268 EXPERIMEXT STATION RECORD. I Vol. 41 



noted above by tbe inclusion of a second Mendelian cliaracter, the autJior 

 studies by algebraic metliods the behavior of two alleloujnrpliic pairs, United in 

 any degree, under (1) random mating, (2) a type of selection in which the only 

 zygotes allowed to breed ai'e dominants with respect to one of the pairs, and 

 (3) self-fertilization. The topics are among those discussed by Jennings (E. S. 

 II., 38, p. 268), but witli the use of neater methods niucli gi-oater generality is 

 secured. 



In all three systems of breeding, the relative proportion of each kind of 

 gamete approaches a definite limit as the number of generations increases, and 

 under random mating these limits are independent of tlie degree of linkage. 

 The formulas indicate clearly the conditions necessary for stability when 

 mating is at random. As is the case with only a single factor, the heterozygous 

 types tend to disappear under self-fertilization. 



Random mating with the exception of sister by brother mating, K. B. 

 RoBBiNs iGcnetics, 3 (JO J 8), No. 4, pp. .i.','0-J.f*0').— Theoretical study of the fate 

 of a single Mendelian character in a populaticjn in which mating is at random, 

 except that brotlier and sister mating does not occur, shows that as the num- 

 ber of generations increases the proportions of the three possible types of indi- 

 viduals approach a fixed limit. Constant number of offspring to a pair is 

 assumed, and if this number be 3 or more the limits approached are found to 

 be the same as tliose of standard random mating. If the number of offspring 

 is 2, the proportion of heterozygotes in the limiting population is higher. In 

 complete brother and sister mating, as the author has previously shown (E. S. 

 R., 38, p. 3G7), the limit for heterozygotes is zero. 



Numerical effects of natural selection acting upon Mendelian characters, 

 H. C. Wakren {Genetics, 2 (1911), No. 3, pp. 3().j-3J2).—When only one pair 

 of allelomorphs is considered, it is well established that the jiroportion of domi- 

 nants to recessives in a population remains fixed after the first generation, pro- 

 vided mating is at random and there is neither ditferential fertility nor selec- 

 tive eliminations of one or the other class of individuals. This paper discusses 

 the changes that occur when a type of selective elimination is admitted such 

 that there is a constant relative difference in the juvenal death rates of the 

 two classes. With the aid of H. S. Jennings, a general formula is derived. 



For a given difference in death rates, it is found that if the higher rate is 

 characteristic of the dominants their elimination takes place more I'apidly 

 than would the elimination of the recessives if the latter class were the less 

 viable. 



The influence of the male on litter sizes, E. N. WENT^voKTH (Proc. loiod 

 Acad. Sci., 24 (1917), pp. 305-308). — Statistics are presented showing the aver- 

 age size of litters got by sires classified according to the size of litter in which 

 they were born. Probable eri'ors of the averages considered, no significant dif- 

 ferences in the breeding performance of the different classes of sires of the same 

 type of animal were apparent. The records include 9,026 Southdown rams, 415 

 Chester White boars, and 23 collie dogs. The rams in pedigrees started from 

 single and from twin births are recorded separately. 



The material was assembled mainly because Harris (E. S. II., 40, p. 662), in 

 examining the litter frequencies reported by Went worth and Aubel (E. S. R., 

 35, p. 68) for swine and by Rietz and Roberts (E. S. R., 34, p. 73) for sheep, 

 found slight indications of an influence of sire on litter size. 



Inheritance of fertility in sheep, E. N. Wentworth (Trans. Kans. Acad, 

 Sci., 28 (1016-17), pp. 243, 2-}.}).— Data from the Southdown births mentioned 

 above are tabulated, as in a paper previously noted (E. S. R., 38, p. 574), to 

 show the relative influence of sire and dam on litter size. It is concluded that 



