CHAPTER 



4 



Introgression in Finite 

 Populations 



Up to this point our discussion has considered the effects 

 of linkage in restricting the kinds of recombinations that 

 can occur in a species cross. Linkage also restricts their 

 frequencies, a fact that becomes important when we proceed 

 to discuss the probable fates of hybrid generations beyond 

 the F2. Since the individuals of the first hybrid generation 

 are essentially similar genetically, it made very little dif- 

 ference in considering the recombinations achievable in the 

 F2 w^hether w^e w^ere considering populations of scores, or of 

 hundreds, or of thousands. Any two or three Fi plants if 

 crossed together will give essentially the same F2 as will any 

 two or three others. With the F3 this is all changed. In a 

 species cross the number of genetically different F2 in- 

 dividuals certainly runs into the hundreds and might well be 

 in the thousands. Therefore, in any finite F2 population, 

 most of the plants will be genetically distinct, and there may 

 be great differences between different F3 populations. In 

 considering what would happen in the F3, we must not only 

 calculate the F2 types that might occur and become the 

 parents of the F3 ; we must also consider which are inost likely 

 to occur. 



To facilitate the discussion of these matters, let us con- 

 struct a h^-pothetical case of linkage between 2 multiple- 

 factor characters, leaf pubescence and leaf shape. Let us 

 suppose that there are 2 pairs of genes, A vs. a and C vs. c, 

 which have simple additive effects on leaf shape, so that 

 AACC is broad at the apex, w^hile aacc is narrow at the apex 

 and broad at the base, and AaCc is exactly intermediate. 

 In the same way we shall imagine genes B vs. h and D vs. d 

 affecting pubescence so that BBDD is strongly pubescent, 



49 



