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 XLVII, 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 AA and aa 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 XLVII.—Composition or PorpuLaTION 
0.837; while the tatio of Generation AA Aa aa Ratio r/y* 
heterozygous dominants to 
the total dominants in 1 0.95 0.10 0.95 0.95 
the fourth generation is 2 0.928 | 0.146 | 0.928 | 0.927 
0.27. Hence, in this and : 0.919 | 0.167 | 0.919 | 0.917 
later generations the chance ETN | MUTE Ue nay Ue 
are 5 0.914 | 0.179 | 0.914 | 0.911 
of selecting a heterozygous 
dominant is about one in * x = proportion of homozygotes in the popula- 
four. Again, with 50 per tion; y = value of total population. 
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- 
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