Agentization of Two Population-Driven Models of Mathematical Biology

TL;DR

This paper introduces an agent-based model that reproduces and compares two key population models in mathematical biology, revealing their agreements and limitations under relaxed assumptions, especially in chaotic regimes.

Contribution

The paper presents an agent-based modeling framework that unifies and tests two classical population models, highlighting their differences and robustness in complex dynamics.

Findings

Agent-based model reproduces classical models accurately.

Models agree well in oscillating regimes but diverge in chaotic regimes.

Homogeneous mixing assumption limits extinction predictions.

Abstract

Single species population models and discrete stochastic gene frequency models are two standards of mathematical biology important for the evolution of populations. An agent based model is presented which reproduces these models and then explores where these models agree and disagree under relaxed specifications. For the population models, the requirement of homogeneous mixing prevents prediction of extinctions due to local resource depletion. These models also suggest equilibrium based on attainment of constant population levels though underlying population characteristics may be nowhere close to equilibrium. The discrete stochastic gene frequency models assume well mixed populations at constant levels. The models' predictions for non-constant populations in strongly oscillating and chaotic regimes are surprisingly good, only diverging from the ABM at the most chaotic levels.