[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] This thesis is a new proposal for analysing spatial point patterns in spatial statistics using the outputs of popular techniques of (classical, non-spatial, multivariate) cluster analysis. The outputs of a chosen hierarchical algorithm, named fusion distances, are applied to investigate important spatial characteristics of a given point pattern. The fusion distances may be regarded as a missing link between the fields of spatial statistics and multivariate cluster analysis. Up to now, these two fields have remained rather separate because of fundamental differences in approach. It is shown that fusion distances are very good at discriminating different types of spatial point patterns. A detailed study on the power of the Monte Carlo test under the null hypothesis of Complete Spatial Randomness (the benchmark of spatial statistics) against chosen alternative models is also conducted. For instance, the test (based on the fusion distance) is very powerful for some arbitrary values of the parameters of the alternative. A new general approach is developed for analysing a given point pattern using several graphical techniques for exploratory data analysis and inference. The new strategy is applied to univariate and multivariate point patterns. A new extension of a popular strategy in spatial statistics, named the analysis of the local configuration, is also developed. This new extension uses the fusion distances, and analyses a localised neighbourhood of a given point of the point pattern. New spatial summary function and statistics, named the fusion distance function H(t), area statistic A, statistic S, and spatial Rg index, are introduced, and proven to be useful tools for identifying relevant features of spatial point patterns. In conclusion, the new methodology using the outputs of hierarchical clustering algorithms can be considered as an essential complement to the existing approaches in spatial statistics literature.

The aim of the thesis is to create a pack of functions in Wolfram Mathematica software to simulate spatial point patterns of chosen hard-core and Gibbs processes. Then it tries to apply these models to real data, estimate the parameters of models for real data and test the validity of models. The thesis can serve as introduction into the theory of spatial point processes.

Invasive exotic plants can persist and successfully spread within ecosystems and negatively affect the recruitment of native species. The exotic invasive Ailanthus altissima and the native Robinia pseudoacacia are frequently found in disturbed sites and exhibit similar growth and reproductive characteristics, yet each has distinct functional roles such as allelopathy and nitrogen fixation, respectively. 1) A four-month full additive series in the greenhouse and 2) spatial point pattern analysis of trees in a silvicultural experiment were used to analyze the intraspecific and interspecific interference between these two species. In the greenhouse experiment, total biomass responses per plant for both species were significantly affected by interspecific but not by intraspecific interference (p <0.05). Competition indices such as Relative Yield Total and Relative Crowding Coefficient suggested that A. altissima was the better competitor in mixed plantings. Ailanthus altissima consistently produced a larger above ground and below ground relative yield while R. pseudoacacia generated a larger aboveground relative yield in high density mixed species pots. However, R. pseudoacacia exhibited more variation for multiple biomass traits, occasionally giving it an above ground advantage in some mixed species pots. Analysis of spatial point patterns in the field with Ripley's K indicated that the two species were positively associated with each other along highly disturbed skid trails in the majority of the field sites. Locally, increased disturbances could lead to more opportunities for A. altissima to invade, negatively interact with R. pseudoacacia (as was evident in the greenhouse study), and become established in place of native species. / Master of Science

Les forêts tropicales représentent un ‘hotspot’ de diversité avec un nombre considérable d’espèces qui coexistent jusqu’à une échelle locale fine. Plus particulièrement, 16 000 espèces d’arbres coexistent en Amazonie, 1 800 en Guyane française et entre 120 et plus de 200 espèces d’arbres par hectare. Cependant, le maintien de cette diversité face aux changements globaux actuels et à venir (qu’ils soient anthropiques ou climatiques…) est incertain. Avant de pouvoir prédire l’évolution de la diversité face aux changements globaux, un travail fondamental est nécessaire afin de comprendre les processus d’assemblage des communautés, processus qui maintiennent cette diversité. Ce travail est réalisé depuis de nombreuses années en écologie et reste d’actualité vu l’absence de consensus quant à l’importance relative des processus d’assemblage. Cette thèse s’inscrit dans la continuité de ce travail fondamental en utilisant une approche intégrative innovante, qui aborde de manière multi-échelle trois types de diversité : diversité taxonomique, fonctionnelle et phylogénétique. Nos résultats questionnent sur l'importance du filtrage environnemental quant aux propriétés hydrologiques et chimiques des sols, et sur celle des interactions biotiques dans l’assemblage de la communauté étudiée. Par ailleurs, nos résultats suggèrent que les distributions d’espèces puissent être influencées par la dynamique forestière en lien avec les chutes d’arbres et donc avec la disponibilité en lumière. Enfin, nous avons mis en évidence l’importance de la limitation de dispersion. / Tropical forests are a biodiversity hotspot, with the coexistence of numerous species until a fine spatial scale. Particularly, 16.000 tree species coexist in Amazonia, 1.800 in Frenche Guiana and between 120 and more than 200 tree species per hectare. However, there are some uncertainties in maintaining diversity in regard to global changes. Hence before predicting the diversity evolution face of global changes, fundamental studies are needed to understand which assembly processes are involved in the maintenance of diversity. These fundamental studies still relevant given the lack of consensus on the relative importance of assembly processes. This thesis is a continuation of these fundamental studies, using innovative integrative approach, at multi-scale, to address three types of diversity: taxonomic diversity, functional and phylogenetic. Our results challenge the importance of environmental filtering for hydrological and chemical properties of soils, versus the importance of biotic interactions on community assembly. Furthermore, our results suggest that species distributions could be affected by forest dynamics related to falling trees and therefore by light availability. Finally, we have highlighted the importance of dispersal limitation on community assembly.