HERITABLE AND NON-HERITABLE DIFFERENCES 



The size of the covariance relative to some standard gives a 



measure of the strength of the association between the relatives. The 



standard taken is that afforded by the variances of the two separate 



distributions, in our case of fathers' and daughters' heights. We may 



compare the covariance with either of these variances separately, 



and we do this by calculating regression coefficients which have the 



W W 



form, — - (regression of daughters on fathers) or, less usefully, ~~ 



(regression of fathers on daughters). We may also compare the 

 covariance with the two variances at once in a correlation coefficient 



W^ 



found as — =^=. Were the correlation coefficient to have its 



maximum value of i, it would signify a complete association, a full 

 determination of a daughter's height by her father. Independence of 

 father's and daughter's height would be shown by a coefficient of o, 

 because, of course, W^y would itself then be o. Values between 

 o and I show partial determination of a daughter's height by her 

 father. The coefficient actually observed in man by Galton was just 

 under 0-5, for reasons which we shall see later. 



Heritable and non-Heritable Differences 



In 1900, when Mendel's results first received wide 'attention, 

 Galton and his successor Pearson had already established by means 

 of correlation studies the heritable nature of continuous variation 

 in a variety of characters in man, in dogs and even in sweet peas. 

 The results were used as the foundation of the so-called Law of 

 Ancestral Heredity. Their approach suffered, however, from one 

 weakness which we can now see to have been fatal to any theory 

 of hereditary transmission. While Galton had an idea that the 

 hereditary materials might be particulate, neither he nor his fol- 

 lowers ever grasped the distinction between the determinant and 

 the effect, the genotype and the phenotype. 



Mendel supphed the missing principle of the determinant and 

 demonstrated its vahdity in his peas. He was, however, dealing with 

 discontinuous variation and it was held by the biometrical school 

 that his principles would not apply to continuous variation. Indeed 

 it was considered that the segregation of mendelian differences could 



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