Duplicate genes for capsule-form iu Bursa bursa-pastoris. HI 



such a deviation would scarcely rail for rüniiiiciit wi'ie it not for tlie 

 rather remarkable circumstance that this deficiency in the number of 

 homozygous dominants almost exactly balances a similar deficiency 

 already reported (Shull 1911) in the recessives in the same family, a fact 

 which will be considered more at length below. 



The families recorded in the foregoing tables present a considerable 

 range of variation in the percentages of dominants, and the question 

 may arise whether the discontinuity is real, which is implied by their 

 grouping into different sections of the tables accordingly as they are 

 assumed to be theoretically referable to the ratio 3 : 1 on the one hand, 

 or to 15:1 on the other; or whether the close agreement of each group, 

 taken as a whole, with the theoretical ratio to wlüch such group is 

 referred, is simply an artefact produced by the association of families 

 so balanced on either side of the expected ratio that their average must 

 closely approximate that ratio. The perfectly continuous series of ratios, 

 1:1, 2:1, .3:1, 4:1, .5:1, 6:1, &c., may be divided into gi'oups 

 which will average very near to the Mendeliau ratios, the first five 

 members of the series having an average of 3 : 1, the next 20 terms, 

 (from 6 : 1 to 2.5 : 1 inclusive) averaging 15%5 : 1, and so on. The dis- 

 continuity iu the ratios in my tables is perhaps sufficiently obvious on 

 simple inspection, as there is no ratio between 4'79 : 1 and 10'3 : 1, 

 that is, between 82'83 per cent dominants and 91'14 per cent domi- 

 nants, but the exact significance of the interval can be easily grasped 

 only when the data for the several families are re-tabulated in the form 

 of variation-curves, as is done in fig. 5. Each little square in this 

 figure represents a possible family of Bursa, the position being deter- 

 mined by the percentage of individuals having the triangular type of 

 capsule, as indicated by the schedule of percentages at the base of the 

 figure. The two dotted lines running vertically through the figure 

 represent the position of the two expected percentages, 75 and 93"75. 

 The dark squares are the actual families produced and the radiating 

 arrows represent the lines of descent. In order to separate the groups 

 belonging to the higher ratios the expedient is adopted of decreasing 

 the class-ranges regularly from left to right, each class having a range 

 0'124 less than the adjacent class to the left. The consequences of 

 this changing class-range will be easily seen in the fact, for instance, 

 that the class in which 75 per cent occurs, extends from 73'86 per 

 cent to 76'34 per cent, a class-range of 2'48 per cent, while the class 

 which contains 93*75 per cent is limited by 93'()8 per cent and 94'32 

 per cent, thus having a range of only r24 per cent, — exactly half as 



