Nonequilibrium Statistical Physics in Ecology: Vegetation Patterns, Animal Mobility and Temporal Fluctuations

This thesis focuses on the applications of mathematical tools and concepts brought from nonequilibrium statistical physics to the modeling of ecological problems. The first part provides a short introduction where the theoretical concepts and mathematical tools that are going to be used in subsequent chapters are presented. Firstly, the different levels of description usually employed in the models are explained. Secondly, the mathematical relationships among them are presented. Finally, the notation and terminology that will be used later on are explained. The second part is devoted to studying vegetation pattern formation in regions where precipitations are not frequent and resources for plant growth are scarce. This part comprises two chapters. • The first one studies the case of mesic savannas. These systems are characterized by receiving an intermediate amount of water and by a long term coexistence of layer made of grass and shrubs interspersed with irregular clusters of trees. Aminimalistic model considering only long range competition among plants and the effect of possible fires is presented. In this later case, adult trees protect the growth of juvenile individuals against the fires by surrounding them and creating an antifire shell. This introduces a local facilitation effect for the establishment of new trees. Despite the range of facilitative interactions is taken to its infinitesimally short limit, the spectrum of patterns obtained in models with competitive and facilitative nonlocal interactions is recovered. Finally, considering the stochasticity in the birth and death dynamics of trees, the shapes of the structures reproduce the irregularity observed in aerial photographs of mesic savannas. • The second chapter investigates the formation of patterns in arid regions, that are typically more regular than in mesic savannas. Previous studies attribute the origin of these structures to the existence of competitive and facilitative interactions among plants acting simultaneously but at different spatial scales. More precisely, to the combination of a short-range facilitation and a long-range competition (scale-depedent feedback ). The