50 ANNALS NEW YORE ACADEMY OF SCIENCES 



In so far as possible, it is the dynamic aspect of the distribution of the 

 South American fishes that I shall consider in the following pages. 



On page 9 of the same remarkable book, Tower states the following ten 

 criteria which have been used by Adams, Allen and others to determine 

 the center of origin of a fauna when no fossils are known : 



1. Location of the greatest differentiation of a type. 



2. Location of dominance or greatest abundance of individuals. 



3. Location of synthetic or closely related forms. 



4. Location of maximum size of individuals. 



5. Location of greatest stability and productiveness in crops. 



6. Continuity and convergence of lines of dispersal. 



7. Location of least dependence upon a restricted habitat. 



8. Continuity and directiveness of individual variation or modifica- 

 tions radiating from the center of origin along the highways of dispersal. 



9. Direction indicated by biogeographical affinities. 



10. Direction indicated by animal migration in birds. 



After critically considering the above ten criteria, Tower 25 states that 

 the following four are adequate for determining the centers of origin or 

 adaptive radiation, without the introduction of any of doubtful value : 



1. Location of greatest differentiation of a type. 



2. Continuity and convergence of lines of dispersal. 



3. Location of synthetic or closely related forms. 



4. In some cases, location of dominance or great abundance of indi- 

 viduals. 



I quite agree with Tower that these criteria are sufficient to determine 

 the point of origin, if the four criteria themselves can be correctly deter- 

 mined, and I believe that these four criteria can be correctly determined 

 in a given genus like Leptinotarsa, but when the genus becomes very 

 widely distributed, with many distinct species and varieties, it is more 

 difficult, if not impossible, to determine these four criteria. At any rate, 

 they cannot be correctly determined for the families and orders of animals 

 without the aid of fossils, because the factors and conditions become so 

 complicated that the determination would be nothing more than an 

 opinion of the individual. For example, I have been able to show that 

 certain species in a certain genus of Cichlida? have evolved from another 

 species, but which of the many species in a widely distributed genus is 

 the ancestral one cannot be easily and correctly determined. Further- 

 more, even though we are able to determine that one particular genus of 

 the twenty odd genera of the cichlids is the most primitive and that most 



25 Op. cit., p. 13. 



