138 



CHAPTER 10 



+ + + 0.31 



a b c 0.31 



+ b c 0.14 



a + + 0.14 



+ + c 0.01 



a b + 0.01 



+ b + 0.04 



a + c 0.04 



+ + + 0.31 



a c b 0.31 



+ c b 0.14 



a + + 0.14 



+ c + 0.01 



a + b 0.01 



+ + b 0.04 



a c + 0.04 



1.00 



1.00 



figure 10-6. Determination of gene order 

 from a test crossed trihybrid. 



cause the genes at the two ends to shift 

 relative to each other) or are noncrossovers. 

 Accordingly, the maximum frequency of re- 

 combination of 0.5 holds for the endmost 

 genes (and, therefore, of course, for any 

 genes between them). 



If two genes in a chromosome are suffi- 

 ciently far apart, the frequency with which 

 they undergo recombination will be near 0.5. 

 Since a recombination frequency of 0.5 

 means that nonalleles are independent in 

 their segregation, one cannot conclude from 

 such a recombination frequency that non- 

 alleles are on the same chromosome. Ac- 

 cordingly, two pairs of genes that show re- 

 combination frequencies near 0.5 can be 

 either far apart in the same pair of homologs 

 or located in different pairs of homologs. 

 However, if two nonalleles segregate inde- 

 pendently but are both linked to a third 

 nonallele, all three are linked to one an- 

 other. 



Whenever the number of gene pairs in- 

 vestigated is considerably larger than the 

 Dumber of chromosome pairs, the number 

 of groups of linked genes equals or ap- 

 proaches the number of chromosome pairs. 

 The result is a limitation in the number 

 of linkage groups, the maximum number 

 equalling the haploid chromosome number. 

 (Examination of the linkage groups of the 

 garden pea now reveals that two of the first 

 seven gene pairs studied ' arc in the same 

 linkage group although a considerable dis- 

 tance apart. The initial recombination data 

 were sufficiently meager for acceptance of 

 the hypothesis that the genes were segregat- 

 ing independently.) 



The sequence of three linked genes can 

 be determined from the results of a single 

 cross. Suppose the trihybrid -+- -+- + /a b c 

 is test crossed, and the frequencies of the 

 various phenotypes in the progeny are those 

 shown at the left in Figure 10-6. These 

 values, we remember, represent the fre- 

 quencies of the corresponding genotypes in 

 the gametes of the trihybrid. The middle 

 gene in the actual sequence is the one which 

 switches least often from the original gene 

 combinations (+ -\ — h and a be), because 

 only the middle one requires two chiasmata 

 for its switch. Consequently, this gene is 

 identified as c, and the actual gene order is 

 acb (or be a). This reasoning may be 

 easier to follow if the data are examined 

 with the genes listed in their correct order, 

 as shown at the right in Figure 10-6. 



The frequency of observed crossovers be- 

 tween the a and c loci is 0.30; between c 

 and b it is 0.10. Between a and b the fre- 

 quency of single crossovers is 0.36. Cross- 

 over frequency between a and b, however, 

 also includes double crossovers. Since each 

 double crossover represents two single cross- 

 overs between the end genes, the frequency 



1 By G. Mendel. 



