On Niche Width and Genetic Variation, Parametrical Problems, and Gene Pool Differentiation in Drosophila

In a recent paper (Steiner 1977) I had reason to believe that I had found a significant positive regression of genic heterozygosity in Hawaiian Drosophila, as measured by electrophoretic studies, on the number of plant species used for oviposition by these drosophiloid species. The statistic of interest was generated using the method outlined in chapter 6 of Snedecor and Cochrane (1969) and confirmed using the programmed technique outlined in the statistics program catalogue which accompanies the TI-59 Texas Instrument Calculator. Hallett (1979) has criticized this approach, saying in effect that by partitioning out the variation due to deviations from regression, the observed relationship may no longer be significant. Hallett's contention and analysis is well taken and holds true especially for cases where bivariate normal distributions are involved. In this case, however, neither of the information indices are normally distributed and curves for the data would tend to be heavily skewed to the right; thus it probably would have been better to use a nonparametric test to examine the expectation that a relationship might exist in these data. Such a test is offered by the rank correlation utilizing Kendall's tau (X-) as a measure of significance (Snedecor and Cochrane 1969, p. 194). The test measures the degree of concordance between two rankings and is a more appropriate statistic since basic assumptions underlying the regression analysis (which was originally used to determine only if there was a significant relationship present) may be violated. For example, in the standard linear regression for . each X selected there should be a normal distribution of Y from which a sample is drawn at random. In this case, table 1 in Steiner (1977) shows that six Y values can be obtained for an X equal to one oviposition site with the Y values ranging from 1% to 14.4% heterozygosity. There is no indication that a normal distribution exists in this small subset, or in the subsets involving two or three oviposition sites. The subset involving five oviposition sites may have a normal distribution but the set is too small to draw any conclusion. Thus the application of Kendall's T, with a null hypothesis that no relationship exists between genic heterozygosity and number of plant oviposition sites in Drosophila, yields a nonparametric value of T = 0.468 which is significant at the 5% level. Correction for tied values, however, yields X = 0.30 (P = .10) which only approaches significance (see Kendall 1948, pp. 25-36). Interestingly, by dropping the two samples which deviate strongly in this data set, those for D. engyochracea and D. recticilia, the uncorrected X then equals 0.623, which is significant at the 1% level. It is these two individuals, which contribute about one-third of the total variance in the deviations, which I discussed briefly in Steiner (1977). Hallett's concern is appreciated, since it pinpoints the problem in statistical approach and has forced a reevaluation of the data. In studies such as these, drawing genetic values from different populations of different species only com-