320 GENETICS IN RELATION TO AGRICULTURE 
to note in passing that there is a possibility in particular cases of dis- 
covering and overcoming the bars to self-fertility which are normally 
operative in such cases. 
Populations of Plants Normally Self-fertilized—Continued self- 
fertilization in a population normally results in the automatic elimina- 
tion from it of all heterozygous individuals. The operation of this 
principle can be seen very clearly by considering the simplest case, a 
heterozygote for one pair of factors self-fertilized through:a number of 
generations. Thus we see from Table XLVI that the general expression 
in this case for the percentage of heterozygotes after n generations of 
: baal ; 
inbreeding is 5,. If we set this value equal to 1 per cent., we get 
2” = 100, n = 6.64+. 
Accordingly beginning with a population made up entirely of individuals 
heterozygous for one pair of 
Taste XLVI.—Prorortions or Drr- factors, it would take only seven 
FERENT GENOTYPES AND PERCENTAGES generations of inbreeding to 
or HeTrRozyGores IN A POPULATION 
reduce the proportion of hetero- 
OF SELF-FERTILIZED PLANTS 
zygotes within the population 
| Percentage of 
Generation||ias | ao | “44 | heterozygotes. below 1 per cent. As a limiting 
lasrwe 7 value such a population would 
: adi : a to of course consist of 50 per cent. 
: 3 9 3 Sela AA and 50 per cent. aa. 
3 7 2 7 12.5 Jennings and others have 
4 15 DENS 6.25 given generalized formule for 
5 31 2 | 3l eas determining the percentage of 
mn |22 —1/ 2 |e —] Fn heterozygotes where any num- 
ber, m, of pairs of heterozygous 
factors is involved in the 
original population. Thus starting out with a single plant having m 
pairs of heterozygous factors, or a population consisting wholly of 
such plants, the value for h, the proportion of heterozygous individuals, 
is given by the expression: 
This expression is very useful for determining the degree of homo- 
geneity which a hybrid population may be expected to exhibit after a 
given number of generations of self-fertilization. Thus assuming that 
there are 10 pairs of factors in a given cross, what proportion of hetero- 
zygotes will there be after five generations of sowing? The formula is 
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