314 



The Journal of Heredity 



result of random matings of D individ- 

 uals inter se as follows : 



D animals crossed inter se 



Ratio of DD or DR 

 Ratio of animals in animals to RR in 

 population [ progeny of random 



, ! matings 



Table II 

 Matings D and D 



(a) 1 DD : 2 DR 



(b) 1 DD : 1 DR, 



(c) 2 DD : 1 DR 



8 : 1 

 15 : 1 

 35 : 1 



Similarly the incidence of DD and DR 

 types in a relatively fixed proportion 

 in any population will result in definite 

 ratios from the back cross of D with 

 R individuals. Any population which, 

 in respect to a given pair of factors, 

 gives, when D animals are crossed 

 inter se, a ratio of type (a), (6), or (c), 

 should approach the corresponding ratio 

 in back crosses of D animals w4th R as 

 follows : 



D animals crossed with R 



Ratio of animals in 

 population 



Ratio of DD or DR 



animals to RR in the 



progeny of random 



matings 



(a) 1 DD : 2 DR 



(b) 1 DD : 1 DR. 



(c) 2 DD : 1 DR 



2 : 1 



3 : 1 

 5 : 1 



(a) The factor D for intensity; d for 

 dilution 



Matings involving these two color 

 phases are tabulated in Tables II, 

 III, and IV. In each case the 

 mating designations refer to Table I. 



It will be seen from Table II 

 that the ratio of intense to dilute 

 animals is approximately 15 : 1. We 

 have, in the bottom three lines of the 

 table, data which will serve to test how 

 closely the observed figures conform 

 with the expected numbers under an 

 8 : 1 and a 15 : 1 ratio. Figures for a 

 35 : 1 ratio are not, in this case, given 

 because of the fact that it is obvious 

 that the observed numbers are in 

 closer agreement with a 15 : 1 ratio 

 than they would be with a higher ratio. 



The probable errors calculated in each 

 case on the smaller phenotypic class 

 show that between the observed num- 

 bers and the 15 : 1 ratio, there is a 

 difference of 21 ±7. 5. The difference, 

 which is 2.7 times the probable error, 

 makes it not unlikely that the observed 

 figures represent a chance deviation 

 from this ratio. On the other hand, 

 the difference between the observed 

 figures and an 8 : 1 ratio is 86±9.5. 

 In this case the difference is 9.0 times 

 its probable error, and the odds are 

 practically certain that the observed 

 figures depart significantly from an 

 8 : 1 ratio. This being the case, Table 

 III, which records the cross of intense 

 animals with dilute, should show a 

 closer approximation to a ratio of three 

 intense to one dilute than to a 2:1 

 ratio. This proves to be the case, 

 although the numbers are so small that 

 the difference between the observed 

 figures and the 2 : 1 ratio cannot be 

 considered as certainly eliminating the 

 possibility that a 2 : 1 ratio is involved. 

 However, inasmuch as the difference 

 between the observed figures and the 

 3 : 1 ratio are less than the probable 

 error, it seems extremely likely that the 

 3 : 1 ratio is the actual one involved. 



