198 PHYSIOLOGIC GENETICS 



dark. Suppose, for example, that the degree of genetic determination is thought to 

 be 40 per cent, which is a reasonable figure to guess for many quantitative characters; 

 how many animals must be measured to obtain an estimate with a standard error of, 

 say, 10 per cent? Herecr g = 0.1, and 1 — g = 0.6. Entering these values in equation 

 (5) gives N = 144. Therefore about 144 animals must be measured in each group, 

 or 288 altogether, to obtain a result that would read g = 40 + 10 per cent. To 

 take another example showing how the relationship might be used the other way 

 around, suppose a character is difficult to measure and it is decided that the greatest 

 number of animals that could be measured would be 40, twenty of each group. Would 

 it be worth while to try to estimate the degree of genetic determination? Reading 

 graph (b) in figure 34 from the upper and right-hand margins, cr g /(l — g) is 

 approximately 0.44. So, if g were 40 per cent, its standard error would be 

 0.44 x 0.6 = 0.26. Thus the expected result of the experiment would be g = 40 + 26 

 per cent. The estimate would not be significantly different from zero, and therefore 

 even demonstrating the existence of any genetic variation at all could not be expected. 

 From all this it will be evident that the degree of genetic determination cannot be 

 precisely estimated without a very considerable expenditure of effort, especially if the 

 character is only weakly heritable. But an estimate with a standard error even as 

 high as 20 per cent would not be entirely without interest, and, if suitable data could be 

 accumulated from routine measurements made for the other purposes, information of 

 great interest could be obtained. 



HERITABILITY 



The degree of genetic determination, although of great intrinsic interest, is of 

 little practical use. It cannot be used to predict the speed of progress to be expected 

 if selection were applied to the character. For this prediction it is necessary to deter- 

 mine the heritability of the character. The determination of the heritability involves 

 the further partitioning of the genetic component of variation into two parts, although 

 the method of partitioning is now entirely different. The need for the additional 

 partitioning arises from the mode of hereditary transmission — from the fact that gametes 

 are haploid and that genes, and not genotypes, are transmitted from parents to offspring. 

 The idea of heritability is therefore of fundamental genetic importance. The genetic 

 variation is of two sorts. Part of it may be thought of as arising from the genes con- 

 sidered singly, instead of paired in the diploid genotype. This component of the genetic 

 variation is called the additive variance. The heritability is the ratio of the additive 

 variance to the total phenotypic variance ; or, in other words, the fraction of the total 

 variance made up by additive variance. The other part is the additional variation 

 that arises from the genes coming together in pairs to form genotypes. This component 

 is called the nonadditive variance. The cause of nonadditive variance, in terms of the 

 properties of individual genes, is dominance and interaction (epistasis) between different 

 loci. If there is no dominance and no epistasis there can be no nonaddititive variance; 



