CYTONUCLEAR DISEQUILIBRIA IN HYBRID ZONES USING RAPD MARKERS.

Random Amplified Polymorphic DNA (RAPD) (Williams et al. 1990; Welsh and McClelland 1990; Cruzan and Arnold 1993; Thorpe et al. 1994) markers can be a useful tool for genetic mapping, DNA fingerprinting, and for studies in population genetics (Williams et al. 1990; Arnold et al. 1991; Hadrys et al. 1992; Marsolais et al. 1993; Milligan and McMurry 1993). In particular, RAPDs can be used to sample a genome for polymorphisms to characterize population structure even in organisms with low heterozygosity at allozyme loci. When codominant nuclear markers are combined with cytoplasmic markers in hybrid zone studies, their associations can, in principle, be used to examine: (1) the directionality of crosses between conspecifics, (2) levels of gene flow, (3) degree of assortative mating between conspecifics, (4) age of reproductive barriers, and (5) mechanisms of selection (Arnold 1993). Here we examine the utility of RAPD markers in hybrid zone studies and present statistical tools for one cytonuclear disequilibrium measure (D3) when RAPD markers are in use. One simple example will illustrate the important role of cytonuclear disequilibrium measures to understand processes at work in hybrid zones. After confirming that the RAPD markers analyzed are simple Mendelian traits, Cruzan and Arnold (1993, 1994) found significant cytonuclear disequilibria in a hybrid zone of irises. The existence of cytonuclear disequilibrium can have many causes, but they argued that natural selection or the mating system was the explanation. Without the initial characterization of cytonuclear disequilibrium, further field studies to measure natural selection and assortative mating would not have been initiated (Cruzan and Arnold, in press). As the use of RAPDs becomes more widespread, it is clear that there is a general need to analyze efficiently this kind of multilocus data (Snow and Lewis 1993). Likelihood methods provide one such approach and have desirable large sample properties (Rao 1973) for a broad array of models. In previous analyses of cytonuclear disequilibria in hybrid zones it has been assumed that codominance holds between alleles at nuclear loci in the cytonuclear system (Asmussen et al. 1987; Arnold et al. 1988; Asmussen et al. 1989; Asmussen and Arnold 1991; Arnold 1993). In the first part of this paper, methods of analyzing cytonuclear disequilibria based on data collected from nuclear RAPD markers simultaneously with cytoplasmic markers will be examined. In the second part, the efficiency of RAPD markers relative to codominant markers to estimate cytonuclear disequilibria will be considered. This analysis is appropriate for any study which consists of at least one dominant nuclear marker with a cytoplasmic marker. The primary phenotypic data collected on RAPD alleles are scores of each individual as either dominant or recessive, i.e., the band(s) is (are) either seen (dominant) or not seen (recessive) on the gel. For practical purposes this screening system dictates that only four phenotypic classes are seen, instead of the usual six genotypic cell classes as in a codominant analysis (Asmussen et al. 1987; Arnold 1993). Nevertheless, it will be shown that only these four classes are necessary for estimating the nuclear and cytoplasmic allele frequencies as well as the one cytonuclear disequilibrium measure (D3) associated with them. For this statistical model, only two assumptions will be made. (1) The two-locus phenotypes of individuals in a sample are independently and identically distributed, and (2) the probabilities that an individual has a particular phenotype are as given in Table 1.