Spatial Stochastic Modelling of Ecosystems

The modelling of spatial effects in ecological systems has often been overlooked for its intrinsic complexity, both from a computational and a mathematical point of view. But real ecological systems are spatially extended and there is proved empirical evidence that this strongly influences their dynamics. At its core this thesis analyses a simple spatial extension of a birth death process with linear rates. In the regime of large fluctuations the model is amenable to analytical treatment, which, for example, leads to an explicit formula for the probability distribution of the number of individuals living in a given volume in any dimension. Comparison to simulated data shows excellent agreement where expected. Despite the lack of time reversibility at the individual level, at the community level the dynamics of the model satisfies time reversibility. These results are applied to infer the spatial empirical distributions of tree species in two lowland tropical forest inventories. In fact, the model allows to link observations of some of the most important ecological descriptors into a unified framework, and the predictions are shown to match data well. An extension of the model is also considered that aims at giving a first account of the effect of environmental fluctuations on large scale patterns. Analytic formulas are obtained, and comparisons to simulated data show again excellent agreement. The conclusions drawn from the present work can help to shed a light on the effects of spatial dispersal on large communities of living organisms and on the mathematical analysis of spatial stochastic processes. This could ultimately lead to the design of more effective conservation strategies, and to further unveil the delicate laws governing the coexistence of living organisms in complex natural systems.