Spontaneously Broken Neutral Symmetry in an Ecological System

TL;DR

This paper investigates how ecological systems can exhibit spontaneous symmetry breaking, leading to biodiversity and stability, by extending neutral theory to include density-dependent birth and death rates.

Contribution

It introduces a model where species-symmetric birth and death rates depend on population density, resulting in spontaneous symmetry breaking and stable biodiversity.

Findings

Stationary states with biodiversity emerge from density-dependent dynamics.

Neutral symmetry can be spontaneously broken in ecological models.

The model aligns with empirical biodiversity patterns.

Abstract

Spontaneous symmetry breaking plays a fundamental role in many areas of condensed matter and particle physics. A fundamental problem in ecology is the elucidation of the mechanisms responsible for biodiversity and stability. Neutral theory, which makes the simplifying assumption that all individuals (such as trees in a tropical forest) --regardless of the species they belong to-- have the same prospect of reproduction, death, etc., yields gross patterns that are in accord with empirical data. We explore the possibility of birth and death rates that depend on the population density of species while treating the dynamics in a species-symmetric manner. We demonstrate that the dynamical evolution can lead to a stationary state characterized simultaneously by both biodiversity and spontaneously broken neutral symmetry.