GENETIC BASIS 39 



binations the total number of kinds of gametes will be 2n. 

 Since the total number of possible combinations of unlinked 

 genes is given by 2^, the ratio we are seeking will be 2n/2''. 

 For 3 pairs of gene differences this becomes 3/4; for 4 pairs 

 1/2; for 10 pairs 10/512, or less than 2 per cent. 



Since the same principle will be operating in every cross- 

 over region (tempered only by the occurrence of multiple 

 crossing over), the total hindrance in the entire germplasm 

 will be enormous. An estimate can be obtained by con- 

 sidering the not impossible case of an organism that regularly 

 has a single chiasma in each chromosome. For such an or- 

 ganism the ratio of the possible kinds of gametes to the total 

 number of recombinations will be (2n/2") , in which n equals 

 the numbers of differing loci per chromosome and N is the 

 number of pairs of chromosomes. For even such a slight 

 difference as 4 genes per chromosome and with only 6 pairs 

 of chromosomes this ratio becomes 1/64. For 10 gene differ- 

 ences per chromosome and with 10 pairs of chromosomes it 

 becomes (10/512) ^^ or roughly less than 1 in 100,000,000,- 

 000,000,000. 



It should be emphasized that this restriction is independ- 

 ent of the size of the F2 and constitutes an absolute upper 

 limit to gene recombination in that generation. The ratio 

 (10/512)^^, inconceivably small though it may be, represents 

 the fraction of the total recombinations which could be 

 achieved in a population of infinite size. This is a number so 

 large that it has little meaning to the human mind. 



A graphical example of the recombinations of one chromo- 

 some was worked out in detail (Anderson, 19396). With a 

 few minor corrections, this is presented here as Plate 2. The 

 figure shows all the possible recombinations in the F2. With 

 complete recombination the entire quadrangular coordinate 

 would have been covered and the possible recombinations 

 would have formed a square instead of a diagonal spindle. 



The diagram is restricted to a single pair of chromosomes 

 differing in 6 essential genes affecting 2 different characters. 

 The question of frequencies is not considered. The diagram 



