ce:nte:r of origin and dispersal. II 



distorted or even entirely falsified by recent migrations and introductions 

 that can not be easily detected. 



The third criterion is not different to any extent from the first. None of 

 the species found north of the Rio Grande are closely related. In southern 

 Mexico, however, the species are as a rule closely related, as, for example, 

 L. undecimlineata, signaticollis, angustovittata , and diver sa. This rather unim- 

 portant criterion also points to southern Mexico as the center of origin. 



The fourth criterion is not, in my opinion, one of any great value. 

 Size is a character dependent upon nutrition and specialization. Thus L, 

 dccemli7ieata is larger in New England, New York, and along the southern 

 shore of the Great I^akes than it is in its original area of distribution, in 

 Colorado, Kansas, and Nebraska, the difference in size in the two being 

 about 20 per cent. I^ikewise Pieris rapcB is larger in America than in 

 Europe, and Passer domesticus lays larger eggs in America than it does in 

 Europe (Bumpus). So cases might be multiplied in which it is known that 

 the maximum size of a species is attained, not in the original habitat, but 

 in the area later occupied by it, as in the case of decemlmeata in this genus. 

 It is not possible to apply this criterion to the genus Lepti?iotarsa. 



The fifth criterion, like the preceding, is of comparatively little value. 

 No one would claim that the wild potato of the tropics would under any 

 circumstances give as many tubers per acre as the cultivated potato of Europe 

 and America, or that the wild jungle-fowl in India is as prolific as its domes- 

 ticated races, or that the hare of Europe is as prolific in its native home as 

 it has proven to be in Australia, or that wild grains are as productive as 

 cultivated varieties. Productiveness is a character of high specialization in 

 so many cases, such as cultivated varieties, often, if not always, accompany- 

 ing introduction into a new habitat, that it seems to me to be of little use 

 for the purpose for which Hyde proposed it. Stability, however, is quite 

 another matter, for we may have stability as the result of rigorous selection, 

 as in cultivated varieties, or stability as a specific property of the species, as 

 it occurs in nature. 



The sixth criterion is of prime importance and one which, when the evi- 

 dence is good, is sufficient to determine beyond question the center of 

 adaptive radiation. Rarely can the highways of dispersal be determined 

 from records or from the correlation existing between the movements of ani- 

 mals. In the majority of cases this data can be determined only by a study 

 of the continuity and directness of individual variation and modification 

 along certain lines. Adams's eighth criterion is in reality a highly neces- 

 sary part of his sixth, it being merely a method of determining the impor- 

 tant data in his sixth. This criterion presupposes, however, that all evolu- 

 tion has been by continuous variation. It is quite probable, however, that 

 if the theory of the origin of species by mutation should prove to be of wide 

 appHcation this criterion would be of little use. If the mutation theory 



