132 



CHAPTER 17 



i.e., which are crossover, and that each of the 

 three different types produces a character- 

 istic pattern of noncrossover and crossover 

 types. Note further that the genetic conse- 

 quences of these double chiasmata are differ- 

 ent from what would be obtained following 

 a single chiasma (which, you remember, 

 produces two noncrossovers and two singles). 



In view of the preceding discussion, it 

 should be possible by using an organism like 

 Neurospora, in which all the products of 

 meiosis are recoverable and testable, to learn 

 from the genotypes of the meiotic products 

 the relative frequency with which the four 

 types of double chiasmata occur. If all four 

 types occur with equal frequency, this would 

 mean that the strands forming one chiasma 

 are uninfluenced by those which form an 

 adjacent chiasma. Indeed, work performed 

 with Neurospora shows that all four types do 

 occur. In some experiments the four types 

 occur with equal frequency, and, for our 

 purposes, we can accept the view that there is 

 usually no chromatid interference in chiasma 

 formation, i.e., the chromatids which enter 

 into a chiasma do so uninfluenced by which 

 strands have or have not undergone chiasma 

 formation in an adjacent region. 



Let us consider now the second possible 

 relationship, already mentioned, between ad- 

 jacent chiasmata. Does the occurrence of 

 one chiasma increase or decrease the prob- 

 ability that an adjacent chiasma will occur, 

 regardless of which strands are involved? 

 Suppose, in a genetic system as in Figure 

 17-4, the probability of a single chiasma be- 

 tween a and b is 0.2 and between b and c 

 is also 0.2. Having presumed that each of 

 two regions under observation has a 20% 

 chance of forming a single chiasma, let us 

 again make use of the observation that more 

 than one chiasma can form in a tetrad. If 

 the occurrence of a chiasma in the a-b region 

 is uninfluenced or independent of a chiasma 

 in the b-c region, then, of all tetrads, 20% 

 of the 20% with an a-b chiasma will simul- 



taneously have a b-c chiasma, or 4% will 

 contain double chiasmata. (And from what 

 has been discussed before these 4% will be 

 comprised of the four nonsister types in equal 

 frequency.) It is a general rule that the 

 probability for the simultaneous occurrence 

 of two or more independently occurring events 

 is obtained by multiplying together their sepa- 

 rate probabilities. 



If an experiment studying these regions 

 actually gave 4% double chiasmata, one 

 would conclude there was no chiasma inter- 

 ference; that is, the fact that homologous 

 chromosomes form one chiasma has no effect 

 upon the hkelihood of their forming another 

 one in an adjacent region. If, on the other 

 hand, only 2% double chiasmata were ob- 

 served, this would represent interference of 

 one chiasma with the formation of another in 

 an adjacent region. 



The degree of chiasma interference can be 

 expressed by the fraction: 



double chiasmata observed _ .02 

 double chiasmata expected .04 



= .5 



This fraction is called the coejficient oj co- 

 incidence and expresses the frequency with 

 which the expected coincidence of two chi- 

 asmata is actually observed. So, a coefficient 

 of coincidence of would mean one chiasma 

 completely prevented the other one from oc- 

 curring, while a value of 1 would mean that 

 the one chiasma did not interfere at all with 

 the occurrence of the other. 



In practice, however, one does not deter- 

 mine the actual rates of occurrence and the 

 positions of double chiasmata, since it is not 

 feasible cytologically to score chiasmata in 

 these ways. We are led, therefore, to examine 

 the genetic event of crossing over to see 

 whether it can be used to measure interfer- 

 ence. Since we can be sure that each double 

 crossover observed came from a double 

 chiasmata, let us see if such crossovers can 

 be used to calculate the coefficient of coin- 

 cidence. The expected frequency of double 



