PRINCIPLES OF HEREDITY 655 



genetic mechanism responsible for the 3:1 ratios obtained by Mendel in 

 his pea breeding experiments is now evident. 



The appearance ot an individual with respect to a certain trait, the 

 end result ot the action ot the gene, is known as its phenotype; the 

 individual's genetic constitution is called its genotype. In the Fo gen- 

 eration ot the guinea pig mating, the phenotypic ratio is 3 black : 1 

 brown; the genotypic ratio is 1 BB : 2 Bb : 1 bb. Guinea pigs which are 

 BB and Bb have similar phenotypes— both have black coat color— but 

 they have different genotypes which could be distinguished only by 

 further breeding tests. It is also possible, as we shall see later, for in- 

 dividuals to have similar genotypes but different phenotypes. 



271 . Laws of Probability 



It is important to realize that all genetic ratios are expressions of 

 probability, based on the laws of chance or probability; they do not 

 express certainties. If two heterozygous black guinea pigs are mated and 

 have exactly four offspring there is no guarantee that there will be 

 exactly three black ones and one brown one. All might be black, or all 

 might be brown, though this would occur only rarely (one can calculate 

 from the laws of probability that there is one chance in 256 of having 

 four brown guinea pigs in such a mating). Any of the combinations of 

 3 black : 1 brown, 2 black : 2 brown, or 1 black : 3 brown might appear. 

 But if enough similar matings are made to produce a total of 400 

 otfspring, the ratio of black to brown among the offspring will be very 

 close to 300 to 100. The theoretical 3 : 1 ratio is approximated more 

 and more exactly as the total number of individuals increases; this is 

 predicted by the laws of probability and actually found when genetic 

 tests are made. One can state, perhaps more exactly, that in the mating 

 of two individuals heterozygous for a given trait there are three chances 

 out of four that any particular offspring will show the dominant trait 

 and one chance out of four that it will show the recessive one. Each 

 mating, each union of an egg and a sperm, is an independent event 

 which is not influenced by the results of previous matings. No matter 

 how many black-coated offspring have been produced by the mating of 

 two heterozygous black ones, the probability that the next offspring to 

 be born will have a brown coat is one chance in four, and the prob- 

 ability that it will have a black coat is three chances in four. 



272. Test Crosses 



In the ¥-2 generation of a monohybrid cross, one-third of the in- 

 dividuals with the dominant phenotype are homozygous and two-thirds 

 are heterozygous. In the guinea pig mating (Fig. 32.1) the black-coated 

 individuals in the F2 generation include some with the genotype BB and 

 some with the genotype Bb. These can be distinguished by a test cross, 

 in which the black-coated guinea pig is mated with a brown-coated one 

 (genotype bb). If all of the offspring are black, the parent is probably 



