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The Influence of Selection and Assortative Mating on the Ancestral 

 and Fraternal Correlations of a Mendelian Population. 

 By E. C. Sxow, M.A., D.Sc, Biometric Laboratory, University College, 

 London. 



(Communicated by Prof. Karl Pearson, F.R.S. Received March 1, — Read 

 March 28, 1912.) 



The actual effects of selection and assortative mating on the variability and 

 correlation of organs have long been known. The general numerical 

 resemblance between the correlations found for gametic characters on the 

 Mendelian hypothesis for random sampling and mating and those computed 

 from actual data is now also well established, though the fundamental 

 difficulties in the way of reconciling the deductions from that hypothesis with 

 the distributions and regressions actually obtained for, say, coat-colour in 

 mice, have not been diminished. It is of importance, therefore, to ascertain 

 what conclusions can be reached as regards the numerical effects of selection 

 and of assortative mating on the basis of the Mendelian mechanism, and to 

 this end an analytical investigation was entered upon on a more general 

 and rigorous foundation than any which have previously been used to attempt 

 to solve the problem. 



Dealing first with the correlations for gametic characters. In general 

 terms, it was established that the effect of taking a selected sample instead 

 of a random one from a population showing a zero coefficient of assortative 

 mating would be to find the ancestral and fraternal correlations within that 

 sample less than those of a random sample, so long as the variability was 

 diminished by the selection. If an ancestor be selected, the correlations 

 between that ancestor and descendants diminish in geometrical progression. 

 On the whole, selection of parents appears to affect the correlations between 

 them and their offspring to a greater extent than it affects the relationship 

 between those offspring themselves. For all ancestral cases the regressions 

 appear to be more stable properties of a particular population than the 

 corresponding correlations ; frequently the regression of offspring on ancestor 

 is the same as for a random sample, though the correlation is changed. The 

 investigation also brought out that the value - 5 in each case for the fraternal 

 and parental correlations obtained when random samples of a general 

 Mendelian population are dealt with does not depend upon the fact that the 

 samples are random ones, but upon the fact that for such a population the 

 frequency of the heterozygote is twice the geometric mean of the frequencies 



