334 AN INTRODUCTION TO MODERN GENETICS 



a group of individuals; they may be a group all possessing some char- 

 acteristic, such as blue eyes, or they may be all the individuals we can 

 take the trouble to collect. Then let measurements be made of some 

 character, such as height. It will in general be found that intermediate 

 values of the measurement are the more frequent, and if we plot 

 against a measurement X the frequency with which it occurs, we 

 obtain a typical bell-shaped frequency curve with its highest point in 

 the middle of the range and falHng off towards the extremes at each 

 end. The variance is a measure of the am.ount of scatter in measure- 

 ments of this kind; it is related to the area enclosed under the curve 

 and it is calculated from the squares of the deviations of individual 

 measurements from the average. 



Correlation coefficients are measures of the degree of relationship 

 between pairs. Suppose we measure the heights of a set of brothers; 

 then a high correlation (i.e. nearly i) means that there is a strong 

 tendency for tall boys to have tall brothers, and short ones short 

 brothers; a correlation of o means there is no connection between the 

 height of a boy and his brother, while a negative correlation coeffi- 

 cient means that tall boys tend to have short brothers. 



Perhaps the simplest use of correlation coefficients in genetics is to 

 calculate the correlation between different relatives, e.g. between 

 fathers and sons, parents and offspring, etc. This procedure has been 

 carried out in great detail by the biometric school, led by Galton and 

 Karl Pearson. They found that the correlation between offspring and 

 parent, for many characters, was about a half, while between offspring 

 and grandparent it was about a quarter. At first the conclusion was 

 drawn that characters which show continuous variation are inherited 

 by blending inheritance, that is, that discrete hereditary units were not 

 involved and that no segregation and recombination occurred.^ It was 

 supposed that each parent contributed half the genetic constitution of 

 the child, which was a sort of average of its father and mother. A 

 considerable controversy developed on this question between Pearson, 

 who argued on the basis of statistical averages, and Bateson, who 

 upheld MendeHsm on the basis of observations of individual matings . 

 The issue was finally settled when it was shown, partly by Pearson 

 himself and finally by Fisher,^ that the data of the biometricians could 

 be entirely harmonized with the requirements of Mendelian theory. It 

 is possible to calculate the magnitude of the correlation between various 

 relatives from MendeUan principles,^ but only if certain assumptions 



^ Cf. Pearson and Lee 1903. ^ Fisher 1918. ^ Cf. Hogben 1933a. 



