Duplicate genes for capsule-form in Bursa bursa-pastoris^^ 143 



titative differences, b) the inheritance of apparently blended characters, 

 c) the apparent modification of a unit- character by means of selection, 

 or d) the origin of an apparent recessive mutant. For each of these 

 propositions there are certain simple corollaries whose demonstration 

 will give a better basis than is now available for judging of the probable 

 correctness of this method of interpretation. It may be useful to point 

 out several of these corollaries as constituting hopeful points of attack. 

 No attempt is made to be exhaustive and other criteria will readily 

 present themselves. 



a) For continuous characters, if the hypothesis be true, it should 

 be demonstrable that the F2 is not only more variable than the Pi and 

 Fi, as is now well established in a large number of cases, but also 

 that it does actually include the two parental conditions in respect to 

 the particular quantitative character under consideration, when suffi- 

 ciently large numbers are grown. This must be shown to be a general 

 rule, for occasional instances of this sort can come about by the same 

 fortuitous circumstances that produce striking transgressive variations 

 in other special cases. In F 3 there should be not only a range of 

 variation-coefficients extending from the value of the Pi and Fi coefficients 

 to the F 2 coefficients; it ought to be demonstrated also that the individuals 

 taken from the extreme classes of the F 2 and later generations yield 

 progenies which tend to have lower variation coefficients and less va- 

 riation among the coefficients themselves, than individuals taken from 

 the middle classes of the same generation. Extensive comparisons between 

 progenies from extreme minus-variants and extreme plus-variants of any 

 given generation should give evidence as to the extent to which heterosis 

 is distorting the effects of the hypothetical size-determining genes. 



b) According to hypothesis, blended characters are only a special 

 case of a), in which the number of determiners is supposed to be large 

 compared with the number of offspring available. If the small number 

 of available offspring is due to limitations in the breeding capacities of 

 the individual organism, as is the case in all higher animals, the dem- 

 onstration will be rendered the more difficult. Indeed, it may be that 

 with such material it will be possible to show only that, as far as they 

 go, the empirical results are in harmony with those in other cases which 

 are capable of more complete analysis. 



c) For apparently modifiable unit-characters, the crucial test of 

 the hypothesis should be the reversibility of the process. If selection 

 is a "creative force", the selection to one extreme should raise no barrier 

 to the attainment of the opposite extreme without the introduction of 



