A CONDITION FOR GROUP SELECTION TO PREVAIL OVER COUNTERACTING INDIVIDUAL SELECTION

The importance of group selection as an evolutionary force has been much debated (see Wilson, 1973; Maynard Smith, 1976; Wade, 1978, for recent critiques). Whenever a population is subdivided into groups of mating individuals (i.e., demes) between which there is complete or partial isolation, the differential extinction or proliferation of those groups becomes a possible force for directional genetic change, to be superposed on selection at the individual level. Of particular interest, and this is the problem which I address, is whether group selection can prevail over individual selection to bring about the evolution of an altruistic trait. An altruistic trait is here defined as a trait which is detrimental to the fitness of the individual who expresses it but which confers an advantage on the group of which that individual is a member in the form of, for example, a reduced probability of group extinction. Seminal papers on the subject are Haldane (1932) and Wright (1945). The basic problem of group selection is how the genetic differentiation of groups, a sine qua non for group selection to occur, can be maintained when many forces including group selection tend to diminish it (Slatkin, 1980). More concretely, in the haploid one-locus two-allele no mutation model which we analyze in this paper, where genetic differentiation of groups is generated in most part by random genetic drift and reduced partly by migration, are the parameter values, e.g., deme size, migration rate, etc. which need to be postulated to permit the evolution of altruism by group selection, of realistic magnitude? A related question is, what is the appropriate measure of genetic differentiation? There are differing definitions and formulations of group selection (see Maynard Smith, 1976; Wade, 1978; Uyenoyama, 1979). The model which I analyze is based on the models of Levins (1970) (see also Boorman and Levitt, 1980 p. 289-32 1), Eshel (1972), and Levin and Kilmer (1974). The intuitive concept of a group is a partially isolated set of mating individuals with potential continuity across many individual lifetimes. Some examples are a "clan" of hyenas, an "unit group" of chimpanzees, a "settlement" of Pleistocene hominids. In addition to the aforementioned authors, Boorman and Levitt (1972, 1973) and Cohen and Eshel (1976) also appear to adopt this view of a group. However, in some recent models (D. S. Wilson, 1975; Matessi and Jayakar, 1976), a "group" has but an ephemeral existence, the group structure being dissolved each generation to form a random mating whole. The model actually analyzed by Uyenoyama (1979) also has this property. The life cycles of many species do indeed comply with this pattern, particularly if the "group" is identified with a sibship. Such models should perhaps be referred to as hierarchically-structured to distinguish them from the "traditional" (Wade, 1978) group models. With respect to the origin or maintenance of the between-group variation so necessary for group selection to be effective, the models of Levins (1970), Eshel (1972), and Levin and Kilmer (1974) invoke random genetic drift; those of Wilson (1975), Matessi and Jayakar (1976), Cohen and Eshel (1976), and in effect Boorman and Levitt (1972, 1973) depend on the "founder" effect; and Uyenoyama's model (1979) is new in that it introduces I Contribution No. 1387 from the National Institute of Genetics, Mishima, Shizuoka-ken, 411 Japan.