Li: MUTATION, SELECTION, AND POPULATION FITNESS 33 



natural populations. One is that the balanced condition is maintained 

 by the opposing forces between selection and mutation. The other is 

 that the equilibrium is the result of conflicting selection effects alone 

 and that mutation plays a very little role. In this communication, only 

 one or two examples of each kind will be given to illustrate the 

 properties of equilibrium. A minimum bibliography is cited from 

 which further discussions and other references may be found (1, 

 8, 10, 16). 



A. Gametic Selection 



Consider the two alleles A and a which reproduce or transmit 

 to the next generation in the ratio \:w, where w is called the (relative) 

 fitness of gene a. If w is smaller than unity, we may write w — 1 — s, 

 where s is called the selection coefficient against gene a. Suppose that 

 the initial frequencies of A and a in a population are p and q. Then, 

 after one generation of selection, their frequency ratio will be 

 p:q(l—s); that is, new p = p/(l—sq) and new q = q(\— s) /(l — sq). 

 The decrease in frequency of a per generation is 



q ( ! ~ s ) - s P <1 



A q = new q — old q = — q = 



\ — sq 1 — sq 



Gene a will be eliminated from the population if the selection 

 continues unopposed. Now, suppose that the rate (or probability) of 

 mutation from A to a is u per generation, where u is a small number 

 of the order of 10~ 5 or 10°. A mutation may occur at any time and 

 at any stage of the life cycle; but for the sake of algebraic simplicity, 

 let us assume that mutations occur after the operation of selection. 

 Then, among the p/ (Isq) A genes, a small fraction u of them will 

 mutate to a per generation. Selection tends to decrease q, but muta- 

 tion tends to increase it. These two forces will balance each other so 

 that there will be no change in gene frequency when 



s p q p u 



1 — sq \—sq 

 That is, sq = u, or q = ujs 



This is the simplest type of equilibrium between mutation and 

 selection. The equilibrium is stable. That means, if q in any genera- 

 tion is greater than ujs, it will decrease until the value of ujs is 

 reached. If q is smaller than ujs, it will increase until the value of 



