The Detection of Sympatric Sibling Species Using Genetic Correation

Four models are presented describing zygotic frequencies a t two loci for one or two sympatric but genetically differentiated populations or “gamodemes.” Linkage disequilibrium within gamodemes is allowed in two of the models. Maximum likelihood criteria are used to fit the models to the observed numbers of zygotes in a sample. A fitting-testing sequence for choosing a best model is described and the power of the test is analyzed. The statistical characteristics of the genetic parameter estimates were examined by simulation studies. In general, estimates were reliable when allele frequency differences between gamodemes were greater than 0.30 at both loci. This method may be used to study the population structure of samples with fewer heterozygotes than expected for Hardy-Weinberg populations, including the detection and genetic description of sibling species having overlapping ranges.-An example is given for Drosophila longicornis and D. propachuca, two sibling species within the mulleri complex of the repleta group which have been studied in detail using more conventional techniques. The reanalysis using the approach derived in this paper confirmed the reproductive isolation of these two species, and hinted at the possibility of further subdivision within D. propachum. ANY biologists intuitively feel that a species designation ought to reflect the Mreproductive cohesion of its member populations and their genetic discontinuity with populations of other species. Although taxonomic decisions based on morphological differences between populations usually achieve these standards for some groups of organisms, morphological distinctions become more difficult with decreasing anatomical complexity. New complexes of sibling species (morphologically similar or identical natural populations that are reproductively isolated, MAYR 1963) are frequently distinguished on the basis of inherited Supported by AEC Contract AT-(40-1)-4023. Public Health Service Training Grant GM-00337; this work was presented in partial fulfillment of Ph D. Public Health Service Career Development Award GM 47350 1 equlrements Genetics 86: 665-678 July, 1977. 666 M. E . M A K E L A A N D R. H. RICHARDSON characters other than gross morphology, especially among insects and other invertebrates. PIELOU (1975) had emphasized that the detection of cryptic species is of central importance in the study of ecology and natural history, as well as in the genetic study of populations and their evolution. Clearly, more sensitive and efficient indicators of divergence and reproductive isolation are needed. Abundant variation occurs at many loci coding for soluble enzymatic proteins assayed through electrophoresis. As a taxonomic tool, electrophoretic variation has several recommending features, including the simultaneous assay of many enzyme systems per individual and simple Mendelian inheritance of relative electrophoretic mobilities (“electromorphs”) without dominance for most loci. Upon isolation of two populations, various directed and random forces act to differentiate allele frequencies between them at all loci. When these divergent populations occur sympatrically and are sampled as a single population, the result is a deficiency of heterozygotes compared to expectations based on HardyWeinberg equilibrium (WAHLUND 1928; NEI 1965) and is known as the “Wahlund effect.” Loci which diverge completely are diagnostic (AYALA and POWELL 1972) and can be used to group individuals. Other loci, while less divergent between populations so that individual identity is less certain, can be used to characterize a fragmented population (MAKELA 1975). When two populations are sufficiently different at several loci, a serious reevaluation of their conspecificity is warranted. In this paper we describe a method for determining the number of distinct populations (gamodemes) within a sample. If two gamodemes differ in allelic frequencies at two loci, they have zygotic frequencies distinct from those of a single population. Statistical procedures presented here are based on these differences and can be used to ( 1 ) test for gene pool heterogeneity, (2) estimate the proportion of each population in a sample, and (3) estimate electsomorph frequencies at one or more loci for each population. Problem The term “gamodeme” was proposed to denote a deme composed of individuals that can all interbreed within the limits of the breeding system (GILMOUR and HESLOP-HARRISON 1954). In our model we assume a gamodeme to be a group of sexually reproducing diploid organisms that mate at random with respect to two loci, A and B. We construct two allele classes by combining multiple alleles into two groups. Dominance and selection are assumed to be absent. Let ai be the frequency of the first allele class ( A ) at the A-locus and ( 1 aj) be the frequency of the other allele class ( a ) in the j-th gamodeme. For the B-locus, pi is similarly defined. Coupling and repulsion phases of the double heterozygote, AaBb, are not distinguished, giving a total of nine zygotic classes. Linkage disequilibrium within the j-th isolate is 6, = f A B 3 ‘ f a b l f A l l l f a B 3 ( 1 ) where AB, is the frequency of the AB gamete in the j-th gamodeme. When two gamodemes are sampled in proportions p and (1 p ) , the observed gametic fre66 7 DETECTION O F SYMPATRIC GAMODEMES FIGURE 1.-The mixing of two isolated gene pools (gamodemes) gives a sample with averaged allele frequencies but with gamete frequencies different by an amount A = p(1 p ) (011 4 (P1P z ) . quencies are the sums of the weighted gametic frequencies in each gamodeme. These are presented in Figure 1. where a = pa1 + (1 p)az P = pP1 + (1 PIP2