T1352 DR. R. R. GATES: A STUDY OF NORTH AMERICAN 
- general conceptions of definiteness and discontinuity in variation are sound, 
then the principles that arise from these conceptions should serve as a touch- 
stone when applied to the study of the origin and relationships of living 
species. The present work is published as an example of what may be 
accomplished in this direction. It will doubtless be criticized from many 
points of view, but it is hoped that as a first step it will not be entirely 
without justification. 
This work is the outcome of a study which began with several pairs of 
species *, taken at random as regards their distribution, differences, and 
probable manner of origin. The group Melanthaceze was selected on account 
of its compactness and because it is far removed from the Onagracem. The 
conceptions here applied to these families will doubiless apply equally well 
to many others. That variations are often marked and definite, who will 
now deny? It is with the hope of convincing systematic workers that these 
conceptions are not only useful but necessary, if we are to reach an under- 
standing of specific differences, that this publication is undertaken. The 
definite conceptions of germinal variation or mutation, which are founded 
on careful analytical, experimental, and cytological work, need to be incor- 
porated into the biological thinking of the time, and this can only be done 
by applying the results of experiment to groups where experiment has not 
taken or cannot take place. 
On the other hand, it soon becomes clear that, while many variations have 
been sharp and definite, this is by no means universally the case. The con- 
tinuous and indefinite variations which sometimes lead from species to species 
are the difficult ones to analyze. It may be admitted that their evolutionary 
significance is at present insufficiently analyzed and practically unknown, 
despite the current assumption that * fluctuations” are not inherited and are 
therefore not of evolutionary value. The present paper, while pointing out 
frequent cases of such “ continuous variation," is equally concerned with the 
cases of discontinuity. Many of the latter are obviously due to gaps caused 
by extinction, but many more are undoubtedly the result of discontinuous or 
definite variations. Is it, for instance, probable that a verticillate arrange- 
ment of the leaves, as in certain species of Polygonatum, in the related family 
Convallariaceze, arose gradually from an arrangement opposite, in pairs? 
And, again, is it not more reasonable to assume that the “knee” in the 
peduncle of Streptopus arose as a definite and marked variation, than that it 
was slowly and gradually evolved? It appears that in many cases differences 
which are now used as generic characters originated by a marked and definite 
step. The argument that extinction accounts for their present distinctness is 
certainly often excluded. 
Moreover, the mere fact that related genera showing marked differences 
* “On Pairs of Species,” Bot. Gazette, lxi. 1916, pp. 177 212, figs. 12. 
