22G The Law of Ancestral HeredUji 



point to be noted is that while two or three generations of selection would carry us 

 iip to 80 or 90 por ccnt. of the desircd charaoter, teii generations following this of 

 merely in-brecding without an}- selection would not have cost us 50 per cent. of 

 the character so acquired. Quick influence of selection, slow efifect of regression 

 would bc the result of conibiiiing the uctually observed values with Mr Galton's 

 thcory as to what should hold for a stable population. 



The reader must not forget that the Illustration here given is absolutely 

 hypothetical ; the Statistical constants obtained are deduced from material to 

 which Mr Galton's conditions hardly apply even as a rough approxiination. Yet 

 it is possiblc that something of the kind here indicated may occur in special 

 cases. But if so, we ought to be very cautious of using vague categories in prob- 

 lems of heredity. If the mean tint of a seed, say, be yellow, and // would carry us 

 well into the green end of the scale, '4/1 niight still be green,and certaiuly for three 

 and possibly for a good many more generations wo might consider the stock arising 

 from a single selection to be breeding true to itself, although actually it might be 

 slowly regressing to the original tint of the early ancestry. It seems absolutely 

 necessary in all such cases to have some colour Standard and determine quanti- 

 tatively whether successive generations do or do not tend to slowly approach or 

 depart from it. The statement that ancestry has no inHuence might well be 

 deduced by the use of a rough category, which would still class ü'lh with '52/1. 



(9) Conclusions. 



(a) In all cases as those of man, horse and dog, where parents of identical 

 character do not produce identical offspring, the theory of statistics shows us that 

 closer prediction may be obtained wheii we predict from many instead of few 

 relatives. This follows from the cousideration that all the heredity coefficients are 

 positive. 



Attention is therefore properly paid to ancestry in such cases, and it is very 

 mislcading to suggest that any law of heredity can be universal which neglects 

 ancestry. 



(b) The law of ancestral heredity in its most general form is not a biological 

 hypothesis at all, it is simply the statement of a fundamental theorem in the 

 Statistical theory of multiple correlation applied to a particular type of statistics. 

 If statistics of heredity are themselves sound the results deduced from this theorem 

 will remain true whatever biological theory of heredity be propounded. 



(c) The law of ancestral heredity as founded on the theory of multiple 

 correlation involves no biological theory of regression. The term regression has 

 unfortunately been taken from Statistical theory and iuterpreted in a biological 

 sense. In statistics the regression is alwajs to the mean of the forecasted charac- 

 ter, but no assumption is niade that this mean is identical with that of the fore- 

 known character*. Further, if thore be a number of cognates, we can d priori, 



• There is a "regression" for exsmple if we predict breadth of skull from its length. I think it might 

 be useful to adopt the word " predicate " for the forecasted and " cognate " for the foreknown character. 



