MAINTENANCE OF THE THREE SEX CHROMOSOME POLYMORPHISM IN THE PLATYFISH, XIPHOPHORUS MACULATUS.

Abstract

The color and sex chromosome polymorphisms of the poeciliid fishes present classical problems in ecological genetics. (See Gordon, 1947, 1951; Gordon and Gordon, 1957; Haskins et al., 1961, 1970; Kallman, 1973, 1975.) One such polymorphism is the presence of three sex chromosomes in the platyfish, Xiphophorus maculatus. In all but two natural populations of this species, there are three types of females: WY, WX, and XX, and two types of males: XY and YY (Kallman, 1973). This species is also polymorphic at several sex-linked and autosomal pigment loci. The sex chromosomes have not been identified cytologically but the many visible markers segregating with the segments determining gender and the constancy of the sex ratios in broods produced by the various possible matings attest to their existence. Although recombination in low frequency (1%) is observed between the W and Y (Gordon, 1937) and the X and Y (MacIntyre, 1961) chromosomes in the laboratory, the W chromosomes of females from natural populations invariably possess the dull colored wildtype alleles at the sex-linked pigment loci (Kallman, 1970, 1973), while the X chromosomes possess both wildtype and colored -alleles at such loci. Kallman argues that predators can more easily. see brightly colored individuals and that there is natural selection against the XX females carrying colored alleles. In addition, wildtype X chromosomes will be selected against in males, as brightly colored poeciliid males have higher mating success than dull colored males (Fisher, 1930; Sheppard, 1953; Haskins et al., 1961; and Endler, 1978). Such selection for coloration never occurs against wildtype W chromosomes as they do not appear in males. Subsequently, Borowsky and Kallman (1976) found that dull colored, wildtype WY females had more offspring than such females with sex-linked color patterns which suggests that there may be an intrinsic sex limited disadvantage to the colored alleles. On the basis of these observations it is reasonable to conclude that the WY and WX females have higher fitnesses than both colored and wildtype XX females. Kallman (1970) suggested that the sex chromosomal polymorphism is transitory due to the higher fitnesses of WY and WX females and thus that the X chromosome would disappear from natural populations. However, this hypothesis ignores the effects of different male fitnesses, which were not investigated. By analysis of a mathematical model we have derived the necessary and sufficient conditions for the maintenance of the sex chromosomal polymorphism. Our model assumes non-overlapping generations and random mating, with the possibility that some males mate more often than others being reflected in higher fitness values. Let Pwy, Pwx, and Pxx be respectively the frequencies after selection of the WY, WX, and XX females (as fractions of the total population of males and females). Similarly let the frequencies of the XY and YY males be qxy and qyy so that Pwy + Pwx + Pxx + qxy + qyy = 1. Each genotype also has an associated fitness value