A MATHEMATICAL MODEL OF HALDANE'S RULE.

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In 1940, H. J. Muller offered a now-classic explanation of Haldane's rule-the remarkable observation that, when only one hybrid sex is sterile or inviable in crosses between species, it is the heterogametic (XY or WZ) sex (Haldane 1922). Although geneticists had long recognized that hybrid sterility and inviability caused by incompatibilities between different loci (e.g., Dobzhansky 1937), Muller emphasized two points. First, he argued that hybrid sterility and inviability probably most often involve incompatibilities between X-linked loci from one species and autosomal loci from other [Haldane (1932) had implicated incompatibilities between the X and Y chromosomes]. More important, Muller emphasized that whereas some of the alleles causing these incompatibilities might be fairly dominant, others are more or less (1940, p. 203). In homogametic (XX) hybrids, these recessive alleles would be masked as heterozygotes whether they resided at autosomal or X-linked loci. Among heterogametic hybrids, however, any X-linked recessive (or partial recessive) would be fully expressed. If this allele happened to be incompatible with an autosomal allele from the other species, some hybrid sterility or inviability might result. Thus, Muller argued, it is not surprising that heterogametic hybrids sterile or inviable far more often than homogametic ones: dominant and recessive X-linked alleles affect heterogametic hybrids, whereas only the former can affect homogametic hybrids. Moreover, Muller (1940, p. 204) noted, this theory can also account for the observed large effect of the X chromosome on hybrid fitness (see Coyne and Orr 1989). Muller's theory has become the standard text-