The basic problem in analyzing the genetics of human variation is to find a means of quantitating the degree of resemblance between related individuals from their overt characteristics. Geneticists have tackled this problem by partitioning the variation in observed characteristics—that is, in the phenotype (from the Greek phainein ''to show'') of individuals in a population—into components attributable to hereditary causes and those attributable to environmental causes. If the relative sizes of the hereditary and environmental components were known (or could be determined), it should be possible, on the further assumption of Mendelian inheritance, to predict the degree of resemblance between related individuals.
These ideas were first put on a quantitative footing in 1918 by Ronald Fisher13 who proposed the phenotypic variance (VP) be considered as the sum of the variance of genetic factors (VG) and the variance embracing all of the environmental factors (VE). He partitioned the genetic variance into three subcomponents: those due to the additive effects of all allelic genes (VA), the variance due to dominance effects (VD), and the variance due to interactions between loci (VI). The total phenotypic (observed) variance in Fisher's model is thus
VA is a function of the difference between homozygotes—it is usually the most important of the subcomponents that comprise VG both biologically and numerically. VD refers to deviations of the heterozygotes from the mean of the two homozygotes. VI is less well understood, and D.S. Falconer suggested that VI contributed only a small amount to the total VG and neglecting it was not likely to introduce a serious error (see Chapters 8 and 914).
Fisher also showed that certain quantitative relationships could be defined from correlations and regressions between relatives of different degrees on the
Table 5.1 Phenotypic Resemblance Between Relatives of Different Degrees3
Relatives Regression (b) or correlation (t) Covariance
Offspring and midparent b = VA/ VP /VA
Fullsibs t = [/Va +'/4Vd + V£]/Vp /2Va +/VD + Ve aSource: Adapted from Falconer, 14 Table 9.4. For a more complete account of the theoretical basis for these relationships, see Falconer, Chapters 8 and 9.14
supposition of Mendelian inheritance (Table 5. 1 ). From Table 5. 1 , the resemblance between relatives of different degrees expressed by the variances composing VP is apparent. For instance, the regression of offspring on one parent is twice the correlation between half-siblings, and the correlation between full siblings (in the absence of dominance and environmental contributions) is twice the correlation between half-siblings. Intuitively, both of these relationships are reasonable.
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