CASTLE. — LAWS OP HEREDITY. 233 



"Mendel's Laws, so far from being in any way inconsistent with the 

 Law of Ancestral Heredity, lead then directly to a special case of that 

 law, for the dominant attribute at least. For the recessive attribute it 

 does not hold." Let us see how Yule reaches this curious conclusion, 

 that certain Mendelian predictions are only a special category of the 

 more general predictions of the law of ancestral heredity. 



After a statemeut of the Galton-Pearsou law, whereby it is limited to 

 no particular series, geometrical or otherwise, but is made to include any 

 set of empirical averages of the characters of the ancestors, which can be 

 made the basis of predictions, he proceeds as follows : " The first question 

 to be asked is one that does not seem to have occurred to any of Mendel's 

 followers, viz. : what, exactly, happens if the two races A [dominants] and 

 a [recessives] are left to themselves to inter-cross freely as if they were one 

 race ? " In answer to this question, Yule draws the correct conclusion 

 that the first cross-bred (or hybrid) generation will consist exclusively of 

 dominants, but that all subsequent generations will consist of dominant 

 and recessive individuals in the proportions, 3 dominant : 1 recessive, 

 [provided no selection is practised and all individuals are equally fertile]. 

 Yule next inquires, if I understand him rightly, what will be the effect 

 of eliminating in each generation all the recessive individuals. Starting 

 with 300 dominant individuals, which are in the Mendelian proportions, 

 100 pure: 200 hybrid, he finds that the successive generations will con- 

 tain the following proportions of dominant individuals : — 



.83333 

 .85000 

 .85294 

 .85345 

 .85354 



He considers it useless to carry the series farther, as it " tends toward 

 the limiting value .85355339 . . ." Now, what, in plain unmathemat- 

 ical language, does this mean ? It means that when a dominant form 

 has once been crossed with a recessive (as a pigmented animal, for exam- 

 ple, with an albino), the stock of the former is forever contaminated, and 

 cannot be freed entirely from the albino character by mere elimination 

 of white individuals, however long the process is continued. Ever after- 

 ward the cross-bred dominant stock will produce on the average at least 

 fourteen or fifteen white individuals in every hundred born. This con- 

 clusion is absurd, as every breeder knows. There is certainly something 

 wrong with Yule's figures, for they do not accord with observation. In 



