THE NUMBER OF GENOTYPES 385 



The Number of Genotypes in the Second Genera- 

 tion is constajit for any particular type of mating and 

 depends, of course, on the number of kinds of gametes 

 which the first generation hybrid can produce. 



Here only back-crosses and interbreeding can be con- 

 sidered. The first is so simple as barely to need mention, 

 for if n kinds of pure gametes are mated to one kind of 

 sperm (or egg) (and a pure recessive can form only one 

 kind) they will of course give rise to n different combina- 

 tions of genes or genotypes and all will occur in equal 

 numbers. In interbreeding the matter is not quite so 

 simple but is easily understood in the following way: 

 Parents a x a' produce the hybrid aa' and it produces 

 gametes a and a' which combine in the second generation 

 genotype combinations laa; 2aa'; la'a', i.e., 3 genotypes. 

 If a second gene and character difference t>-b' is added 

 genotype aa may become aabb, aabb\ or aab'b', i.e., is 

 multiphed by 3. The same thing is true for the aa' and 

 aV genotypes, hence adding another gene and character 

 difference in the hybrid multiplies the number of F2 

 genotypes by 3. Stated generally, a hybrid involving n 

 pairs of independent characters and genes forms 3"" geno- 

 types in the second hybrid generation by interbreeding. 



The Phenotypes of the Second Generation. — Two 

 independent pairs of genes assort in the reduction divi- 

 sions of the hybrid so as to give four kinds of gametes 

 and these unite by chance to produce four phenotypes in 

 the second hybrid generation. If the genes are linked 

 two phenotypes may be missing altogether, or when 

 crossing-over occurs, appear in greatly reduced numbers 

 in comparison with ratios expected in independent 

 assortment. It is now possible to consider a second reason 

 for variation from the usual ratios of independent assort- 

 ment. The ratios discussed in previous paragraphs are 

 those which occur when a character difference depends 

 on a single differential gene, but there are many charac- 

 ter differences which depend on more than one differential 



