STATISTICS OF SEXUAL ISOLATION

Sexual isolation is the tendency ofindividuals to avoid mating with those ofanother strain, race, or species. Isolation has been measured in Drosophila using a variety ofmethods and indices of isolation (e.g., Spiess, 1970; Parsons, 1973 for reviews). Statistical examination helps us evaluate the biological validity of these methods and indices. The multiple choice method, a common experimental design, counts the instances of four types of matings when males and females of two races are placed together. This is diagrammed in Table 1. If the like-type (homogamic; cells A and D of the diagram) matings occur more frequently than expected by chance, the races are said to exhibit isolation. Statistics that are commonly used to measure such isolation are the Joint Isolation Index (Joint 1) and Chi-square (Malogolowkin-Cohen et al., 1965; Zouros and d'Entremont, 1980). Two additional statistics which can measure isolation are Yule's Vand Yule's Q(Bliss, 1967). These statistics differ in their properties (e.g., bias) and their utility for measuring isolation. How they differ and which are best depend on several factors. Wattiaux (Wattiaux, 1964; Wattiaux and Elens, 1970; Elens et al., 1973) documented and discussed changes in measures ofisolation over the time course of experiments (up to 120 min) with Drosophila melanogaster. The relative numbers ofhomogamic and heterogamic matings change; thus, measured isolation values depend on how long observations are continued. This may in part be due to changes with time in the sexual interactions in the pool of available mates, but part of this can be measurement bias due to sampling from the pool without replacement. Sampling without replacement occurs in most isolation experiments because, even ifmated pairs are not physically removed, their copulation and subsequent refractory period for further mating biologically remove them from the pool of available mates. The ratios of available types, and the probability of matings, can change due to this removal, even though the presumed intrinsic isolation, or choice, probabilities remain unchanged. Manly (1980) discusses problems ofestimating such intrinsic choice probabilities when sampling without replacement. Another source of error in isolation estimates is the effect of vigor differences between races. Two hypothetically distinct properties th\1t determine whether matings occur are choice and vigor. We define vigor to be the likelihood that a male or female will engage in courtship and copulation, regardless ofits partner. We define choice as the joint likelilIood that a given male and female combination will mate, once they have initiated courtship. Sexual isolation occurs when choice is exercised between races, but vigor is usually considered distinct from isolation. In multiple choice experiments, vigor is measured from the marginal totals for a sex (F1 vs. F 2, and M, vs. M 2 in Table 1). Choice, or isolation, is measured from the interaction term (A + D vs. B + C). Care should be exercised in relating these two population properties to underlying biological processes. A final source oferror considered here is the effect that unequal pools ofmates may have on estimating intrinsic choice values. Unequal pools ofmates are used in frequency-dependence experiments to establish whether scarcity or overabundance ofa race will influence the intrinsic choice values. We examine here the ability of four statistics to distinguish choice from vigor or unequal pools, and their sensitivity to sampling without replacement. The statistics, Joint I, Yule's V, Chi-square, and Yule's Q,are tested using simulated multiple choice experiments. They are compared under conditions of no intrinsic isolation, symmetrical isolation, asymmetrical isolation, vigor differences, and unequal pools ofmates. The effects of sampling without replacement from a limited pool of mates are compared with asymptotic measures (i.e., sampling from an infinite pool).