Index Frequency Method 529 



obtained separately for each character of each hybrid individual. 

 These individual hybrid indices may then be tabulated for all 

 the hybrids to show how one character in all the hybrids com- 

 pares with the mean value of that character in each parental 

 type, or all the indices of any hybrid individual may be averaged 

 together to give a composite picture of all the characters of that 

 individual for comparison with the ensemble of each parental 

 form. In computing the hybrid index for a given character, the 

 average of one parental type is assigned the value 0, whereas 

 the average of that character in the other parental type is valued 

 at 100. The value, Vh, of that character in the particular hybrid 

 is calculated, and the position, P, of the hybrid is calculated by 

 the formula 



° M2 - Ml , 



wherein Mi and M2 represent the mean values of the two par- 

 ents. The hybrid index, /, is 100 times P. Mi is usually ap- 

 plied to the parental species which seems to be the more primi- 

 tive, if that is possible. For hybrid populations, the mean 

 value of all the hybrids, Mh, is used in place of Vh in the 

 above formula. In many hybrid populations the standard error 

 of the hybrid index may also be computed. 



The hybrid index is valuable as a test for hybridity and for 

 mode of inheritance. If the putative hybrids are not hybrids 

 but merely selected specimens of the two species, or if each char- 

 acter studied is determined merely by one pair of alleles, a curve 

 obtained by plotting the individual indices would be a bimodal 

 curve with one hump at either end of the scale. If, however, the 

 putative hybrids are actually hybrids, a unimodal curve would 

 result with the hump in the neighborhood of 50 on the scale. 

 This curve w^ould indicate characters determined by polygenes 

 or, which is highly improbable, characters determined by genes 

 that show^ed incomplete dominance. Hubbs considers that if 

 unimodal curves were obtained for two or more unrelated traits 

 in a given set of individuals, those individuals could be assumed 

 to be hybrids. Hubbs has applied this method to interspecific 

 and intergeneric crosses among suckers. A comparison of the 

 hybrids and parents in five scale counts in several sucker popu- 



