1903.] of Alternative Inheritance. 509 



(5). To sum up: The memoir shows that any physiological 

 hypothesis, such as a generalised theory of the pure gamete, is not 

 a priori inconsistent with the broad conceptions of linear regression, 

 parental correlation, ancestral influence, and with the distribution of 

 frequency actually observed in populations. The theory under dis- 

 cussion, indeed, leads to these results, and they have only escaped 

 the Mendelians because they did not develop their formulae for the 

 case of a population crossing at random, but confined their attention 

 too much to the hybridisation of pure races, and to self-fertilising 

 individuals. On the other hand, there are marked numerical 

 divergences between the results observed for populations and those 

 deduced from the generalised theory of the pure gamete, which seem 

 to definitely prevent its acceptance as a general theory of heredity. It 

 would be of very great value to have a physiological theory which 

 would not only lead up to the general laws of inheritance involved 

 in the principles of regression and of ancestral influence this is 

 actually achieved by the present theory but which would also lead to 

 numerical results in reasonable accord with experience. Such a theory 

 will, no doubt, be discovered in time, but the touchstone of its truth 

 will be that it gives, not only a formula which does not vary from 

 one simple case of crossing to a second, but also general principles 

 and numerical values in accordance with those which have been 

 observed for large populations, whether they breed at random, or 

 exhibit homogenic tendencies. I think we are justified in asking 

 any future propounder of Mendelian formulae to apply this touchstone, 

 and to remember that the statistical view of inheritance is not at 

 basis a theory, but a description of observed facts, with which any 

 physiological theory must be in accord. 



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