244 Kansas Academy of Scietice. 



But one conclusion seems possible from the above — that there 

 is no difference in breeding quality between twins and singles, 

 and that consequently their genetic constitution must be nearly 

 alike. Further evidence on the same point is found from a 

 study of the mean breeding qualities of twins and singles. 

 Combining the two sets of statistics, hav'mg due regard to the 

 f7'equency in which tivins and singles ordinarily occur, the 

 mean breeding records for ewes are as follows : 



Ratio cases. 



17,958 



9,052 



The difference between them is 0.0170 ± 0.00422— a differ- 

 ence nearly large enough to be statistically significant if the 

 actual numbers given under the ratio existed. If the actual 

 cases arising from each type of pedigree are considered, how- 

 ever, the differences are not significant. 



Evidences of Mendelian inheritance are difficult to obtain 

 owing to the impossibility of determining the genetic type of 

 the grandparents, but such as exist are presented nevertheless. 



If there is a true segregation of fecundity factors a com- 

 parison of the maternal grandparents with the birth rank of 

 the progeny should give some idea of the factors being trans- 

 mitted. It is inconceivable that the sire mated to a ewe should 

 influence the number at a birth; but in order to test such an 

 effect, statistical studies were made which showed that the 

 birth rank of the sire had no effect on the immediate progeny. 

 When both grandparents were single the average lambing was 

 2.07 ; when one was a single and the other a twin, the aver- 

 age was 2.11 ; and when both grandparents were twins, the 

 average was 2.05. None of these differences are statistically 

 significant, hence one could again conclude that twins and 

 singles are not genetically different. However, when one of 

 the grandparents was a triplet, the average was 2.43, which 

 would suggest that in order to produce triplets, factors not 

 present in twin or single producers must be present. The 

 chance that the difference in favor of the triplet grandparents 

 is significant is only two and a half to one, due to the small 

 numbers from which triplet grandparents could be discovered. 

 However, the uniformity with which this result holds, no 

 matter how varied the source of the figures, gives the writer 

 confidence in the conclusion that there is no genetic difference 

 between twins and singles, but that triplets in sheep differ 

 from either. 



