MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
101 
and yet the prepotency of the dam in coat-colour is very marked. But in the 
present case there is on the average only a slight, if indeed it be a real, prepotency of 
the dam. Further, if we turn to the correlation, no longer of siblings of the same 
sex, but of opposite sexes, we find the correlation of the whole siblings is approxi¬ 
mately double that of the half siblings, as we should d priori have expected. 
Taking averages on the assumption that the correlation for whole siblings should 
be double that for half siblings, we have the following results :—■ 
Correlation between colts based on results for whole and half siblings . *6667 
Correlation between fillies based on results for whole and half siblings . 7729 
Correlation between filly and colt based on results for whole and half 
siblings.‘5747 
Mean correlation of siblings based upon all results for whole siblings . '6329 
Mean correlation of siblings based upon all results for half siblings . . 7100 
Mean correlation of siblings based upon results for both whole and 
half siblings. ,'6714 
We can draw the following conclusions :— 
(i.) In whatever manner we deduce the fraternal correlation it is very much larger 
than the '4 for whole brethren, or the "2 for half brethren, required by the unmodified 
Galtonian law. Such values, as we see above, could be deduced from the modified 
Galtonian law by taking y greater than unity, # but this would involve values for 
the parental correlation sensibly less than those given by theory. We are again 
compelled to assert that the modified as well as the unmodified theory of blended 
inheritance, based on the Galtonian law, does not fit the facts. The above values, 
however, are quite compatible with the theory of exclusive inheritance on the 
assumption that there is an individual (not a sexual) prepotency from one pairing to 
another. 
(ii.) In whatever way we consider it, it would appear that the average value of 
the fraternal correlation, as deduced from siblings with the same dam only, is 
greater than that deduced from siblings with both the same dam and the same sire. 
I am not able to explain this in any way, for I cannot assert a very substantial 
prepotency of the dam. All I can say from the data at present available is that for 
horses and dogs there appears to be no simple numerical relation between the correla¬ 
tion of whole and half brethren. 
(iii.) Offspring of the same sex are more alike than offspring of opposite sexes. 
This appears to be generally true, so far as our data at present extend, and will be 
fairly manifest from the table below. 
* ‘Roy. Soc. Proc.,’ vol. 66, p. 140 et seq. 
