SINGLE LOCUS CLINES.

Abstract

Bazykin (1969) found the form of a single locus cline arising from viability selection against heterozygotes when two populations, initially fixed for alternative alleles, come into contact in a continuous, one-dimensional habitat. Here I have generalized Bazykin's results for the case of postmating reproductive isolation in the form of fertility selection as well as premating reproductive isolation. Analysis of natural zones of hybridization has become a very popular field of research in recent years. This analysis provides insights into the nature of species, the development of barriers to gene exchange, the strength and mode of natural selection, the number of genes involved, and the dynamics of the speciation process (Endler 1977; Barton and Hewitt 1981, 1985, 1989; Harrison and Rand, 1989; Harrison 1990, 1993; Barton and Gale 1993). Many hybrid zones are thought to be maintained by a balance between selection and dispersal. Selection could act in many different ways, of which a very common one is selection against hybrids, recombinants, and rare phenotypes (Barton and Hewitt 1981, 1985, 1989; Barton and Gale 1993). A classical model for a hybrid zone in a one-dimensional, continuous habitat arising from selection against heterozygotes at a single locus was proposed and solved by Bazykin (1969). Mallet and Barton (1989) have shown that Bazykin's cline describes hybrid zones arising in a simple model of selection against rare phenotypes. Further studies (e.g., Slatkin 1973, 1985; Nagylaki 1975, 1976, 1994; Barton 1979a,b, 1983, 1986; Barton and Begtsson 1986; Mallet and Barton 1989; Barton and Gale 1993) of more complex models have advanced the understanding of hybrid zones in many directions. The purpose of this note is to generalize Bazykin's results for the case of fertility selection and premating reproductive isolation. These are very common types of reproductive isolation mechanisms which, however, were left outside the scope of recent developments in the hybrid zone theory. At the end of this note, I will show that single locus clines arising from fertility and viability selection against heterozygotes also describe hybrid zones arising in some models of selection against rare phenotypes.