98 I The Process of Evolution 



fluctuation of gene frequency due to chance occurrences is known 

 as genetic drift. The term drift is quite descriptive, as the frequency 

 of p seems to drift around without approaching any particular vakie, 

 unhke the directional movements caused by the so-called systematic 

 pressures of mutation, selection, and differential migration. 



Figure 6.1 shows the probability distribution of p in 50 and 5,000 

 offspring from a parental population in which the gene frequency 

 was p = .50. In this and succeeding examples it will be assumed that 

 all the conditions for maintaining a Hardy-Weinberg equilibrium are 

 present, except in the factor under study. In other words, the factors 

 will be manipulated one at a time to show how they may alter the 

 equilibrium. 



The possible values of p in the two different groups of offspring 

 are given in the two histograms of Fig. 6.1. The ordinate represents 

 the approximate probability of p falling in each interval. As expected, 

 the chances for large fluctuations due to sampling error are much 

 greater for the smaller group of offspring. 



Figure 6.1 also shows the fates of large numbers of loci, all of 

 which were at gene frequency of .50 in their parental population. 

 With N — 50, one would expect only 3 loci in 100,000 to fluctu- 

 ate to a value greater than .70, whereas with N = 5,000 only 3 loci 

 in 100,000 would fluctuate to a value greater than .52. On the other 

 hand, one may wish to consider the distribution of the gene frequency 

 of a given locus in a large number of populations, all with an initial 

 gene frequency of .50. According to Fig. 6.1, with N = 5,000, we 

 would expect 99.994 percent of the populations to have a gene fre- 

 quency between .48 and .52 for the specified locus, whereas with 

 A/ = 50 the same percentage would have a range from .30 to .70. 



Decay of Variability 



The possible consequences of drift in a small population are shown 

 diagrammatically in Fig. 6.2. The gene frequency is analogous to a 

 pinball; moving down the slope (through time), it ricochets from 

 value to value, as long as it stays on the table. However, in the 

 absence of mutation and migration, the values of (loss) and 1.0 

 ( fixation ) are dead ends; once the ball drops into one of these slots 

 it stays there. That is, gene A is either fixed ( all individuals AA ) or 

 lost (all individuals aa). Thus the gene frequency of A can move 

 from any intermediate value to the end points and 1 but not vice 

 versa; the gene frequency will ultimately be or 1 if the population 

 is left undisturbed long enough. Since, when the gene frequency 

 reaches or 1, heterozygotes no longer can be formed at the locus. 



