440 BROOKLYN BOTANIC GARDEN MEMOIRS 
notorious inharmonies between the inheritance ratios in the Oenotheras 
and the expectation based on the usual Mendelian methods of segre- 
gation and recombination, one may well suspend judgment regarding 
this case as an instance of duplication, until it has been shown by 
further analysis of one of these 15:1 ratios, that the rubricalyx 
individuals will yield three kinds of families, characterized respec- 
tively by the ratios I :0, 15 : 1, and 3: 1, and that these three kinds 
of families are produced in approximately the ratio 7: 4:4. Unless 
this should be the result of the further study, the 15’: I ratio noted in 
several of the Fy and F; families must have been brought about by 
some combination of circumstances, other than the typical Mendelian 
distribution of two duplicate factors for the rubricalyx pigmentation. 
Gates discusses at some length two of the several methods by 
which one may reasonably suppose duplication of factors to come 
about. He seems to imply (Gates, 1915, p. 204) that my discussion 
of this subject does not adequately cover the several possibilities. He 
then proceeds to present two of the same possibilities as if they were 
original propositions of his own. These several possibilities are (a) 
the occurrence of independent mutations affecting in the same or 
closely similar manner non-homologous chromosomes; (b) the mating 
of non-homologous chromosomes; and (c) the transposition of parts 
of chromosomes by what I have called a ‘“‘sort of longitudinal crossing- 
over”’ (Shull, 1914, p. 139). Only the first two of these propositions 
are considered by Gates and he agrees with me that both of the proc- 
esses (a) and (b) have probably actually resulted in the duplication 
of factors. He thinks that repeated mutations were responsible for 
the duplication of red pericarp color in Nilsson-Ehle’s wheats, and 
that mismating of chromosomes will explain the duplication which he 
believes to have taken place in his Oenothera rubricalyx crosses. 
Upon unpublished evidence Bridges (1917, p. 454) refers to two 
cases of duplication in Drosophila which seem to result from essentially 
the longitudinal rearrangement of genotypic materials that I had in 
mind when suggesting the possibility of ‘longitudinal crossing-over,”’ 
though the details of the process as understood by him are somewhat 
different. He states that a section from the mid-region of one X 
chromosome appears to have been removed from its accustomed place 
or locus in that chromosome, and to have become attached to the 
end of the other X chromosome, its mate. The full account of this 
case will be awaited with interest. 
Accepting the validity of these several methods of duplication, 
one may well ask in each specific case whether circumstances make 
possible a judgment as to which method was probably responsible 
for the duplication in question. I have assumed that the complexity 
