440 INTRODUCTION TO EVOLUTION 



The four arrows in the diagram represent the four possible combinations 

 of germ cells. Probability of occurrence is the same for all four combina- 

 tions. Two combinations result in MM offspring, two in Mm offspring. 

 Thus the chance that the first offspring will be MM is 14, and the chance 

 that the second offspring will be MM is also 14 • Hence, the chance that 

 both of two offspring will be MM is Yj, ■ % or M- But if both the offspring 

 are MM, an event of great significance has transpired: the m gene has 

 been irrevocably lost. The population will revert to its original all-MM 

 constitution and remain so until such time as a fresh mutation from M to 

 m occurs. We note, moreover, that the chance of losing a mutation in this 

 way is not a small one; it is one chance in four, or 25 percent. 



But what other constitutions may the two offspring possess? The chance 

 that the first offspring will be Mm is K, the chance that the second off- 

 spring will be Mm is also %. Thus the chance that both of the two will 

 be Mm is V2 ' V2 ^"^ V-i- It is to be noted that in this case the number of 

 m genes is doubled; the parents, only one of which possessed the m gene, 

 have been replaced by two offspring both of which possess the gene. 



The chance that the first offspring will be MM is ^/^^ the chance that the 

 second will be Mm is H. Hence, the chance that the two will have the 

 designated respective constitutions is U • V. or ^4 • Finally, the chance that 

 the first offspring will be Mm is ^{>, the chance that the second will be 

 MM is v., the chance for the combination being ^/2 • % or i/4- Thus the 

 chance that either one of the two offspring will be MM and the other Mm 

 is % + ^/4 or y.2- These combinations represent retainment of the status 

 quo: the parents, MM X Mm, are merely replaced by two offspring having 

 the same constitutions as themselves. The frequency of the m gene has 

 neither increased nor decreased. 



In sum, we find that, owing to the operation of chance in the reproduc- 

 tion of a relatively stationary population, we may expect "new" mutations 

 to be lost from the population about 25 percent of the time, to be doubled 

 in frequency about 25 percent of the time, and to remain unchanged in 

 frequency about 50 percent of the time. 



Suppose we assume that the second possibility is the one which occurs — 

 that the parents are replaced by two offspring, both Mm in constitution. If 

 these two are of opposite sex, they may mate together, thus making pos- 

 sible the actual appearance of gray offspring, as diagramed above (p. 

 438). But the chances of their mating together are not large; if they do 

 not do so they obviously must mate with MM individuals. The result 

 would be two matings like those of the original parents: 



