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AN INTRODUCTION TO MODERN GENETICS 



but it can be shown with a high degree of certainty that in some cases 

 chiasma formation has involved a crossing-over. The simplest case is 

 that of a heteromorphic bivalent (e.g. one of the sister chromosomes has 

 a deficiency) which divides into two equal halves (equationally) at the 

 first division : either the two chromatids at one attachment constriction 

 were not sisters or there has been a crossing-over, and the first of these 

 possibihties can be ruled out as inconsistent with all genetic data. 



If a chiasma involves a crossing-over, the sister chromatids remain 

 paired together through their length. This must be so, and thus the 

 chiasma must involve a cross-over, in all cases in which it can be 



Fig. 58. Chiasmata and Crossing-Over. — ^The "classical" interpretation of a 

 chiasma is shown in A; no crossing-over is involved, as may be seen from the 

 anaphase figure below. The "chiasmatype" interpretation is shown in 6; note that 

 sister chromatids remain together in all parts of the bivalent. The lower part of 6 

 shows the anaphase configuration, with partially terminalized chiasma; note that 

 crossing-over has occurred. 



shown that the paired threads on each side of a chiasma have acted 

 together as a unit. If we find the two threads of one pair coiled as a 

 unit round the two threads of the other pair, this must mean that each 

 pair represents a single chromosome, and that the members of the 

 pairs are sisters. The other special cases in which a cross-over can be 

 shown to be associated with a chiasma are more complicated.^ (Cf. 

 Fig. 62.) 



The generalization of these deductions to the theory that aU chias- 

 mata involve crossing-over is prompted partly by a desire to simplify 

 the working hypotheses. It has to its credit two main predictions. 



In the first place, it enables one, by ascertaining the average chiasma 

 frequencies of different bivalents, to predict the length in cross-over 

 units of the genetic maps of these chromosomes, since the average 

 occurrence of one chiasma between two points is equivalent to 50 per 

 cent crossing-over. This has been done for maize j^ and the predicted 



^ Cf Darlington 1930a, 1937. ^ Darlington 19346. 



