The concept of inclusive fitness plays a key role in much of sociobiology. Yet most theoretical studies concerning the evolution of social behavior circumvent inclusive fitness by mobilizing the concept of frequency dependent individual fitness. Given certain assumptions, it is shown that models based on these two different concepts are dynamically equivalent. The models do differ, however, in bookkeeping methods which are advantageous under different circumstances. A knowledge of these circumstances should prove of value to students of social behavior. It is then shown that evolution acts according to an adaptive landscape based on Hamilton's inclusive fitness in the absence of strong selection and inbreeding. This yields an inclusive fitness analogue to much of traditional population genetics. For example, heterozygote superiority in inclusive fitness yields stable polymorphisms, while intermediate dominance results in fixation of one of the alleles. When individuals do not affect one another's fitnesses, the inclusive fitness topography collapses to one based on individual fitness. A general rule for the evolution of social behavior under intermediate dominance is shown to yield Hamilton's Rule as a special case. Next, a general model for examining the evolution of social behavior is developed which, unlike inclusive fitness models, does not require that benefits received be linear functions of the number of social donors encountered. The subsocial route for the evolution of eusociality in haplodiploid organisms is then examined within the context of this model. Nonlinearities render conditions for frequency independent fixation or loss of sister-helping alleles more stringent than expected from models based on the assumption of linear benefits. In particular, both stable polymorphisms and frequency dependent selective thresholds for sister-helping behavior may commonly obtain.

Errata is pasted onto front end-paper. / Bibliography: leaves 166-171. / ix, 171 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis considers the question of fixation probabilities and mean absorption times for alleles when a population is divided into a number of subpopulations with asymmetric migration between the subpopulations. The emphasis of the thesis is on small populations and conservation genetics. Results have important implications for management of remnant subpopulations in order to maintain genetic diversity when migration between the remnant subpopulations is not symmetric. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1999?

The aim of this study is to place a wide variety of two-phenotype frequency-dependent selection models into a unified population-genetic framework. This work is used to illuminate the possible genetic constraints that may exist in such models, and to address the question of evolutionary modification of these constraints. The first part of Chapter 1 synthesizes from the literature a general framework for applying a genetic structure to a simple class of two-phenotype models. It shows that genetic constraints may prevent the population from achieving a predicted phenotypic equilibrium, but the population will equilibrate at a point that is as close as possible to the phenotypic equilibrium. The second part of Chapter 1 goes on to ask whether evolutionary modification of the genetic system might be expected to remove these constraints. Chapter 2 provides an example of the application of the framework developed in Chapter 1. It presents re-analysis of a model for the evolution of social behavior by reciprocation (Brown et al. 1982). The genetic results of Chapter 1 apply to this model without modification. I show that Brown et al. were unnecessarily restrictive in their assumptions about the types of genetic systems that support their conclusions. Chapter 3 discusses some models for the evolution of altruism that do not fit the assumptions of Chapter 1, despite their two-phenotype structure. These models violate the fundamental assumption of Chapter 1, this being the way in which individual fitness is derived from the behavioral fitnesses. The first part is a complete, in-depth analysis of diploid sib-sib kin selection. I show that some results from the basic model can be used, provided the behavioral inclusive fitness functions are substituted for the true behavioral fitnesses. The second part is an analysis of the validity of the concept of behavioral structure, as introduced by Michod and Sanderson (1985). I show that this concept is flawed as a general principle. Chapter 4 extends the basic model to the case of sex-allocation evolution. I show how many of the central results of sex-allocation theory can be derived more simply using a two-phenotype framework.