MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
91 
parents light, one parent light and one medium, one light and one dark, we reach the 
following results :— 
Parents’ eye-colour. 
Children, actual. 
Light-eyed children, calculated. 
Total. 
Light-eyed. 
Exclusive 
inheritance. 
Ancestral law with 
knowledge of parents 
and grandparents. 
Both light .... 
355 
334 
355 
321 
Light and medium . 
215 
170 
161 
160 
Light and dark . . 
211 
107 
105 
117 
Here the exclusive inheritance leads us to misplace thirty-two and the ancestral 
law thirty-three children. The evidence, therefore, of the correctness of the latter is 
hardly greater than that of the former. Indeed, if the former were modified for 
reversion, it would very possibly give better results than the latter. 
I am inclined accordingly to look upon eye-colour inheritance as an exclusive 
inheritance modified by reversion, and, to some extent, by assortative mating, rather 
than a mixture of exclusive inheritance with a slight amount of blending. In either 
case exclusive inheritance gives results like the above so closely in accord with the 
ancestral law that the latter might be supposed to hold. But, theoretically, I do not 
understand how the ancestral law is compatible with exclusive inheritance. 
Theoretically, we have values of parental, avuncular, and grand-parental correlation 
greater than the ancestral law would permit of, and these theoretical values are, on 
the whole, closer to observation, as we shall see in the sequel, than those given by the 
law of ancestral heredity. The following table gives the two systems :— 
Table I.—Theoretical Values of the Regression Coefficients. 
Relationship. 
Blended inheritance, 
ancestral law. 
Exclusive inheritance, 
absolute, no reversion. 
Parent and offspring. 
•3 
. 
•5 
Grandparent and offspring . . . 
•15 
•25 
Great-grandparent and offspring . 
•075 
T25 
Brethren . 
•4 
•35 to -5* 
Uncle and nephew. 
T5 
•25 
1 
Now, if exclusive inheritance be modified by reversion or assortative mating, or if 
blended inheritance be modified by “ taxation,”! then we shall get values different 
* This varies with the size of the family, 
t ‘ Roy. Soe. Proc.,’ vol. 62, p. 402, 
