428 INTRODUCTION TO EVOLUTION 



pendent upon color of the coat. Under such conditions a melanistic indi- 

 vidual would be equally likely to mate with another melanistic one or 

 with a gray one, // the two were present in equal numbers. Similarly, a 

 gray hamster would be equally likely to mate with a melanistic one or with 

 a gray one, if the two were present in equal numbers. But in this instance 

 the two types are not present in equal numbers; there are three times as 

 many black individuals as there are gray ones. The same principle of ran- 

 dom mating will hold, however: the chances of an individual's mating with 

 one type or the other will be in proportion to the relative frequency with 

 which the types occur. Or, in terms of this specific example, the chance of 

 any individual hamster's mating with a black individual will be •%, the 

 chance of its mating with a gray individual will be V^. It is necessary, how- 

 ever, to go one step further and to distinguish between homozygous black 

 hamsters and heterozygous ones. We have seen that the Fo offspring are as 

 follows: 1/4 are MM, % are Mm, Y^ are mm. Accordingly, the chance that 

 any individual hamster will mate with an MM individual is Y^; the chance 

 of mating with an Mm individual is -/^ or Y2 '■> the chance of mating with an 

 mm individual is Y4- 



We can now rephrase the question: What will be the nature of the off- 

 spring from a population consisting of YMM individuals, Y2Mm ones, 

 and ^mm ones? (We shall assume that no sex differences are involved, 

 that these proportions are true of both males and females.) 



The answer may be obtained by making a "checkerboard" diagram in 

 which the male parents are listed along the left-hand margin, the female 

 parents across the top. 



In the body of the diagram are placed the different types of offspring 

 produced and their relative frequencies. The frequencies are obtained for 

 each square by multiplying the fraction representing the proportion of 



Female Parents 



Male 

 Parents 



