Surfaces of Selective Value Revisited

Provine, in his generally favorable discussion of my shifting-balance theory of evolution, severely criticized the concept of "surfaces of selective value" (1986, p. 307). I think that he was looking for something more mathematical than was intended. Professor E. M. East, as organizer of the program of the Sixth International Congress of Genetics (held in 1932 in Ithaca, New York), had asked me to present a brief, nonmathematical account of the views on evolution that I had presented in a long (63-page) paper in 1931. I agreed to do this. Most early geneticists thought of the phenotype as if it were a mosaic of unit characters, each determined by a single locus, with effects as conspicuous as those that they used in their experiments. They thought of alleles as having constant relative selective values. The consequences of this assumption were worked out most exhaustively by Haldane in a series of papers beginning in 1924 and summarized in 1932. In addition, he worked out less fully some of the consequences of various other assumptions, also summarized in this book. The early viewpoint changed with the demonstration by Nilsson-Ehle (1909) and East (1910) that quantitative variation usually depends on the total effect of multiple minor factors. This implied that numerous uperior combinations could exert more or less similar effects and that the selective value of any gene depends on the rest of the genome. Two superior combinations that differ by two or more gene replacements may both be superior to the intermediate ones. A similar situation arises whenever different combinations enable individuals to surmount the difficulties oftheir environment indifferent ways. The occurrence of "multiple selective peaks" in the array of genotypic selective values in either of these cases does not depend on strict or even approximate additivity of the effects of the component genes. There may be gene interactions (epistasis) of various sorts. My 1931 paper had been devoted to working out mathematically the allelic frequencies for pairs of alleles at a single locus under various conditions (summarized in 1932, fig. 3). (For ease of reference, the figures in the 1932 paper are reproduced here, with the permission of Genetics, with the original figure numbers and legends.) The evolutionary implications of multiple loci, each with multiple alleles, were discussed verbally in terms of what I later called the shifting-balance theory, first proposed in an abstract (1929). In answer to Professor East's request, I attempted to construct a pictorial representation ofthe indicated evolutionary processes. I encountered at once a