34 MUTATION AND PLANT BREEDING 



u/s is readied. As long as the "rules of nature" (u and s) hold, the 

 gene frequency will stabilize at the value u/s. Disturbances through 

 artificial means can only increase or decrease the value of q temporari- 

 ly. When the artificial agent is withdrawn and the population is left 

 alone, the gene frequency will gradually restore to u/s. As long as 

 there is a finite probability of mutation from A to a, there is really 

 no permanent way of getting rid of gene a from a population for any 

 appreciable length of time. The condition q = u/s must be accepted 

 as a fact of nature, and by all definitions of normality, it must be 

 regarded as the normal condition. 



B. Genotypic Proportions 



Preparing for the discussion of genotypic selection, let us say a 

 few words about the genotypic proportions in a population. Consider 

 a locus with two alleles A and a, and let /; and q be their respective 

 frequencies in the population (p + q = 1). The proportion of the 

 three genotypes A A, Aa, aa (Table 1) depends upon the mating system 

 being practiced in the population. Continued close inbreeding will 

 result in complete homozygosis, and random mating yields the binom- 

 ial proportions. The more general situation, especially in plants, is 

 probably intermediate between the two extreme cases. The inbreed- 

 ing coefficient F is formally defined as the coefficient of correlation 

 between uniting gametes (Wright, 1922). 



Consider a plant population in which a fraction 6 is self- 

 fertilized and the remaining fraction (1 -- 6) is open-crossed (random 

 mating) in each generation. It may be shown that after a few genera- 

 tions the inbreeding coefficient for such a population is 



6 



F = 



2-6 



For instance, if 8 = 40 per cent of the plants is self-pollinated in 

 each generation, the inbreeding coefficient F will be 0.40/(2.00 — 

 0.40) = 0.25. The genotypic proportions in terms of F are given in the 

 fourth column of Table 1. Note that such a population may be 

 regarded as consisting of two components, viz., (1 — F) random and 

 F inbred. 



Mating system determines how often the genes A and a are 

 associated into the three types of pairs (genotypes) but does not 

 change the frequency of the genes. Thus, in each of the middle three 



