Related Experiment Video
Updated: Jul 3, 2026

Following the Dynamics of Structural Variants in Experimentally Evolved Populations
Published on: February 3, 2023
A stochastic model of evolutionary dynamics with deterministic large-population asymptotics
1Department of Mathematical Sciences, University of Colorado Denver, Campus Box 170, P.O. Box 173364, Denver, CO 80217-3364, USA. Burt.Simon@cudenver.edu
Abstract:
An evolutionary birth-death process is proposed as a model of evolutionary dynamics. Agents residing in a continuous spatial environment X, play a game G, with a continuous strategy set S, against other agents in the environment. The agents' positions and strategies continuously change in response to other agents and to random effects. Agents spawn asexually at rates that depend on their current fitness, and agents die at rates that depend on their local population density. Agents' individual evolutionary trajectories in X and S are governed by a system of stochastic ODEs. When the number of agents is large and distributed in a smooth density on (X,S), the collective dynamics of the entire population is governed by a certain (deterministic) PDE, which we call a fitness-diffusion equation.
Related Concept Videos
Modeling with Differential Equations
Population Growth
Exponential Equations for Modeling Growth
Hardy-Weinberg Principle
Genetic Drift
Exponential Equations with Logarithms: Problem Solving

