A Multivariate Moran Process with Lotka-Volterra Phenomenology

TL;DR

This paper introduces a new multivariate Moran process with frequency-dependent selection, establishing an analytical link to Lotka-Volterra models, enabling insights into ecological and genetic dynamics within finite populations.

Contribution

It develops a novel Moran process that corresponds analytically to Lotka-Volterra phenomenology, bridging finite population models with classical ecological dynamics.

Findings

Analytical correspondence between Moran process and Lotka-Volterra models

Enables study of ecological dynamics in finite populations

Applicable to community ecology, genetics, and game theory

Abstract

For a population with any given number of types, we construct a new multivariate Moran process with frequency-dependent selection and establish, analytically, a correspondence to equilibrium Lotka-Volterra phenomenology. This correspondence, on the one hand, allows us to infer the phenomenology of our Moran process based on much simpler Lokta-Volterra phenomenology, and on the other, allows us to study Lotka-Volterra dynamics within the finite populations of a Moran process. Applications to community ecology, population genetics, and evolutionary game theory are discussed.