Matrix games between full siblings in Mendelian populations

Area of Science:

• Evolutionary Biology
• Genetics
• Game Theory

Background:

• Understanding the interplay between genetic inheritance and evolutionary game dynamics is crucial for explaining social behaviors.
• Familial selection, where survival depends on interactions within families, presents a unique context for studying evolutionary strategies.

Purpose of the Study:

• To develop a unified model integrating evolutionary matrix game theory with Mendelian genetics.
• To define genotype dynamics and analyze evolutionary stability in sexual diploid populations.
• To investigate conditions for the evolutionary stability of specific genotypes under familial selection.

Main Methods:

• Developed a mathematical model combining evolutionary matrix game theory and Mendelian genetics.
• Defined genotype dynamics to track changes in genotype frequencies.
• Analyzed evolutionary stability of genotype distributions and homozygote populations.
• Applied the model to familial selection scenarios, including the prisoner's dilemma and donation game.

Main Results:

• Formal definition of evolutionary stability for genotype distributions implies stability of equilibrium points.
• Payoff matrices and genotype-phenotype maps jointly determine the stability of homozygote populations.
• In familial selection, the 'coordinated' case allows for stable cooperators, defectors, or both, depending on genetic and payoff interactions.
• In the 'anti-coordinated' case, stable cooperators are not possible.
• Hamilton's rule predicts stability in the donation game, precluding bistability.

Conclusions:

• Familial selection, influenced by sibling interactions and genetic makeup, can drive the evolution of cooperation.
• The relationship between genotype, phenotype, and payoff structure is key to determining evolutionary outcomes.
• The model provides a framework for classifying genotype dynamics based on interaction types and stability properties.