Stochastic Spatial Models in Ecology: A Statistical Physics Approach Muñoz Martínez, Miguel Ángel Pigolotti, Simone Cencini, Massimo Molina, Daniel Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions accounting for general empirical patterns in communities of competing species. However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several open problems, limiting the quantitative understanding of spatial biodiversity. In this review, we discuss the state of the art in spatial neutral theory. We emphasize the connection between spatial ecological models and the physics of non-equilibrium phase transitions and how concepts developed in statistical physics translate in population dynamics, and vice versa. We focus on non-trivial scaling laws arising at the critical dimension of spatial neutral models, and their relevance for biological populations inhabiting two-dimensional environments. We conclude by discussing models incorporating non-neutral effects in the form of spatial and temporal disorder, and analyze how their predictions deviate from those of purely neutral theories. 2021-10-04T11:50:51Z 2021-10-04T11:50:51Z 2018-07 info:eu-repo/semantics/article Muñoz, MA; Pigolotti, S; Cencini, M; Molina, D. Stochastic Spatial Models in Ecology: A Statistical Physics Approach, Journal of Statistical Physics 172(8) http://hdl.handle.net/10481/70625 10.1007/s10955-017-1926-4 spa http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España