42 



DISCONTINUOUS VAEIATION. 



mode, of the lower hump. The value so obtained is 

 termed by Davenport and Blankinship the " Index of 

 Isolation." They suggest that if this index be over 50 

 per cent., then one should agree to look upon the two 

 groups as distinct species; if under 50 per cent., then 

 only as varieties. As an example, they adduce a case 

 of two doubtful species of fishes, Leuciscus balteatus, 

 and L. hydrophlox, which differ in the number of rays 

 in the anal fin. On plotting out the frequencies of oc- 



12 14 16 18 20 22 



FIG. 10. Distribution of fin rays in Leuciscus. 



currence of the various numbers of rays in 194 indi- 

 viduals, the curve given in Fig. 10 was obtained. In 

 this case the index of isolation is exactly 50 per cent., 

 hence we are just at the limit of species and varieties. 

 The importance of determining which is the most 

 distinctive character, before drawing any conclusions 

 from the indices of isolation found, is well shown by an- 

 other case adduced by these authors. It concerns the 

 marsh plant Typha, which is found in the eastern 

 United States. Seven characters regarded as probably 

 specific were measured in about 250 specimens, which 

 had been collected at distances of about one metre 

 apart across the swamps in which it occurred. The 

 variation curves obtained in the case of the stem height, 



