72 INBREEDING AND OOTBREEDING 



instead of there being three classes in F 2 , there are five 

 classes, viz., 12, 16, 20, 24 and 28 inches, and they appear 

 in the ratio 1:4:6:4:1. Each grandparental type 

 appears once out of sixteen times. 



The way this ratio is obtained is by simple recombina- 

 tion, but as dominance is absent, each time a single 

 "presence" factor is added, the height is increased four 

 inches. 



1 AABB = 28 inches 



2 AaBB 24 inches 

 2 AABb 24 inches 



( 4 AaBb 20 inches 



1 AAbb = 20 inches 



2 Aabb = 16 inches 



1 aaBB = 20 inches 



2 aaBb = 16 inches 



1 1 aabb 12 inches 



If three independent size characters instead of two 

 were involved in this cross, the F t individuals would fall 

 in the same class as before, but the F 2 classes would be 

 seven in number and the grandparental sizes would each 

 be recovered only once out of sixty-four times. For four 

 factors there would be nine classes of F 2 individuals, and 

 the grandparental types would each occur only once out 

 of two hundred and fifty-six times; while with only 

 eight factors, the forms of the grandparents would each 

 appear only once out of 65,536 times, and it would be 

 quite remarkable if they were ever recovered from an 

 ordinary cross. 



The entire scheme of this type of inheritance can be 

 expressed in mathematical form just like ordinary Men- 

 delian inheritance with full dominance. Let us recall that 



