Genetic analysis of hybrid zones: numbers of markers and power of resolution

Ecology, Dec, 1997 by William J. Boecklen, Daniel J. Howard

INTRODUCTION

Hybrid zones have enjoyed a renaissance of interest over the past 20 yr, as evolutionary biologists and ecologists have come to recognize that hybrid zones are ideal arenas in which to investigate the evolutionary processes that promote reproductive isolation (Littlejohn and Watson 1983, Howard 1986, 1993), stability of hybrid zones (Endler 1977, Moore 1977, Howard and Waring 1991), maintenance of species boundaries (Barton and Hewitt 1981, Harrison 1990, Howard et al. 1997), and the evolutionary mechanisms underlying host-parasite interactions (Manley and Fowler 1969, Sage et al. 1986, Whitham 1989, Boecklen and Spellenberg 1990, Le Brun et al. 1992, Moorehead et al. 1993, Fritz et al. 1994, Preszler and Boecklen 1994, Christensen et al. 1995, Gaylord et al. 1996).

As important as conceptual issues have been in fueling hybrid zone research (Barton and Hewitt 1985, Harrison 1990, 1993), no less important has been the development of molecular genetic techniques that generate taxon-specific markers, permitting genetic analyses of hybrid zones. For example, protein electrophoresis, restriction fragment length polymorphisms (RFLP), and random amplified polymorphic DNA (RAPD) have been used to characterize the physical structure of hybrid zones (Harrison and Arnold 1982, Cothran and Zimmerman 1985, Guttman and Karlin 1986, Howard 1986, Arnold et al. 1991), to characterize individuals as pure species or hybrids (Karlin and Guttmann 1981, Kocher and Sage 1986, Howard and Waring 1991, Chu et al. 1995), and to document patterns of gene exchange and introgression (Hunt and Selander 1973, Woodruff and Gould 1987, Keim et al. 1989, Whittemore and Schaal 1991, Chu et al. 1995, Howard et al. 1997). In addition, ecologists have used RFLP and RAPD markers to assign host individuals to a suite of finely divided taxonomic categories (F1 hybrid, backross 1, backcross 2, etc.) in order to relate host susceptibility to parasites to the evolutionary history of the host (Paige et al. 1991, Floate et al. 1993, Paige and Capman 1993, Fritz et al. 1994).

This effort on the part of ecologists (see also Arnold and Hodges 1995) has brought to a boil an issue that has been quietly simmering among hybrid zone workers for some time (Nason et al. 1992, Nason and Ellstrand 1993, Baird 1995), namely, how many species-specific markers are necessary to document the taxonomic status of individuals from a hybrid zone? Admittedly, the appropriate number of markers will vary according to the resolution required. For example, biologists attempting to separate F1 hybrids from parentals will require fewer markers than will biologists attempting to discriminate between a variety of backcross categories. With regard to the latter situation, Floate et al. (1994) suggest that upwards of 50 diagnostic markers may be necessary to provide reliable resolution between advanced backcrosses and parental individuals. The theoretical basis for this estimate is unclear, but the fact that standards are being suggested underscores the need for a critical examination of the problem.

In this paper, we present statistical models that relate the number of genetic markers examined to their power to discriminate between backcross, F1, and parental individuals. Specifically, our models give the conditional probability distributions for the number of markers indicating mixed ancestory as a function of the number of markers examined for various backcross categories under a scenario of unidirectional backcrossing. For example, our models give the probability that a backcross 1 individual will be confused as a pure species (or as an F1) as a function of the number of markers examined; the models do not give the probability that an individual is a backcross 1 given its complement of markers. In addition, the models do not consider backcross x backcross or F1 x backcross matings. Nevertheless, these models should provide hybrid zone workers a basis upon which to gauge the magnitudes of various classification errors. We consider two classes of markers: codominant markers, such as allozymes and RFLPs, and dominant markers, such as RAPDs.

Model assumptions

We make a number of simplifying assumptions: (1) backcrossing is unidirectional; (2) loci (markers) are independent and inherited in a Mendelian manner; (3) parental taxa are fixed for alternative phenotypes at diagnostic markers: (4) no F1 x backcross or backcross x backcross matings occur; and (5) all genotypes are equally fecund.

Case 1: Codominant markers

We start with a set of definitions. For parental taxa alternatively fixed at a number of loci, let N = number of loci, Z = number of heterozygous loci, i = backcross category, G = number of genotypes, and [[Phi].sub.i](z) = the relative frequency of genotypes with Z heterozygous loci in the ith backcross category.

Since the parental taxa are alternatively fixed (homozygous) at the N loci, the F1's are heterozygous at all N loci. Therefore, the number of recognizable genotypes comprising the first and subsequent backcross categories (hereafter BC-1, BC-2, etc.) is given by G = 2N. For BC-1 individuals, the probability is 0.5 that a given loci is heterozygous. The number of ways of producing BC-1 genotypes with Z heterozygous loci is given by [Mathematical Expression Omitted]. Thus, the relative frequency of BC-1 genotypes with Z heterozygous loci is given by