i:m 



( II \ I'M K Id 



types of the meiotic products, the relative 



frequency with which the tour types oi 

 double chiasmata occur. It all four types 

 occur with equal frequency, the strands 

 forming one chiasma would he unaffected 

 by those which form an adjacent chiasma. 

 Indeed, experiments with Neurospora reveal 

 that all four types c\o occur — in some, the 

 four types occur with equal frequency. For 

 our purposes, we can accept the view that 

 there is usuallj no chromatid interference 

 in chiasma formation; in other words, the 

 particular nonsister chromatids forming a 

 chiasma arc not influenced by nonsister 

 strands which may or may not form a chi- 

 asma in an adjacent region. Thus, nonsister 

 strands crossing over in two different re- 

 gions of the same tetrad are independent. 



Does the occurrence of one chiasma in- 

 fluence the probability that a second chiasma 

 will occur in the same tetrad, even though 

 when both chiasmata occur there is no chro- 

 matid interference? 



Suppose that in the genetic system of Fig- 

 ure 10-4, each of the two regions under 

 observation has a 20% chance of forming 

 a single chiasma. If the occurrence of a 

 chiasma in the a-b region is independent of 

 a chiasma in the b-c region, then, of all 

 tetrads, 20% of the 20% with an a-b chi- 

 asma will simultaneously have a b-c chiasma; 

 that is, 4% will contain double chiasmata. 

 (According to the previous discussion, this 

 4% will be composed of the four nonsister 

 types in equal frequency.) It is a general 

 rule that the overall probability for the si- 

 multaneous or consecutive occurrence of two 

 or more events of independent origin is equal 

 to the product of their separate probabilities 

 of occurrence. 



If 4% double chiasmata were actually ob- 

 served in the a-c region, one would conclude 

 there was no chiasma interference (or better 

 still, no crossing-over interference); that is, 

 the formation of one chiasma would not 



affect the formation o\' another in an adja- 

 cent region. It. on the other hand, only 

 29? double chiasmata were observed, this 

 would mean that some chiasma interference 

 had occurred. 



The degree o\' chiasma interference can 

 be written as 



double chiasmata observed 0.02 

 double chiasmata expected 0.04 



= 0.50 



This fraction, called the coefficient of coin- 

 cidence, expresses the frequency with which 

 the coincidence of two chiasmata is actually 

 obtained. Consequently, a coefficient of co- 

 incidence equal to zero would mean that one 

 chiasma completely prevented the other from 

 occurring; whereas a value of one would 

 mean that the one chiasma had no effect 

 at all on the occurrence of the other. 



In practice, however, because of the errors 

 involved — particularly those stemming from 

 chiasma terminalization (see p. 22) — one 

 does not usually determine the frequencies 

 and positions of double chiasmata cytolog- 

 ically. Can we use the frequency of ge- 

 netically-detected double crossovers as an 

 alternative for measuring chiasma or cross- 

 ing-over interference? 



We can be sure that each double cross- 

 over observed has resulted from multiple 

 crossing over or chiasmata. The expected 

 frequency of double crossovers in the a-b-c 

 region of the example can be calculated in 

 the following way: since each region {a-b 

 and b-c) has a 0.2 chance for one crossing 

 over, the chance for a double crossing over 

 is 0.2 times 0.2, or 0.04. (If, as before, the 

 coefficient of coincidence were 0.5, one 

 would expect 0.02 tetrads to have double 

 crossing over.) Recall that the double 

 crossing over can occur in four ways and 

 can involve 2, 3, or 4 strands of a tetrad. 

 If these alternatives occur with equal fre- 

 quency, only one quarter ( % 6 ) of all mei- 

 otic products from double crossing over will 



