Stochastic spatial models in ecology: a statistical physics approach

Abstract

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.

18 pages, 12 figures. Included in the special edition "Statistical Theory of Biological Evolution" of Journal of Statistical Physics

References in corpus (29)

• Statistical physics of social dynamics
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Neutral Theory and Relative Species Abundance in Ecology
• Critical Coarsening without Surface Tension: the Voter Universality Class
• Does a Single Zealot Affect an Infinite Group of Voters ?
• On the Role of Zealotry in the Voter Model
• Genetic Demixing and Evolutionary Forces in the One-Dimensional Stepping Stone Model
• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• Statistical Mechanics of Ecological Systems: Neutral Theory and Beyond
• Heterogeneous Voter Models
• Nonlinear Voter Models: The Transition from Invasion to Coexistence
• Spatial effects on species persistence and implications for biodiversity
• Species lifetime distribution for simple models of ecologies
• Spatial Scaling in Model Plant Communities
• Species coexistence in a neutral dynamics with environmental noise
• Speciation-rate dependence in species-area relationships
• Impact of environmental colored noise in single-species population dynamics
• Quasi-Neutral theory of epidemic outbreaks
• What ecological factors shape species-area curves in neutral models?
• Heterogeneous Catalysis on a Disordered Surface
• Species abundances and lifetimes: from neutral to niche-stabilized communities
• The effect of quenched disorder in neutral theories
• A Multivariate Moran Process with Lotka-Volterra Phenomenology
• Eco-evolutionary Model of Rapid Phenotypic Diversification in Species-Rich Communities
• Spontaneously Broken Neutral Symmetry in an Ecological System
• Coexistence and invasibility in a two-species competition model with habitat-preference
• Absence of Detailed Balance in Ecology
• Coexistence in neutral theories: interplay of criticality and mild local preferences
• Neutral Aggregation in Finite Length Genotype space

Cited by in corpus (8)

• Evidence of scale-free clusters of vegetation in tropical rainforests
• Emergent spatial patterns of coexistence in species-rich plant communities
• Species exclusion and coexistence in a noisy voter model with a competition-colonization tradeoff
• Spatial patterns emerging from a stochastic process near criticality
• Delays in fitness adjustment can lead to coexistence of hierarchically interacting species
• Joint assessment of density correlations and fluctuations for analysing spatial tree patterns
• Interplay of spatial dynamics and local adaptation shapes species lifetime distributions and species-area relationships
• Emergence of vertical diversity under disturbance