June 5, 1908] 



SCIENCE 



897 



\ 



a similar meaning. Wiile we have assumed 

 the series A^ to A^" to be continuous, this 

 series may have gaps in it not bridged over 

 by living intermediate forms. Each of these 

 " allelomorphs " is supposed to be phylogen- 

 etically related to the others in the same 

 series, and the differences between them may 

 be supposed to be analogous to the differences 

 between the individuals of a large and vari- 

 able species. We have merely taken the case 

 in which the series is continuous to show that 

 such continuity is consistent with the phe- 

 nomena under consideration. 



TABLE I 



A» A' A' A* A' A' A' A' A' A'" 

 B' B' B' B* B' B' B' B' B' B" 

 C^ C C^ C* C C C C C C" 



TABLE II 



(1) (2) (3) (4) (5) (6) (7) (8) 



A^A': A> A' A> A' A" A' A' A' 



B'B'. B' B» B» B' B" B= B» B' 



CO': C C C- C C G' C C 



TABLE in 



(l)X(l) 



(2)X(2) 

 (3)X(3) 

 (4)X(4) 

 (5)X(5) 

 (6)X(6) 

 (7)X(7) 

 (8)X(8) 



C'C. 

 C-G\ 



C'C. 



cc 



C'C. 



cc. 



C'C. 



Under our hypothesis all the various forms 

 of A will be allelomorphic ; likewise those of 

 B and those of 0. In order to have a concrete 

 case, suppose that the three characters consid- 

 ered are characters of the corn plant. A may 

 govern the length of the tip on the corn husk, 

 the various exponents indicating the relative 

 development of this tip. B may represent 

 breadth of leaf and length of internode. 

 It is to be understood, of course, that we are 

 referring now only to differences which are 

 hereditary and our exponents refer to degrees 

 of difference which are hereditary. Now let 

 us select an individual corn plant at random 

 from a field. Suppose the gametic constitu- 

 tion of the plant selected is that shown in the 

 first column of Table II. With reference to 



the length of the husk tip it is heterozygote, 

 one of the allelomorphs tending to produce a 

 very short tip, the other a tip of medium 

 length. With reference to the breadth of 

 leaf, our selected plant is also heterozygote, 

 one of the allelomorphs tending to produce a 

 moderately narrow leaf, the other a moderately 

 wide leaf. With reference to the length of 

 internode, the allelomorph C would corre- 

 spond to a short internode, while C° corre- 

 sponds to a moderately long one. Now on the 

 well-known behavior of Mendelian character 

 pairs, when our com plant, after close fertil- 

 ization, produces reproductive cells, we shall 

 obtain, with reference to the three characters 

 considered, eight types of gametes, as shown 

 in Table II. The fortuitous union of these 

 eight types of gametes produces sixty-four 

 fertilizations, consisting of twenty-seven dif- 

 ferent types, eight of which are homozygote 

 with reference to each of the characters con- 

 cerned. These eight homozygote types are 

 shown in Table III. Now, if we neglect any 

 evolutionary changes which may have occurred 

 in each of these hereditary characters during 

 one generation, each of these types shown in 

 Table III. will reproduce so true to type that 

 there will be no variation at all except that 

 due to environment; and we have eight so- 

 called elementary species, each reproducing as 

 true to type as branches from the same twig 

 of an apple tree. 



It is very clearly seen that each of these 

 elementary species is merely a cross-section 

 of the real variable species, and that the major 

 part of the variation in a corn field is ac- 

 counted for simply as a result of the recom- 

 bination in each generation of Mendelian 

 characters, each of which may vary between 

 wide extremes just as a species varies under 

 the Darwinian theory of evolution. For in- 

 stance, the first elementary species in Table 

 III. is a cross-section of the species through 

 A\ B' and C of Table I. 



By properly selecting the parent plant we 

 could get other so-called elementary species 

 intermediate between any two of those shown 

 in Table III. An interesting example of this 

 arose at the recent meeting of the American 

 Breeders' Association. Dr. Shull reported his 



