The N-Gene Model for Evolutionary Games

Abstract: In this study, we develop a novel evolutionary model that incorporates Mendelian genetics, continuous strategies, and the potential for multiple genes to contribute to a single phenotypic trait. The evolution of altruistic behavior, which confers benefits to others at a cost to the individual, remains a fundamental question in evolutionary biology. While previous models have investigated the conditions favoring the emergence and stability of altruism, they have often employed simplifying assumptions, such as single-gene inheritance and discrete strategies. We employ a modified dictator game as the framework for evolutionary interactions and explore the stability of altruistic behavior under various conditions. Our primary result demonstrates that when considering heterozygous genes, altruism can be evolutionarily stable at cost-to-benefit ratios exceeding unity, even with initially low frequencies of altruists in the population. This finding contrasts with the case of homozygous genes, where altruism is only stable at cost-to-benefit ratios greater than 2. The generality of our approach allows for its application to a diverse range of evolutionary games and interactions, providing a powerful tool for investigating the emergence and maintenance of social behaviors and personality traits. Our results contribute to the understanding of the evolutionary mechanisms underlying altruism and underscore the importance of incorporating genetic complexity in evolutionary models. This work has implications for the study of social evolution and the genetic architecture of complex behavioral phenotypes.