Interference and Coincidence 179 



over the three crossover percentages, we should see that 7.75 

 per cent is the smallest. Therefore, the Bm pr V and bm Pr v 

 combinations must represent the double crossovers. Since the 

 Bm and V genes and the b?n and v were the parental combina- 

 tions, the pr and Pr genes must have been the middle of the 

 three genes in the series. This simple fact is an aid in determin- 

 ing the order in which the genes were located. 



Interference and Coincidence 



It was shown earlier that one chromatid of each of two 

 paired chromosomes may break at a given spot and that the 

 two chromatids may then rejoin in a new arrangement, result- 

 ing in genetic crossing over. Although the cause is not well 

 understood, it is an observed fact that when a break occurs at 

 one particular spot, another break cannot occur for a certain 

 distance from the first. The effect of this is to reduce the num- 

 ber of double crossovers that would be expected on the basis of 

 chance alone. Thus, when one crossover occurs at a certain 

 point, another is prevented from occurring within a certain dis- 

 tance from it. This prevention of or interference with the forma- 

 tion of a second crossover is known technically as interference. 

 The cause may not be a purely mechanical matter, for the de- 

 gree of interference is not the same in all chromosomes of the 

 same species or even in all parts of the same chromosome. 



The phenomenon of interference can be observed by consid- 

 ering the percentage of double crossovers in its relation to the 

 theory of probability. In Chapter 8 we saw that when two 

 independent events occur, the probability that they will occur 

 at the same time is the probability that one will occur alone 

 multiplied by the probability that the other will occur alone. 

 In the problem in maize, the crossover value between bm and 

 pr was 22.27 per cent, or the chance of getting one crossover 

 between these genes was 22.27 out of 100. The chance of getting 

 a crossover between pr and v was similarly 43.37 per cent. The 

 chance of getting two crossovers in those two regions, and hence 

 between biri and v, is 0.2227 X 0.4337, or 9.66 per cent. In other 

 words, if there were no interference 9.66 per cent of double cross- 

 overs should be obtained, whereas actually there were only 7.75 

 per cent. The difference is due to interference. This discrepancy 

 can be expressed as the coefficient of coincidence (also called 



