POPULATION GENETICS AND EVOLUTIONARY CHANGE 429 



males of the constitution concerned by the traction representing the pro- 

 portion of females of the constitution concerned. Thus the frequency in the 

 square in the upper left-hand corner is I4 ■ ' , or ' , ,;. The upper row repre- 

 sents the offspring to be expected when the MM males, constituting i;, of 

 the total males, mate with the three different types of females in proportion 

 to the relative frequencies of the latter. The diagram shows that ' 1 ,-, of the 

 matings will occur between MM males and MM females, 71 ,-, between MM 

 males and Mm females, Vi r, between MM males and mm females. The other 

 two horizontal rows are to be interpreted similarly. 



The offspring from some of the matings are all of one type — shown in 

 the corner squares of the diagram. In four other squares two types of off- 

 spring occurring in equal numbers are shown. An example is the middle 

 square of the top row; here MM males are mated to Mm females. 



MM X Mm 



M^M] 



sperms- 



>ova 



[M^m] 

 offspring: MM, MM, Mm, Mm 



In such a mating MM offspring and Mm offspring are to be expected in 

 equal numbers. Hence, the -i,-, of the offspring arising from such matings 

 resolves itself into ^-ir.MM offspring and ^{f-Mm offspring. 



The central square of the diagram represents a still more complex situa- 

 tion, in that both parents are heterozygous. Mm X Mm. As we noted 

 earlier, offspring from such parentage are expected to appear in a 1:2:1 

 ratio; hence the ^^,; of this square is resolved into \{,;MM, 'jn^Mm, and 

 y^yjnm, as indicated. 



If now we assemble the results shown in the diagram, we find that fi,j of 

 the offspring will be expected to be MM, % ,; will be Mm, Y-^ ,j will be mm. 

 This is our 1:2:1 ratio again. The proportions of the different types of indi- 

 viduals are the same in the F,, generation as they were in the F^,. Evi- 

 dently, then, our artificial population is in equilibrium; so long as random 

 mating occurs the proportion of y^MM to VUMm to ^ ^mm may be ex- 

 pected to continue generation after generation. 



Gene Pool 



There is a simpler and more direct way of working the problem discussed 

 above. Let us concentrate upon the genes, rather than upon the combina- 

 tions of genes in the various parents. Turning our attention to the male 



