A. D. Darbishirb 
9 
parents which has taken place in this as in all other hybridising experiments. These 
results are extremely complex, and cannot be predicted without long and difficult 
enquiry ; some of them have, however, been examined by Pearson (" Mathematical 
Contributions to the Theory of Evolution," Phil. Trans., Vol. 200 A, 1902), who shows 
that " sexual and natural selection can sensibly modify the intensity of inheritance 
as measured by the coefficient of correlation ; the former tends to raise, the latter 
to lower its intensity " (p. 43). 
The original statement embodied by Galton and Pearson in the Law of 
Ancestral Heredity relates to a population in which two conditions hold, namely, 
(i) all mating is at random ; in other words the correlation between the characters 
of male and female mates in any generation is 0, and (ii) all the individuals 
in the generation have an equal chance of producing young. Now it is a fact, 
which is often forgotten, and on which I wish to lay great emphasis, that in the 
experiments described, and in all cases where two races or breeds are systemati- 
cally crossed, the first of these conditions is deliberately destroyed, and a process of 
assortative mating is performed, such that the coefficient of correlation between 
parents is given the value — 1 instead of zero. Thus, in the present case, if we 
know that the father of the hybrid is an albino, we may certainly infer that the 
mother is not, and vice versa. The effect of this perfect negative correlation 
between the parents must be to reduce the coefficient of correlation between 
parents and offspring to 0 (i.e. to destroy the correlation altogether) in every 
case in which the results of reciprocal crosses are identical. 
This may be readily seen by a simple illustration : if we call waltzers with 
more colour fi, and with less a, and the albino parents A, and if we write the 
female first, the possible unions are : 
aA, 
PA, 
Aa , 
Afi. 
And if reciprocal crosses produce the same results, the offspring of aA and Aa 
will be identical, as will those of /SJ. and A/3. Now suppo.se that the pairs aA or 
Aa each produce a offspring of one kind, 6 of a second kind, while the pairs /SA 
or Afi produce c young of the first kind and d of the second: if we make a table 
of the correlation between (say) matei'nal character and character of young, it will 
have the form : 
Young. 
1 
3 
Totals 
a or ^ 
a + c 
b+d 
(a + b + c + d) 
A 
a + c 
b + d 
(a + b + c + d) 
Totals 
2 (a + c) 
2{b + d) 
2{a + b + c + d) 
Biometrika iii 
2 
