Mean-Field Game for Gene Expression of Beetles

TL;DR

This paper applies mean-field game theory to model and analyze gene expression probabilities in beetle populations, considering competitive interactions between large and small beetles.

Contribution

It introduces a novel application of mean-field game theory to biological gene expression modeling in beetles, including proof of solution existence and uniqueness.

Findings

Model captures competitive effects on gene expression probabilities.

Simulation results demonstrate the dynamics over finite time.

Theoretical proof ensures model's mathematical validity.

Abstract

In this paper, we investigate the probability of the expression of genes that control the size of beetles under competitive relationships. We use the mean field game (MFG) theory in multiple populations to characterize the different competitive pressures of large and small beetles in the population, and simulate the probability of gene expression in finite time $[0, T]$. Therefore, we prove the existence and uniqueness of the solution of the equation under some assumptions.