OCCURRENCE OF LINKAGE IN RATS AND MICE. 31 



recessives. In both cases the Fi individual was of the formula PpRr, 

 the double recessive was of the formula pprr. 



The only difference in the two cases was that in one case the Fi 

 arose from a union of Pr with pR, and in the other from a union of 

 pr with PR. But the importance of this circumstance is seen in the 

 different results obtained in the two cases. In one case (where p and 

 r enter the cross separately) 10 per cent of the j'oung were dark, in 

 the other case (where p and r enter the cross together) more than 

 40 per cent of the young were dark. The exact figures for the repulsion 

 series have already been given, 174 dark young in a total of 1,714, or 

 10.1 per cent dark young. For the coupling series the figiu'es are 

 1,255 dark young in a total of 3,032, or 41.3 per cent dark young. 

 To compare the strength of repulsion with the strength of coupling we 

 vasiy estimate the percentage of cross-over gametes produced in each 

 case. Either sort of Fi individual would produce 4 kinds of gametes, 

 PR, Pr, pR, and pr. But in the repulsion series PR and pr would arise 

 from crossing-over, whereas in the coupling series Pr and pR would 

 arise from crossing-over. In either case dark-eyed individuals would 

 arise only from the same type of Fi gamete, viz, PR, but in the repul- 

 sion series this would be a cross-over gamete, whereas in the coupling 

 series it would be a non-cross-over gamete. WTiile in the repulsion 

 series the number of dark-eyed young would measure half the total 

 number of cross-overs, in the coupling series it would measure half 

 the total number of non-cross-overs. Applying these criteria, we have 

 found in the repulsion series, as already stated, that the number of 

 dark-eyed young being 174, the probable number of cross-over gametes 

 is twice this, or 348, in a total of 1,714, which is 20.3 per cent. 



Turning now to the coupling series, we find that the total number of 

 dark-eyed young is 1,255. Doubling this we have 2,510 as the probable 

 number of non-cross-over gametes. Deducting this number from 

 3,032, the total number of young, we have 522 as the probable nvmiber 

 of cross-over gametes, which is 17.2 per cent. This we may compare 

 with the 20.3 estimated for the repulsion series, and the earlier esti- 

 mate of 18.5 based on the census of an F2 population (publication 241). 

 These differences are not large enough to lead us to think that there 

 is any consistent difference between the strength of repulsion and the 

 strength of coupling between the same two genes. The chromosome 

 theory would not lead us to expect the existence of any such difference. 

 This case therefore fully accords with that theory. If we combine the 

 results obtained from both the repulsion and the coupling series we 

 have as the average linkage strength (either repulsion or coupling, as 

 the case may be) 18.3 per cent. This is based on a total of 4,746 

 young produced by the back-cross of Fi with the double recessive. The 

 figures are large enough to have significance and agree remarkably 

 well (almost too well) with the estimate based on the F2 population, 



