Deviations from Hardy-Weinberg Frequencies Caused by Assortative Mating in Hybrid Populations

Abstract

The conventional formulas for genotype frequencies in a hybrid population H produced by interbreeding from ancestral populations P(1) and P(2) involve only one hybrid parameter M, equal to the fraction of alleles derived from P(2). For the one-parameter model to be accurate, all individuals of H must have probabilities for alleles determined by one and the same M. When H contains subpopulations that have different values of M, the correct genotype frequencies can be predicted by use of two parameters: (i) M(H), the average of M for all individuals of H and (ii) eta(H), defined like the eta devised by C. A. B. Smith for testing the Hardy-Weinberg Law and computed with a formula like G. R. Price's eta, which involves assortative mating covariance-in this case for the M values of the parents of H. If parents of H have equal average M values for males and females, and mate at random, eta(H) vanishes. For perfect assortative mating, eta(H) is the variance of M for H. As for Smith's eta, eta(H) provides a test of fit of prediction to observed that is sensitive to signs of deviations. Using eta(H) with T. E. Reed's data for Gm in Oakland, California Negroes, his one-parameter fit ("good" by his chi-square test) is significantly rejected (P = 0.04). A simultaneous good fit of Reed's Gm data and his Duffy data results (chi-square, 1 df = 0.88, P > 0.30) from the use of previously published values of 0.23 and 0.047 for M(H) and eta(H). It is concluded that Reed's conclusion that these values were in error is itself in error, as is also his view that differences between M values from different genes and deviations from frequencies expected within genes are not likely to give significant information about variance of M.