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 XL VI that the general expression 

 in this case for the percentage of heterozygotes after n generations of 



inbreeding is ^-. 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 

 TABLE XLVI. PROPORTIONS OF DIF- 

 FERENT GENOTYPES AND PERCENTAGES 

 OF HETEROZYGOTES IN A POPULATION 

 OF SELF-FERTILIZED PLANTS 



factors, it would take only seven 

 generations of inbreeding to 

 reduce the proportion of hetero- 

 zygotes within the population 

 below 1 per cent. As a limiting 

 value such a population would 

 of course consist of 50 per cent. 

 A A and 50 per cent. aa. 



Jennings and others have 

 given generalized formulae for 

 determining the percentage of 

 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: 



(On _ 'l 

 TT 



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 



