QUANTITATIVE INHERITANCE 199 



and, conversely, if no nonadditive variance is found, it can be concluded that there is 

 no dominance or epistasis: the genes are then said to act additively. Methods are 

 available for separating the different sorts of nonadditive variance. 538 



Because the amount of additive variance reflects the variation that is transmitted 

 from parent to offspring it is responsible for the resemblance between relatives, and 

 its estimation depends on the measurement of the degree of resemblance between 

 relatives. The most commonly encountered sorts of relationship are between offspring 

 and their parents, and between full or half sibs. It can be shown from theoretical 

 considerations that the degree of resemblance, measured as a regression or correlation 

 coefficient, in these relationships is related to the heritability as follows (the symbol 

 h 2 stands for the heritability) : 



Regression of: 



offspring on one parent = \h 2 



offspring on mean of two parents = h 2 



Correlation (intraclass) of: 



half sibs = ih 2 



full sibs > \h 2 . 



Thus, for example, to estimate the heritability from the resemblance between half 

 sibs it is only necessary to compute the intraclass correlation and multiply this by four; 

 or, from offspring and parents, to compute the regression of the offspring on the mean 

 of their two parents which itself estimates the heritability. A graphic illustration of the 

 resemblance between offspring and parents is shown in figure 35, with the regression 

 which estimates the heritability. 



There are, however, two complications which have an important bearing on the 

 choice of the relationship from which to estimate the heritability. The first concerns 

 only full sibs. The genetic cause of resemblance between full sibs is not confined to 

 the additive variance, and the correlation is augmented by part of the non-additive 

 variance if any is present. Therefore an estimate of the heritability from full sibs is, 

 strictly speaking, valid only in the absence of nonadditive variance. The error is, 

 however, seldom likely to be serious, and an estimate from full sibs is by no means to 

 be rejected as valueless on these grounds alone. The second complication is much 

 more important. It arises from the fact that there are often nongenetic causes for the 

 resemblance between certain sorts of relative, which may increase the regression or 

 correlation and lead to a serious overestimation of the heritability. These non- 

 genetic causes of resemblance are particularly prevalent in mammals. They arise from 

 maternal effects and circumstances generally referred to as common environment. 

 For example, large mothers tend to give more milk to their young than small mothers. 

 Therefore the offspring of large mothers tend to be larger than the offspring of small 

 mothers, and so the offspring tend to resemble their mothers in body size for purely 

 nongenetic reasons. Also, for the same nongenetic reason, offspring of the same mother 

 tend to resemble each other in body size. It is in the full-sib relationship that 



