homogeneous Poisson point process model. Then we prove the asymptotic normality of a vector of such statistics for different scales and compute its covariance matrix. From these results, we derive a test statistic that is chi-square distributed. By a Monte-Carlo study, we check that the test is numerically tractable even for large data sets and also correct when only a hundred of points are observed
ISSN: 1292-8100

hal-01502640
https://hal-agroparistech.archives-ouvertes.fr/hal-01502640
DOI : 10.1051/ps/2012027