Volume 1

Principles and practice of medical genetics / editors, Alan E.H. Emery, David L. Rimoin ; assistant editor, Jeffrey A. Sofaer ; editorial assistant, A.P. Garber ; foreword by Victor A. McKusick.

Date:
1983
Catalogue details

Licence: Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)

Credit: Principles and practice of medical genetics / editors, Alan E.H. Emery, David L. Rimoin ; assistant editor, Jeffrey A. Sofaer ; editorial assistant, A.P. Garber ; foreword by Victor A. McKusick. Source: Wellcome Collection.

    115/784 (page 87)
    Table 8.6 The different kinds of‘affected x affected’ and ‘affected x non-affected’ matings, their frequencies and the frequencies of ‘affected’ and ‘non-affected’ offspring expected at Hardy-Weinberg equilibrium. Allele A is completely dominant over a and produces the ‘affected’ phenotype. The frequencies of the different kinds of mating are taken from Table 8.3. Offspring frequency Mating Mating frequency Affected Non-affected AA x AA P 4 P 4 0 Affected X affected AA x Aa 4 P 3 q 4 P 3 ? 0 Aa x Aa 4pV 3pV P 2 ? 2 Total p\\ + 2q) P 2 ? 2 Relative 1+2 q ? 2 AA X aa 2pV 2pV 0 Affected x non-affected Aa x aa Apq i 2pq 3 2 pq* Total 2pq 2 2pq i Relative 1 ? Proportion of non-affected individuals among the offspring of: affected x affected matings = q 1 K\ + 2q + q 2 ) — [qi( 1 + q)] 2 affected x non-affected matings = ?/(! + q) zygote are distributed simply as the corresponding gene frequencies. In the random bred part, all three genotypes are distributed according to the Hardy-Weinberg expec tations. The overall genotype frequencies in the popu lation are therefore: Genotype Frequencies Inbred Random bred Total AA Fp G -F)p 2 P 2 + Fpq Aa (1 - F)2pq 2pq - 2Fpq aa Fq (1 ~F)q 2 q 2 + Fpq When the incidence, m, of individuals affected by a rare recessive disorder is known, together with the aver age coefficient of inbreeding, F, it is possible to estimate the gene frequency, q, and the incidence of carriers, h, because: m = q 2 + Fpq — q 2 + Fq and: h = ( 1 - F)2pq These equations have been used, for example, to calcu late the gene frequency and carrier incidence for albinism among the Hopi indians of Arizona (Woolf & Dukepoo, 1969). It also follows from the relationship m — q 2 + Fq that the incidence of a recessive disorder is approximately twice the incidence expected under random mating when F = q, three times when F = 2q and n times when F = ( n -1)^. The highest levels of inbreeding recorded for human populations are in the region of F = 0.04, but such extreme values are very rare (Cavalli-Sforza & Bod mer, 1971). Genetic heterogeneity in recessive disorders The offspring of consanguineous marriages are more likely to be homozygous at any given locus than the off spring of unrelated parents. The frequency of consan guineous marriages among parents of individuals with recessive disorders is therefore higher than for the pop ulation at large. Furthermore, the rarer the recessive allele, the greater the frequency of consanguinity among parents of recessive homozygotes compared with the gen eral population. This is illustrated in a recent study of a number of recessive disorders (Tchen et al, 1977). The majority of consanguinity can usually be attributed to first cousin marriages, so that the relationship between gene frequency and consanguinity can be expressed as: _ C G (1 - Cp) q \6C P -C G C P - 15C g where q is the recessive allele frequency at a single locus, and C G and Cp are the frequencies of first cousin marriages in the general population and among parents of affected individuals respectively. (Dahlberg, 1948). Given C G and Cp it is therefore a simple matter to arrive at an expected value for the incidence of a recessive disorder in the pop ulation, m E , on the assumption that the disorder can only be produced by homozygosity at one particular locus, because, at equilibrium, m E — q 2 . If only one locus is indeed involved, the observed incidence of affected individuals in the population, m Q , should approximate to m E . On the other hand, if the