# A mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory

## TL;DR

This paper establishes a theoretical connection between the stochastic Lotka-Volterra model and various models in population genetics and game theory, enabling new analytical insights into species extinction dynamics.

## Contribution

It provides precise conditions under which the stochastic Lotka-Volterra model maps onto Moran models with different selection regimes, bridging ecological and genetic modeling frameworks.

## Key findings

- Derived conditions for mapping SLVC to Moran models
- Calculated extinction probabilities and times
- Linked ecological competition to genetic and game-theoretic models

## Abstract

The relationship between the M-species stochastic Lotka-Volterra competition (SLVC) model and the M-allele Moran model of population genetics is explored via timescale separation arguments. When selection for species is weak and the population size is large but finite, precise conditions are determined for the stochastic dynamics of the SLVC model to be mappable to the neutral Moran model, the Moran model with frequency-independent selection and the Moran model with frequency-dependent selection (equivalently, a game-theoretic formulation of the Moran model). We demonstrate how these mappings can be used to calculate extinction probabilities and the times until a species' extinction in the SLVC model.