64 CELL HEREDITY 



exactly 0.25. It will also be observed that the frequency of parental 

 types is approximately equal to the frequency of recombinants. Thus 

 when there is 50 per cent recombination in a cross, we may conclude that 

 the factor pairs have assorted independently. No sample of data of this 

 sort is likely to give an exact correspondence with theory because chance 

 enters into each combination, and the average result tends to equal the 

 theoretical as the sample size increases. Table 3.1 shows how such 

 data are objectively assessed. 



LINKAGE, RECOMBINATION, AND GENETIC MAPS 



Independent assortment is frequently observed but, unknown to 

 Mendel, it is far from universal. Exceptions were first discovered by 

 Bateson and Punnett in England; they referred to nonindependent assort- 

 ment as linkage. In Chlamydomonas the factors determining a require- 

 ment for the amino acid, arginine (arg), and the vitamin, para-aminobenzoic 

 acid ipaha), are linked. In a cross of arg^ paha^ x arg~ paha~ strains, 

 5214 gametes were found to be old combinations while only 906 were 

 new. This is a significant deviation from the 3060 of each type expected 

 if the factors had assorted at random. There is a tendency for the factors 

 arg and paba to enter the progeny in the same association as existed in 

 the parents. When the cross was made with the opposite association, 

 arg~ paba^ x arg^ paba~, the parental combinations again predominated, 

 618 to 146. The frequency of recombinations was about the same in the 

 two crosses, 0.19 in the first and 0.15 in the second. It is, therefore, not 

 the particular combination of factors which determines whether it will be 

 present in excess, but rather the coupling with which the factors entered 

 the cross. 



The strains used in the crosses just mentioned differed in another trait, 

 the requirement for the vitamin, thiamin (tJii), so that the genotypes in the 

 crosses may be rewritten: 



arg'^ paba'*' thr x arg~ paba~ thi'^ 

 arg~ paba^ thi^ x arg^ paba~ thr 



The genotypes of the progeny of these three-factor crosses show that thi 

 is also linked to paba. Among the 6884 gametes analyzed, 30 per cent 

 showed new combinations of these genes and, once again, this frequency 

 was independent of the coupling in which they entered the cross. If, as 

 has been shown, arg is linked to paba and paba is linked to ihi, then arg 



