The Theory of Population Genetics 1 117 



two or more pressures act jointly to affect the gene frequency at a 

 given locus. In addition, the gene frequencies at different loci are 

 not independent of each other, and the gene frequency at one locus 

 may have a profound effect on the gene frequency at another. To 

 appreciate this, one need only recall the phenomenon of linkage. 



Some progress has been made in describing mathematically the 

 results of various types of interactions in mendelian populations. 

 Whether a completely satisfactory mathematical description of the 

 simultaneous action of all evolutionary forces (varying with the en- 

 vironment) on an integrated genotype will ever be possible is an 

 open question. Progress in the development of computers gives 

 reason for hope, but the extreme complexity of the situation to be 

 analyzed would require a computer of as yet undreamed-of sophisti- 

 cation. For the moment we must be satisfied with combining gross 

 oversimplifications. There is solace in the fact that these simple 

 models seem to approximate some natural situations and have 

 proved quite useful in describing them. 



As a short excursion into more complex situations, consider Figs. 

 6.5 to 6.12. Figures 6.5 to 6.8 illustrate the effects of different selec- 

 tion pressures in populations of different sizes. In Figs. 6.5 to 6.7 

 mutation and back mutation rates are considered constant and equal 

 (ii = v). In Fig. 6.5 the population size is N = l/40t); in Fig. 6.6, 

 N = 10/40u; in Fig. 6.7, N = 100/40o. In all three figures the sohd 

 line is the case with the least selection (s = — d/100), the broken 

 line the case with selection ten times as severe (not represented in 

 Fig. 6.5 since it is practically indistinguishable from the preceding), 

 and the dotted line the case with selection 100 times as severe. Note 

 that selection in the very small population ( Fig. 6.5 ) merely slightly 

 alters the svmmetry of the distribution, the probability of loss or 

 fixation remaining high. As the population size increases (Figs. 6.6 

 and 6.7) the selection effects become much more pronounced. Fig- 

 ure 6.8 illustrates the distribution when the heterozygotes are favored 

 and there is no difference between the selective values of the two 

 homozygotes. Again u =v, N = l/40t;, and s = lOOu. (Note that in 

 these figures and in Figs. 6.9 to 6.12 the selection coefficient is not 

 used as defined earlier but is given both positive and negative values. 

 Thus s = lOOu is an index of the advantage of the heterozygotes, 

 whereas above s = — u/lOO is an index of the disadvantage of the 

 allele under consideration. ) 



Figures 6.9 to 6.12 show the distribution of gene frequencies in 

 populations of different sizes and different states of subdivision, 

 under various selection and mutation pressures. Figure 6.9 depicts 

 a small population under virtually no selection or mutation pressure. 



