46 THE AMERICAN CHARACIDAE. 



Parnagua, Paranahyba basin, the lateral line "stutters." This species, in other 

 words, is mutuating at Parnagua. Moenkhausia cotinho is similarly locally 

 mutating and the same seems to be true of Hyphessobrycon poecilioides and 

 Astyanax fasciatus. 



The scaling of the caudal I am not able to cope with satisfactorily. It is 

 certain that it has several times been acquired independently by different members 

 of the family, if not by different members of the subfamily under consideration. 



Selective Grouping of Characters. 



Another line of inquiry leads us to consider whether the contrasted unit char- 

 acters are entirely combined as if by chance or whether there is a selected com- 

 bination. The characters from g-q are found in but one or two genera and these 

 may be omitted from the discussion since they would needlessly complicate it. 



Taking only the first six pairs of contrasted characters, there are 62 or 64 

 possible combinations. Considering each combination a distinct genus we 

 should have 64 genera, without considering the characters between g and q. 

 In reality we have but about half as many. 



Taking only the first three characters we should have eight possible com- 

 binations. An examination of the genera shows that six of these combinations 

 are actually found, but not by any means in the same proportions. If we take 

 the first four characters, each of which has probably several times, and inde- 

 pendently, been modified into its contrasted character, these four pairs give us 

 sixteen possible combinations. Of these only eight actually occur. 



A certain amount of selective grouping is thus found, if we take only three 

 contrasted pairs of characters, a greater amount of selective omission if we take 

 four pairs and this increases rapidly as we increase the number of contrasted 

 forms. It is evident that either many of the possible combinations have never 

 arisen, or, having appeared, they have not been preserved. 



POLYPHYLETIC GENERA. 



In my paper, Indiana University Studies, 1914, no. 20, I wrote — 



"This independent origin of characters is responsible for the fact that some of the 

 accepted genera of the Tetragonopterinse are of polyphyletic origin, i. e. our definitions of 

 genera are in many cases enumerations of characters frequently independently acquired, 

 not enumerations of the characters of the ancestral type of the genus from which the species 

 have diverged. A result of this independent divergence is that frequently in a restricted, 

 isolated area the species of different genera represented in the area are more nearly related 

 to each other than to members of their own genera in remote regions. For instance Astyanax 



