A GENERALISED ANALYSIS OF DIALLEL CROSSES

Abstract

ASED on the methods of MATHER (1949) a technique of analysing diallel crosses B between homozygous parents has recently been developed by JINKS and HAY-MAN (1953; HAYMAN 1954; JINKS 1954). They are able to estimate the genetic pa-rameters, D1, H I , HZ and F (following MATHER'S notation) and their standard errors from second degree statistics, and, thence, to estimate such genetic compo-nents as dominance and allele frequency. The present paper details the extension of these methods of diallel analysis to crosses involving parental heterozygosity. The required experimental design comprises all possible crosses, including recip-rocals and selfing, among a number of individuals, and the proposed analysis esti-mates both the degree of parental heterozygosity and comparable genetic components of variation to those of the homozygous analysis. Before embarking on a full description of our method of analysis, a preliminary discussion of notation is necessary. In order to specify completely genotype fre-quencies in a population with three genotypes, two independent parameters are needed. Many schemes involving two such parameters are, no doubt, possible; two schemes will be detailed and a discussion of their relative merits will be useful. Thus, in terms of a one-gene, two-allele model, it is possible to specify the unknown parental population in terms of the parameters U and v (i.e. v = 1 -U), the allele frequencies, and f, the coefficient of inbreeding. Thus, Genotype Frequency A A u2 + uvf Aa 22441 -f) aa v2 + uvj Alternatively, the parental population can be specified as-Genotype Frequency w h e r e a + p + r = 1 A A A a aa The a@y system has been chosen to illustrate the development of the method of diallel analysis in preference to the uvf scheme, even though the latter has the ad-vantage of being in line with current longstanding notation (e.g. WRIGHT 1923; LERNER 1950). At important stages, however, both uvf and a& forms will be given. The two systems are, obviously, completely interchangeable, differing only in the form of presentation of the fundamental genetic variables. Thus, one feature of the a& system is the more obvious manner in which heterozygosity is specified as * Part of the cost of mathematical formulae has been paid by the GALTON AND MENDEL MEMO-RIAL FUND.