Asymmetric Variability: The Impact of Uneven Stochasticity on Competitive Dynamics

TL;DR

This paper develops a mathematical model to analyze how uneven stochasticity in demographic and environmental factors influences competitive outcomes and species persistence in ecological systems.

Contribution

It introduces an analytical framework for two-species competition considering different life histories and stochastic influences, advancing understanding of long-term ecological dynamics.

Findings

Derived expressions for fixation probability and time under various stochastic conditions.

Showed how environmental variability affects species coexistence and extinction risks.

Provided insights into community evenness influenced by stochasticity.

Abstract

Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for the random nature of birth and death processes (demographic stochasticity) as well as the variability of external conditions (environmental stochasticity). Recent studies have highlighted the importance of species life history, showing that differences in life history lead competing species to experience different levels of demographic stochasticity. Here, we propose a simple model of two-species competition with different life histories and derive analytical expressions for various properties (fixation probability, fixation time, absorption time, probability density) under a wide range of conditions, including migration, selection, and environmental stochasticity. These properties provide insights into the long-term outcomes of competition, such as species persistence, extinction risks, and the influence of environmental variability on the evenness of the community.