THE COMPOSITION OF PLANT POPULATIONS 



323 



dominants is 0.16 +. In this or later generations, therefore, the chances 

 of selecting at random a heterozygous dominant, assuming dominance to 

 be complete, are about one in six. 



Table XL VII, shows the composition of the population with ref- 

 erence to a single pair of factors, A and a, in the first five generations 

 when there is 10 per cent, of spontaneous crossing, assuming (1) that be- 

 fore crossing began there were equal numbers of A A and CM plants; (2) 

 that among the 10 per cent, of plants which cross random mating occurs: 

 (3) equal fertility and viability in all individuals. 



Starting again with a population of AA and aa forms we find that, 

 assuming 20 per cent, of crossing in this instance, other conditions being 

 the same, the ratio of homozygotes to the whole population in the first 

 four generations is as fol- 

 lows: 0.90, 0.86, 0.845 and TABLE XL VII. COMPOSITION OP POPULATION 

 0.837; while the ratio of 

 heterozygous dominants to 

 the total dominants in 

 the fourth generation is 

 0.27. Hence, in this and 

 later generationsthe chance 

 of selecting a heterozygous 

 dominant is about one in 

 four. Again, with 50 per 

 cent, of crossing the ratio 



of homozygotes to the whole population in the first four genera- 

 tions is 0.50, 0.625, 0.649, 0.662; and the ratio of heterozygous 

 dominants to the total dominants in the fourth generation is 

 0.50 +, so that the chance of selecting a heterozygous dominant is 

 one in two. In the same way the theoretical expectation for any 

 particular amount of crossing may be calculated. It must be borne in 

 mind, of course, that we have made no allowance for greater relative 

 vigor and productivity in the heterozygous plants. However, the 

 method illustrated may be utilized in working out similar problems in 

 which the genetic relations are disturbed by such conditions as difference 

 in viability or fecundity as well as for various amounts of crossing. 



This brief consideration merely suggests the possibilities of mathe- 

 matical analysis of the composition of populations under assumed condi- 

 tions. It must be clear, however, that such analysis as applied to a given 

 set of conditions would be of very great value in conducting breeding 

 investigations. But it should be remembered that reliable conclusions 

 regarding any particular case cannot be derived from such analysis 

 unless the more important controlling agencies at least have been so 

 carefully investigated that their combined influence can be duly esti- 



x = proportion of homozygotes in the popula- 

 tion; y = value of total population. 



