134 



CHAPTER 10 



I 



FIG1 R] 10-4. Chromatid recombinations pos- 

 sible in a double chiasmata. {See text for 

 details. ) 



products would be crossovers relative to the 

 markers a and c. Since the sum of the dis- 

 tances from a-b and b-c equals the distance 

 between a and c measured directly, the genes 

 of the model would be aligned linearly, just 

 as was observed in the experiment described 

 earlier in this chapter. 



In the model proposed above, the pres- 

 ence of a chiasma in one region automat- 

 ically excludes it from being in some other 

 region. Consequently, the chance that a 

 chiasma will be found in the a-c region is 

 equal to the sum of the separate chances that 

 a chiasma will be found in the a-b and b-c 

 regions. It is a general rule that the overall 

 probability jor the occurrence of any one 

 of a series of mutually exclusive events is 

 equal to the sum of their separate probabili- 

 ties of occurrence. Therefore, the chance 

 of a chiasma occurring between a and / is 

 (20 + 20 + 20 + 20 + 20)%, or 100%. 

 As a result, 100% of the tetrads have one 

 crossing over (that is, one chiasma) which 

 produces 50% crossovers, and the model 

 chromosome has 50 map units. 



The oversimplification of this model can 

 be appreciated by remembering that a given 

 tetrad usually contains more than one chi- 

 asma. This prompts us to ask: When a 

 tetrad contains two or more chiasmata, which 

 strands are involved in the exchanges? 



To answer this question, let us specify the 

 strands in a tetrad as 1,2, 3, 4, where 1 and 

 2 are the sister strands carrying the normal 

 alleles and 3 and 4 the sister strands carry- 

 ing the recessive alleles (Figure 10-4). If 

 one chiasma involves an exchange between 



nonsister strands 2 and 3 in the a-b region, 

 a second chiasma, involving nonsister strands 

 in the b-c region, can result from any one 

 of four exchanges: 2 with 3; 2 with 4; 1 

 with 3; 1 with 4. The positions of these 

 chiasmata are indicated in Figure 10-4. 

 The four types of single chiasma in the b-c 

 region together with the single chiasma in 

 the a-b region form double chiasmata of 

 three types: 



2-strand (the same two strands exchange 

 in both chiasmata); 



3 -strand (one of the two strands of the 

 first chiasma exchanges in the second, there 

 being two ways this double chiasmata can 

 occur); 



and 4-strand (those strands which do not 

 exchange in the first chiasma, exchange in 

 the second). 



Let us examine the genetic consequences 

 of these four nonsister types of double chi- 

 asmata (shown separately at the left of Fig- 

 ure 10-5). The middle column shows the 

 meiotic products of each, and the right 

 column indicates whether these products are 

 noncrossovers, single crossovers, or double 

 crossovers for the a-b-c region. From 2- 

 strand double chiasmata, two of the four 

 meiotic products are genetic noncrossovers 

 (+ + + and a be), and two are double 

 crossovers (+ b + and a + c). The dou- 

 ble crossovers, or "doubles" as they are 

 called, are characterized by a change in the 

 position of the middle gene relative to the 

 end genes. A 3-strand double chiasmata 

 produces one double crossover, two single 

 crossovers (in each, the position of one end 



