Evolutionary Games with Affine Fitness Functions: Applications to Cancer

TL;DR

This paper explores how affine fitness functions influence evolutionary game dynamics, including stochastic models, and applies these insights to tumor-normal cell interactions, revealing strategies that promote tumor growth.

Contribution

It introduces the use of affine fitness functions in evolutionary games and applies this framework to model tumor cell interactions and growth strategies.

Findings

Affine fitness functions modify replicator dynamics and stochastic models.

Interaction with normal cells and increased fitness promote tumor establishment.

The model identifies effective tumor strategies in a three-strategy game.

Abstract

We analyze the dynamics of evolutionary games in which fitness is defined as an affine function of the expected payoff and a constant contribution. The resulting inhomogeneous replicator equation has an homogeneous equivalent with modified payoffs. The affine terms also influence the stochastic dynamics of a two-strategy Moran model of a finite population. We then apply the affine fitness function in a model for tumor-normal cell interactions to determine which are the most successful tumor strategies. In order to analyze the dynamics of concurrent strategies within a tumor population, we extend the model to a three-strategy game involving distinct tumor cell types as well as normal cells. In this model, interaction with normal cells, in combination with an increased constant fitness, is the most effective way of establishing a population of tumor cells in normal tissue.