GENETIC FACTORS IN THE ORIGIN OF DIVERSITY 379 



gray. The remaining % will be expected to be heterozygous black: Mm. 

 Such individuals can arise in two ways: ( 1 ) by an M-containing sperm 

 cell's fertilizing an m-containing ovum (chances of this Y^ ' !{> = M); 

 (2) by an m-containing sperm's fertilizing an M-containing ovum 

 (chances of this ]{, • ^j = %). Since the chance that two mutually ex- 

 clusive events will occur is the sum of the chances that either event will 

 occur alone, the chances that Mm offspring will arise is Y^ + Y^ or 74. 



Mm male X Mm female 



IM^M] 



sperm - 



/•ova 



m -^ m 



F2 offspring: MM Mm mm 



^i H ^: 



black, y4. gray, M 



The above results are sometimes expressed as ratios. The fundamental 

 ratio among offspring of parents both of whom are heterozygous is 1:2:1 

 (1 homozygous dominant to 2 heterozygotes to 1 homozygous recessive). 

 When dominance is present, this fundamental ratio is masked, since 

 homozygous dominants {MM) look like heterozygotes (Mm). Thus on 

 the basis of phenotype (p. 333) the ratio becomes 3 black-colored off- 

 spring to 1 gray one (Fig. 17.1). 



Sometimes dominance is not present. In such cases the 1:2:1 ratio is the 

 ratio of phenotypes as well as the ratio of genotypes. For example, when 

 red snapdragons (RR) are crossed with ivory ones (rr) the F, offspring 

 (Rr) are pink in color. Pink may be regarded as intermediate between red 

 and ivory, a sort of diluted red. Evidently in this case having one R gene 

 results in less red pigment than does having two R genes. When the 

 F-j ofTspring are produced by mating these pink heterozygotes together 

 (Rr X Rr), the ratio of Y red (RR) to 74 pink (Rr) to Y ivory (rr) is 

 obtained. Similarly, Blue Andalusian fowls are heterozygotes (Ww). 

 When Blue Andalusians are mated together the ratio obtained is: ^4 black 

 (WW) to -Y blue (Ww) to 14 splashed white (ww). 



We should emphasize that these 1:2:1 and 3 : 1 ratios, so prominent in 

 writing concerning Mendelian inheritance, depend upon the operation of 

 the laws of chance as set forth above. The ratio expresses the ideal or 

 perfect outcome when two types of sperms fertilize two types of ova. 

 Ratios obtained in actual experiments approach the ideal ratio but seldom 

 conform to it exactly. On the whole, the larger the number of offspring 

 produced, the more closely will the ideal ratio be approached. As is well 



