Journal of Statistical Physics

, Volume 172, Issue 1, pp 44–73 | Cite as

Stochastic Spatial Models in Ecology: A Statistical Physics Approach

  • Simone PigolottiEmail author
  • Massimo Cencini
  • Daniel Molina
  • Miguel A. Muñoz


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 \(D = 2\) 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.


Neutral theory Voter model Community ecology Non-equilibrium phase transitions 



MAM is grateful to the Spanish-MINECO for financial support (under Grant FIS2013-43201-P; FEDER funds), as well as to J. Hidalgo, S. Suweis, A. Maritan, C. Borile for a long term collaboration on topics related to the content of this paper.


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Authors and Affiliations

  1. 1.Biological Complexity UnitOkinawa Institute of Science and Technology and Graduate UniversityOnnaJapan
  2. 2.Istituto dei Sistemi ComplessiConsiglio Nazionale delle RicercheRomeItaly
  3. 3.BCAM - Basque Center for Applied MathematicsBilbaoSpain
  4. 4.Departamento de Electromagnetismo y Física de la Materia, and Instituto Carlos I de Física Teórica y ComputacionalUniversidad de GranadaGranadaSpain

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