... Equation, a profound insight into the nature of selection and the basis for the modern theories of kin and group selection; (ii) the theory of games and animal behavior, based on the concept of the evolutionarily stable strategy; and (iii) the modern interpretation of Fisher’s fundamental theorem of natural selection, Fisher’s theorem being perhaps the most cited and least understood idea in the history of evolutionary genetics. This paper summarizes Price’s contributions and briefly outlines why, toward the end of his painful intellectual journey, he chose to focus his deep humanistic feelings and sharp,

Kin selection arguments, based on Hamilton's (1964) concept of inclusive fitness, provide... of recipient, or other life history components of fitness, the fitness effects on each component are weighted by reproductive value. We illustrate this technique first in a homogeneous population, with examples of group competition and partial dispersal behaviour, and then in a class-structured population, with examples of sex allocation and altruism between age classes.

Introduction Why would an individual sacrifice its own direct reproduction to aid a member of another species? Williams (1966) suggested that mutualistic aid of this sort is unlikely to evolve by natural selection. The problem is that, even if the recipient returned benefits to the donor species, the original donor individual would rarely receive those benefits. Hamilton (1972) and Wilson (1980, 1983a) agreed with Williams's logic but argued that, in many natural systems, limited dispersal keeps individuals of both species in close proximity. Thus aid given to another species is likely to be returned to the original donor (Trivers, 1971) or its immediate neighbors. Because, under limited dispersal, the neighborhood constitutes a kin group, returned benefits enhance the inclusive fitness of the original donor. The Hamilton--Wilson argument focused on genetic variability in the donor, with kin or group selection as the mechanism by which mutualism can evolve. Although there is

showed that a tradeo# between virulence and the host's ability to purge itself of infection (recovery rate) can favor the evolution of intermediate levels of virulence. Finally, Bremermann and Pickering (1983) and Knolle (1989) have shown that competition among parasites within a host can favor the evolution of increased virulence. In this case the group of coinfecting parasites may gain by sparing the host, but competition among parasites within the group favors high transmission and greater virulence. I present a simple model for the evolution of virulence. This model is useful in two ways. First, specific quantitative predictions are given for the relationship between the genetic variability among coinfecting strains and the evolution of virulence. This is important because genetic variability, rather than the number of coinfecting strains (Bremermann and Pickering 1983; Knolle 1989), determines how virulence evolves. In addition, genetic variability of parasites within a h

This technical problem of the joint e#ect on mothers and mates can be handled in one of two ways. First, we can maintain the strict definition of g' as the breeding value transmitted by a recipient rather than the breeding value of the whole o#spring. In this case, each phenotype must be evaluated for its e#ect on the breeding values transmitted directly by mothers, and for its e#ect on the breeding values transmitted directly by fathers. The second approach treats g' as the breeding value of the whole o#spring, which includes the contribution from the mother and her mate. This automatically accounts for the joint e#ect on mothers and mates without the need to bring fathers into the analysis. The second method is commonly used in the literature, and I used it implicitly in the previous section

A dynamical (time-dependent) evolutionary population model featuring two levels of organization (individuals and groups) is studied. The dynamical model is represented by a partial differential equation (PDE) that governs the state of the environment as it evolves in time. The PDE is derived from an underlying stochastic model of two-level selection based on evolutionary birth-death processes. The PDE can be solved numerically to find evolutionary trajectories and equilibrium configurations. A number of important examples of social evolution fit nicely into the modeling framework described here, including virulence, social insect colonies, hunter-gatherer tribes, and other examples where distinct groups of individuals undergo internal evolution, compete with other groups, occasionally fission, and eventually die. The present work is unique in the literature on social evolution because it provides a full solution of a continuous and time-dependent mathematical model, allowing the modeler to predict and study the evolutionary trajectories and equilibrium configurations of the process. The full dynamical solution is possible because complete model generality (e.g., the Price equation) is sacrificed for a slightly less general framework with a more fully exploitable mathematical structure. The analysis here sheds light on some of the philosophical issues surrounding kin selection and group selection explanations of social evolution, but the primary purpose of

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