Physiological Genetics, Ecology of Populations, and Natural Selection

PHYSIOLOGICAL GENETICS, ECOLOGY OF POPULATIONS, AND NATURAL SELECTION* SEWALL WRIGBT, ScJD. The purpose of the present paper is to consider the mathematical framework of the theory of evolution at a succession of levels of complexity . We shaU begin with the very inadéquate theory that can be based on properties assigned the separate genes. At the second level we take cognizance of the basic conclusion of physiological genetics that the effects of genes depend on those with which they are associated. It is still assumed that the selective values of total genotypes are constant within a population of given density in a given environment. At the third level we accept from ecology the fact that the members of a population may interact in such ways that the relative selective values of total genotypes may, after all, be functions of their relative frequencies. At the fourth level we return to physiological genetics to recognize that the deterministic processes considered at the first three levels can carry the population toward only one—and that not, in general, the highest—of a very large number of selective peaks. We are led to consider the possibilities of passage from peak to peak by the joint action of deterministic and random processes. At the fifth level we return to the ecology of populations to consider the consequences of subdivision of the species into partially isolated demes. The problems of species cleavage and the evolution of higher categories are excluded. Discussion will be restricted to populations of sexuaUy reproducing diploids. I. Systems of Gene Frequencies The theoretical genetics of populations may be considered to have begun with Pearson's (1) demonstration that the 1:2:1 MendeHan ratio tends to maintain itself indefinitely in a large random-breedingpopulation * Paper No. 737 from the Department of Genetics, University of Wisconsin, Madison, Wisconsin. The author will present this paper at the Darwin Centennial Celebration to be held at the University of Chicago, November 18-24, 1959. 107 derived from F2 of a cross. A few years later Hardy (2) and Weinberg (3) independently pointed out that any array of gene frequencies at a locus (HqiiAn, where Au is a particular allele at locus Ai and qn is its proportional frequency)1 tends to remain unchanged in a large self-contained population in the absence of disturbing factors such as mutation and selection, and thus that the frequency of the zygotes resulting from random mating becomes stable immediately after attainment of equality of gene frequencies in the sexes in the array (ZqnAn)2 for one locus. If mating is not at random, the zygotic array, in the absence of other disturbing factors, is given by (1 — F)[ZqIiAi,]2 + FZfanAnAu), where F is the inbreeding coefficient, denned as the correlation between uniting gametes with respect to additive effects (4, 5, 6). Random mating will be assumed here unless otherwise stated. It was noted by Weinberg (7) that two pairs of aUeles approach randomness of combination gradually under random mating. Robbins (8) showed that the deviation from random combination falls off in each generation by the mean recombination percentage and thus by 50 per cent for loci in different chromosomes. A fuU demonstration of the behavior of any number of loci in the absence of disturbing factors was given by Geiringer (9). There is gradual approach to the array ?(S's are measured by perpendiculars to the latter, the q's to the former. Figure 8—(P1A1 + p2A2 + P3A3Xq1B1 + q2B2 + q3B3), S? =?,S9= 1. This system is bounded by six triangular prisms. The ^'s are measured by perpendiculars to the three that lack A1, A2, and A3, respectively, and the q's by ones to the three that lack Bi, B2, and B3, respectively. 109 Figure 9—(P1A1 + P2A2 + P3A3)I(I - q)b + qB][(l - r)c + t(7],S?~ 1. This system is bounded by three cubes and four triangular prisms. Figure 10-i(l - p)a + pA][(i - q)b + qB][(i - r)c + rC][(i - s)d + sD]. This is a four-dimensional rectangular co-ordinate system with sides of unit length. There are eight bounding cubes. Four alleles at each of a dozen loci constitute...