Deviations from Hardy-Weinberg Frequencies Caused by Assortative Mating in Hybrid Populations
William Shockley
Abstract
The conventional formulas for genotype frequencies in a hybrid populationH produced by interbreeding from ancestral populationsP1 andP2 involve only one hybrid parameterM, equal to the fraction of alleles derived fromP2. For the one-parameter model to be accurate, all individuals ofH must have probabilities for alleles determined by one and the sameM. WhenH contains subpopulations that have different values ofM, the correct genotype frequencies can be predicted by use of two parameters: (i)MH, the average ofM for all individuals ofH and (ii) etaH, 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 theM values of the parents ofH. If parents ofH have equal averageM values for males and females, and mate at random, etaH vanishes. For perfect assortative mating, etaH is the variance ofM forH. As for Smith's eta, etaH provides a test of fit of prediction to observed that is sensitive to signs of deviations. Using etaH 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 forMH and etaH. It is concluded that Reed's conclusion that these values were in error is itself in error, as is also his view that differences betweenM values from different genes and deviations from frequencies expected within genes are not likely to give significant information about variance ofM.
Keywords: assortative Caucasian-Negro mating, variance of Caucasian admixture, California Negroes
Full text
PDF
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- GLASS B., LI C. C. The dynamics of racial intermixture; an analysis based on the American Negro. Am J Hum Genet. 1953 Mar;5(1):1–20. [PMC free article] [PubMed] [Google Scholar]
- Price G. R. Extension of the Hardy-Weinberg law to assortative mating. Ann Hum Genet. 1971 May;34(4):455–458. doi: 10.1111/j.1469-1809.1971.tb00259.x. [DOI] [PubMed] [Google Scholar]
- Price G. R. Selection and covariance. Nature. 1970 Aug 1;227(5257):520–521. doi: 10.1038/227520a0. [DOI] [PubMed] [Google Scholar]
- Reed T. E. Caucasian genes in American Negroes. Science. 1969 Aug 22;165(3895):762–768. doi: 10.1126/science.165.3895.762. [DOI] [PubMed] [Google Scholar]
- Reed T. E. Critical tests of hypotheses for race mixture using Gm data on American Caucasians and Negroes. Am J Hum Genet. 1969 Jan;21(1):71–83. [PMC free article] [PubMed] [Google Scholar]
- Reed T. E. The population variance of the proportion of genetic admixture in human intergroup hybrids. Proc Natl Acad Sci U S A. 1971 Dec;68(12):3168–3169. doi: 10.1073/pnas.68.12.3168. [DOI] [PMC free article] [PubMed] [Google Scholar]