The primary objective of the proposed research is to study the coevolution of social interactions together with the social framework within which such interactions take pace. Mathematical population genetics models constructed in terms of the dynamics of gene and genotype frequency evolution will be analyzed. In the first phase of the project, models of the separate evolution of cetain aspects of the social system will be studied. In the second phase, we will explore the simultaneous evolution of the social structure and the social interactions themselves. Specifically, the first phase involves the mathematical derivation of equilibrium states and local stability conditions near those equilibria in models depicting the evolution of certain aspects of the social system. We will study the evolution of both structural features, such as the level of inbreeding and sexuality, and the dynamics of genetically=based altruism controlled by one and two loci within particular, well-defined social contexts including partial sib-mating. In the second phase, two locus modifier models of the simultaneous evolution of structural and interactive aspects will be constructed and analyzed. In our models social interactions, such as altruism, will be determined by one locus and structurazl aspects, such as system of mating, controlled by a separate locus. Modifier models require detailed information on the identity and structure of polymorphic equilibria attained at each locus under independent evolution. This information is provided by the studies carried out under the previous project and in the first phase of the proposed project. The proposed research will allow the quantitative investigation of the effects of the selective pressures which arise as direct consequences of social interactions on the course of evolution of such interactions and the social structure as a whole. The study will serve to promote the synthesis of the heuristics of sociobiological theory and the strict mechanistic approach of mathematical population genetics.
