MATHEMATICAL CONSIDERATIONS 



95 



generations it is 99.9' per cent, ajid after 19 generations 

 99.999 per cent. 



Althougli nearly complete homozygosis is theoretically 

 brought about by 7 generations of self-fertilization the 

 attainment of absolute homozygosity is a difficult matter 

 and in practice it may never be reached. The fact that 

 hereditary factors are distributed by the ehromosomes, so 

 that there is not independent recombination among all 

 the determiners, enters as a complicating factor. Lethal 

 factors, which prevent homozygotes from appearing, and 

 increased productivity of hybrid combinations, also tend 

 to prevent the complete elimination of heterozygosity. 



The way in which factor linkage affects reduction to 

 homozygosity may be illustrated by the use of two allelo- 

 morphic pairs of factors. Jennings ^"^ has calculated 

 the effect of three generations of self-fertilization upon 

 the population descending from a dihybrid when the two 

 pairs of factors show a linkage relation of 2 (that is, 33 V{ 

 per cent, "crossovers") in both sexes ; and also when the 

 linkage is complete in one sex, as in Drosophila where 

 there is no " crossing over ' ' in the male. The proportions 

 of completely homozygous, of completely heterozygous, 

 and of mixed individuals — i.e., heterozygous in one pair 

 and homozygous in the other — obtained after three gen- 

 erations of self-fertilization, are compared with what is 

 expected when the two factors are independent as follows : 



Ratio required 



Per cent, of complete homozygotes . 

 Per cent, of complete heterozygotes 

 Per cent, homozygous in one pair but 



not in other 



Per cent, homozygous factors 



Per cent, heterozygous factors 



Two factors 

 independent 



76.56 

 1.56 



21.88 

 87.50 

 12.50 



Linkage ratio 

 2 in both sexes 



77.14 

 2.14 



20.71 

 87.50 

 12.50 



Linkage 



complete in 



one sex, 2 in 



other 



78.70 

 3.70 



17.59 

 87.50 

 12.50 



