( 399 ) 
XV. — The Correlation between Relatives on the Supposition of Mendelian Inherit- 
ance. By R. A. Fisher, B.A. Communicated by Professor J. Arthur 
Thomson. (With Four Figures in Text.) 
(MS. received June 15, 1918. Read July 8, 1918. Issued separately October 1 , 1918.) 
CONTENTS. 
1. 
The superposition of factors distributed inde- 
15. Homogamy and multiple allelomorphism 
416 
pendently 
402 
16; Coupling 
418 
2.. 
Phase frequency in each array 
402 
17. Theories of marital correlation ; ancestral 
3. 
Parental regression 
403 
correlations . . - 
419 
4. 
Dominance deviations ..... 
403 
18. Ancestral correlations (second and third 
5. 
Correlation for parent ; genetic correlations . 
404 
' theories) . 
421 
6. 
Fraternal correlation . . . . . 
405 
19. Numerical values of association 
421. 
7. 
Correlations for other relatives 
406 
20. Fraternal correlation . . . . . 
422 
8. 
Epistacy 
408 
21. Numerical values for environment and domi- 
9. 
Assortative mating 
410 
nance ratios ; analysis of variance 
423 
10. Frequency of phases 
410 
22. Other relatives 
424 
11. 
Association of factors 
411 
23. Numerical values (third theory) 
425 
12. 
Conditions of equilibrium . . . 
412 
24. Comparison of results . . 
427 
13. 
Nature of association . . 
413 
25. Interpretation of dominance ratio (diagrams) . 
428 
14. Multiple allelomorphism 
415 
26. Summary 
432 
Several attempts have already been made to interpret the well-established 
results of biometry in accordance with the Mendelian scheme of inheritance. It 
is here attempted to ascertain the biometrical properties of a population of a more 
general type than has hitherto been examined, inheritance in which follows this 
scheme. It is hoped that in this way it will be possible to make a more exact 
analysis of the causes of human variability. The great body of available statistics 
show us that the deviations of a human measurement from its mean follow very 
closely the Normal Law of Errors, and, therefore, that the variability may be 
uniformly measured by the standard deviation corresponding to the square root 
of the mean square error. When there are two independent causes of variability 
capable of producing in an otherwise uniform population distributions with standard 
deviations oq and o" 2 , it is found that the distribution, when both causes act together, 
has a standard deviation v^i 2 + cr 2 2 - If is therefore desirable in analysing the 
•causes of variability to deal with the square of the standard deviation as the 
measure of variability. We shall term this quantity the Variance of the normal 
population to which it refers, and we may now ascribe to the constituent causes 
fractions or percentages of the total variance which they together produce. It 
is desirable on the one hand that the elementary ideas at the basis of the calculus 
of correlations should be clearly understood, and easily expressed in ordinary 
language, and on the other that loose phrases about the “ percentage of causation,” 
TRANS. ROY SOC. ED1N., VOL. LII, PART II (NO. 15). 62 
