378 INTRODUCTION TO EVOLUTION 



ceding chapter (p. 333), heterozygous individuals produce germ cells of 

 two kinds in approximately equal numbers. About half of the sperms 

 produced by the Mm males will contain M; about half will contain m. 

 Similarly, half of the ova produced by Mm females will contain M; half 

 will contain m. The reason is that sperms and ova arise from cells which 

 contain the pair of genes Mm. In such a paired arrangement the number 

 of M's equals the number of m's. Accordingly, when the members of these 

 pairs separate in the formation of germ cells, M-bearing germ cells and m- 

 bearing ones should be about equal in number. 



Mm male X Mm female 



[M-^M] 



X 



sperms 



>ova 



We may now ask: What are the chances that an M-containing ovum 

 will be fertilized by an M-containing sperm cell? The question may be an- 

 swered in three stages: ( 1 ) What are the chances that any given fertilization 

 will involve an M-containing ovum? Since half the ova are M-containing 

 this chance is 1 in 2, or ^4. (2) What are the chances that any given fertili- 

 zation will involve an M-containing sperm cell? Again, since M-containing 

 sperm cells and m-containing ones are equal in number, the chance that an 

 M-containing one will be involved is i/{,. (3) What, then, is the chance that 

 both an M-containing ovum and an M-containing sperm cell will be in- 

 volved? The probability that two independent events will occur together is 

 the product of the probabilities of their occurring singly. Thus the chance 

 that an MM fertilized ovum will occur is the chance that an M-containing 

 ovum will be involved ( % ) multiplied by the chance that an M-containing 

 sperm will be involved ( V2) J /{> ' V2 = /4- A similar situation arises when 

 two coins are tossed together. What are the chances that both will come up 

 "heads"? The chance that one coin will be "heads" is Y>; the chance that 

 the other coin will be "heads" is X>- Thus the chance that both will be 

 "heads" is 14 • 1/2 or 14. 



Similarly, what are the chances that an w-containing ovum will be fer- 

 tilized by an m-containing sperm? The answer is exactly the same as in the 

 case just described. The chance that an m-containing ovum will be involved 

 is 1/2 ; the chance that an m-containing sperm will be involved is also Y>- So 

 the chance that an mm fertilized ovum will arise is Y^ • /{> or ^. 



We have seen that the chances that offspring will be MM are Y4, and the 

 chances that they will be mm are V^. Thus on the average % of the off- 

 spring may be expected to be homozygous black, 14 to be homozygous 



