28 GENETICS [BoT. Absts., Vol. X, 



144. Wright, Sew all. Systems of mating. II. The effects of inbreeding on the genetic 

 composition of a population. Genetics 6 : 124-143. 12 Jig. 1921. — The results of different sys- 

 tems of inbreeding on the composition of the population are expressed in terms of variation 

 which is purely genetic, although the method of considering the tangible and intangible envi- 

 ronmental factors is demonstrated. The method of path coefficients is shown to be more 

 general in application than the previous metljods of attack on the results of inbreeding, and 

 the series for the percentages of heterozygosis in descendant generations as calculated by 

 previous investigators was shown to agree with the results secured by the method of path 

 coefficients. The series for brother-sister matings, self-fertilization, parent-offspring ma- 

 tings, double first cousins, and single first cousins was developed, followed by more complex 

 systems impracticable of development under the older methods. Such matings as quadruple 

 second cousins, octuple third cousins, half brother and sister, half brother and 2 sisters, half 

 brother and 2 half sisters plus half sister with 2 half brothers, half first cousins and second 

 cousins are developed in detail, and their relation to practical breeding demonstrated. — 

 Edward N . Wentworth. 



145. Wright, Sew all. Systems of mating. Ill, Assortative mating based on somatic 

 resemblance. Genetics 6: 144-161. 7 fig. 1921. — Selective mating based on somatic types 

 such as is commonly followed by practical breeders is analyzed by the method of path coef- 

 ficients. The general theory is discussed, first in the absence of dominance. The author 

 assumes that a certain correlation, rpp, exists between the mated individuals because of their 

 somatic resemblance. He further assumes that the somatic correlation implies a correlation, 

 m, between the zygotic constitutions. This requires that there be a correlation between 

 factors of different sets of allelomorphs which act on the same character. There are 2 types 

 of this correlation, /« representing the correlation between factors of the same set of allelo- 

 morphs, and ju the correlation between factors of different sets of allelomorphs. Assuming the 

 same relative frequency of dominant to recessive factors in the case of all allelomorphs, the 

 author calculates a series of formulae. One interesting contingency arising in the case of 

 matings based on somatic resemblance that does not arise in the case of matings based on 

 blood relationships is that somatic resemblances indicate not only a tendency to mate individ- 

 uals of like genetic composition but also individuals affected by similar external conditions. 

 He then develops a means of separating these 2 effects. Discussions are presented of the ex- 

 pectations in the case of equilibrium in the population, in the case of dominance, and in the 

 case of assortative mating combined with inbreeding. This latter form of mating is demon- 

 strated to be the most rapidly effective since it combines the correlation due to inbreeding 

 with the correlation between uniting gametes due to the relation of the zygotic constitution 

 to the somatic type. — Edward N . Wentworth. 



146. Wright, Sewall. Systems of mating. IV. The effects of selection. Genetics 

 6 : 162-166. 1 fig. 1921 . — After reviewing the expectation in the case of selection for 1 factor, 

 and showing that no fixation of type can occur in the case of heterozygotes lacking dominance, 

 the author considers the effect of selection on a characteristic depending on n pairs of allelo- 

 morphs. He assumes plus and minus factors of each pair to be equally numerous, all factors 

 to be of equal weight, and dominance absent. The distribution of plus factors in (2n -\- 1) 

 classes can be found from expanding (I -f h)-""^, and assuming the coefficients thus obtained 

 to begin with the class having the greatest number of plus factors present. The distribution 

 of the minus factors can be found by the same formula, but it is necessary to begin their appli- 

 cation with the class having the next greatest number of plus factors present. This permits 

 determination of the ratio of plus factors to total factors in any class, it being always \ of 

 the middle class. For a deviation of x classes beyond the middle the ratio q is shown to be 



ti 1 J* 9 • 



— — or in terms of the standard deviation s, | (1 + —j=-). By selecting for mating only indi- 

 2n V2n 



viduals of a middle class, the author shows that the only effect lies in the 1st selection, 

 and return to random breeding reestablishes the same proportions as were found in the orig- 

 inal unselected population. In a population of limited size this intermediate tj'pe may be 



