42 MUTATION AND PLANT BREEDING 



point for a population under a given selection scheme. In more 

 complicated situations, however, such as that involving multiple 

 alleles, multiple loci, local differential selection scheme, differential 

 selection in sexes, mutations of all directions, etc., there may be more 

 than one stable equilibrium value at which the population may be 

 stabilized. The selection scheme may change from time to time and 

 this fluctuation may also keep a population in equilibrium (2). 



IV. Comparison of Population Fitness 



The selection effect that arises from the differential reproduction 

 or transmission of different alleles or genotypes within a population, 

 though quite involved at times, is at least in principle easy to com- 

 prehend. It involves only the relative fitness of the genotypes con- 

 cerned, and the problem of population growth, either in absolute 

 size or in comparison with other similar populations, has not been 

 taken into consideration. When we try to compare two or more popu- 

 lations, difficulties arise because there does not exist a unique cri- 

 terion (or scale) by which different populations may be judged. 



To illustrate the difficulty of comparing two populations, let us 

 once more consider the mutation-selection equilibrium condition 

 Rs = u, or R — u/s. The value of w = 1 - - Rs at the bottom of Table 

 2B is the total of the selected individuals, but it may also be viewed 

 as the average fitness of the three genotypes in the population (average 

 fitness of the population in short), with the understanding that Wy 

 and w 2 are taken to be unity. Thus, Rs is the amount of recessive 

 individuals to be eliminated by selection in each generation, although 

 the same amount will be replaced through segregation of the old 

 and new mutations so that there is no net change in the composition 

 of the population. Mutation rate and selection intensity are param- 

 eters of nature, and have been taken as constants in our models; that 

 is, for short range genetical purposes. (They may vary widely in the 

 history of evolution.) Some hypothetical equilibrium populations are 

 listed in Table 5. The average fitness at equilibrium is 



w=\— sR=\ — s(ujs) = 1 — u, 

 independent of selection intensity. This is also true for several other 



cases (5). 



In populations 1-3, mutation rate varies proportionally to 

 selection intensity, so that the recessive proportion /\ remains the same 



