688 



SCIENCE 



[N". S. Vol. XXXIX. No. 1010 



second filial (F^) generation, though stiU inter- 

 mediate, commonly shows increased variability, 

 the range of which may even extend into or 

 include the size range of one or both parent 

 races. This increased variability of the F, 

 generation is the only evidence of Mendelism 

 in size crosses. In 1911 I was inclined to 

 regard it as sufficient evidence, but in this I 

 was clearly mistaken, as a moment's considera- 

 tion will show. It would be sufficient only 

 (1) if the size differences were due wholly to 

 Mendelian factors, and (2) further these 

 factors were invariable, that is quantitatively 

 always the same. But neither of these assump- 

 tions can be regarded as established. On any 

 hypothesis size differences must depend on 

 many mutually independent factors or causes. 

 This is the prime significance of a frequency- 

 of-error variation curve, however produced. 

 It would be rash to assume that all the factors 

 concerned are Mendelizing factors, in the total 

 absence of the two usual accompaniments and 

 criteria of Mendelism, dominance and segrega- 

 tion in recognizable Mendelian ratios. 



The question whether Mendelian factors are 

 constant or inconstant has been discussed 

 from different points of view by my colleague 

 Dr. East and myseK in the American Natu- 

 ralist (1912), he maintaining their constancy 

 on the ground that they are subjective merely, 

 while I have thought it necessary to assume 

 for them an objective existence in the germ- 

 cell, and am unable to discover any evidence 

 of their constancy from the behavior of germ- 

 cells. It is, of course, possible, as Dr. East 

 maintained, to formulate a description of all 

 heredity in terms of (purely subjective) 

 Mendelian units, provided more and more 

 units are from time to time created (by imagi- 

 nation) as the objective facts show the organ- 

 ism changed. But such an extension of Men- 

 delism fails to interest me, as I think it does 

 many of my readers. What we want to get at, 

 if possible, is the objective difference between 

 one germ-cell and another, as evidenced by its 

 effect upon the zygote, and it is the constancy 

 or inconstancy of these objective differences 

 that I am discussing. If these are quantita- 

 tively changeable from generation to genera- 



tion, then change in the variability of the 

 zygotes composing a generation might arise 

 without factorial recombination. 



By way of illustration let us consider the 

 simplest conceivable case. Suppose two organ- 

 isms to differ by a single genetic factor for 

 size. Suppose one organism to be of size 4, 

 the other of size 8. On crossing, if each trans- 

 mits its own condition and dominance is lack- 

 ing, an intermediate is formed, size 6. On the 

 theory of gametic purity, the gametes formed 

 by this heterozygote of intermediate size (6) 

 should be 4 and 8, respectively, and the next 

 generation of zygotes (F,) should be as 

 follows : 



of zygotes 4, 6, 8, 



Expected frequencies .... 1, 2, 1. 



Here we note that a large part of the Fj 

 generation is intermediate in character, as 

 was F,, but F„ is more variable than Fj, fall- 

 ing into three classes instead of one. This is 

 the regular Mendelian way of viewing size 

 inheritance, gametic purity being assumed. 

 But is the assumption necessary or justifiable? 

 Suppose the assumed size factor were modifi- 

 ahle or partially blending, so that 4 and 8, 

 after association in the F, zygote, emerged as 

 5 and Y, respectively, in the gametes. Then F^ 

 would be : 



Classes of zygotes 5, 6, 7, 



Expected frequencies .... 1, 2, 1. 



In this case, as well as in the supposed case 

 of pure gametes, we should observe an F^ more 

 variable than Fj, though the extreme condi- 

 tions of the parent organisms crossed would 

 not be attained in F, (as, in fact, they rarely 

 are). But even the recurrence of such ex- 

 treme conditions as those of the grandparents 

 might be explained as due to occasional failure 

 of the gametes associated together in F^ to 

 modify each other. 



Now I do not advocate either of these ex- 

 planations. I present the second merely to 

 show that the first is not the only conceivable 

 explanation, and that I was earlier wrong in 

 supposing an increase of variability prima 

 facie evidence of the occurrence of more than 

 a single Mendelizing factor. It might equally 



