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CHAPTER 17 



latter value equaling the product of the ob- 

 served frequencies of single crossovers in the 

 two adjacent regions. 



It is found, in general, that the coefficient 

 of coincidence is for short map distances 

 and becomes larger as the distances do. This 

 means that a tetrad in which one chiasma 

 forms is somehow inhibited from having a 

 second one occur in a region close by, this 

 inhibition becoming less the farther away this 

 second region. In Drosophila, for example, 

 the coefficient of coincidence is for map 

 distances up to 10-15 map units, so that no 

 double chiasmata (hence no double cross- 

 overs) occur within such distances. As the 

 distance increases beyond 15 map units, the 

 coefficient increases gradually to 1, at which 

 time there is no interference with the forma- 

 tion of double chiasmata. 



You remember that, if every tetrad in our 

 model had a single chiasma located some- 

 where between a and /, the maximum fre- 

 quency of recombination for these end genes 

 would be 50%. What happens to the fre- 

 quency of recombination for the end genes 

 when our model is also permitted to have 

 double chiasmata? If, now, each tetrad has 

 one or more chiasmata (and hence cross- 

 overs), you might think, at first, that the end 

 genes would form new combinations more 

 than 50% of the time. However, examination 

 of Figure 17-4 will show you, because each 

 type of double chiasmata is equally likely, 

 that, on the average, there will be eight 

 products which would switch the end genes 

 (being those which are single crossovers) and 

 eight products which would not (being com- 

 posed of four double crossovers, in which an 

 interstitial gene switches but end genes retain 

 their original order, plus four noncrossovers). 

 Accordingly, even if every tetrad has double 

 chiasmata, the maximum recombination for 

 the end genes is again 50%. 



If four genes are studied and three chias- 

 mata occur in each tetrad, one in each region, 

 it turns out that per each 64 meiotic prod- 



ucts 32 will be recombinational for the end 

 genes and 32 will not. One can work out the 

 fact that for cases where there are four or 

 more chiasmata between end genes, the num- 

 ber of meiotic products bearing odd numbers 

 of crossovers (1, 3, 5, etc.) is 50%> In each 

 of these cases one end gene is shifted relative 

 to the other. However, the remaining strands 

 contain either even numbers of crossovers 

 (which do not cause the end genes to shift 

 relative to each other) or no crossovers. 

 Accordingly, there is still a maximum of 50% 

 recombination for the endmost genes (and, 

 therefore, of course, for any genes between 

 them). 



If two genes are located far apart in a 

 chromosome and multiple chiasmata normal- 

 ly fall between them, their rate of recombina- 

 tion will be near 50%. Since 50% recombina- 

 tion is taken to mean independent segregation 

 of gene pairs, you might not be able to con- 

 clude from the recombination rate that these 

 two genes are linked (cf. p. 46). Whenever 

 genes are known to be linked, however, their 

 correct order relative to each other may be 

 determined without concern about the cor- 

 rectness of the distances involved. Moreover, 

 this may be decided from the results of a 

 single cross. Suppose the trihybrid + + +/ 

 a b c is test crossed, and the frequencies of 

 phenotypes in the progeny are as shown at 

 the left in Figure 17-5. These frequencies, 

 you recall, represent the frequencies of the 

 corresponding genotypes in the gametes of 

 the trihybrid. The middle gene would be 

 the one which switches least often from 

 the original gene combinations (H — | — \- and 

 a be), for only it requires two chiasmata to 

 switch. Accordingly, this gene is identified 

 as c, and the actual gene order is ac b 

 (or bed). You may understand this more 

 readily by examining the data when the genes 

 are listed in their correct order, as shown at 

 the right in Figure 17-5. Here the frequency 

 of observed crossovers between the a and c 



loci is 30%, and between e and b 10^ 



(The 



