Stochastic spatial models in ecology: a statistical physics approach

TL;DR

This paper reviews the application of statistical physics to spatial ecological models, focusing on neutral theory, critical phenomena at dimension D=2, and effects of non-neutral factors on biodiversity patterns.

Contribution

It connects spatial ecological models with non-equilibrium phase transition physics and discusses scaling laws and deviations caused by non-neutral effects.

Findings

Scaling laws at critical dimension D=2 are crucial for 2D ecosystems.

Spatial neutral models exhibit non-trivial critical behavior.

Non-neutral effects cause significant deviations from neutral theory predictions.

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.