CHAPTER 4 



The Linear Differentiation of the Chromosomes 



A. CROSSING-OVERi 



I. Cross-over Maps 



The fact on which the building up of a cross-over map is based 

 has been mentioned in Chap, i ; the additive theorem of linkage states 

 that if A, B, and C are three closely linked factors the hnkage value 

 between A and C is the sum of the values between A and B, and B and 

 C. A, B and C can therefore be taken to lie at definite points along the 

 length of a chromosome, the distances between any two being propor- 

 tional to the linkage value between these two. A chromosome may 

 therefore be represented by a simple straight line with the position 

 of the genes marked on it according to a scale in which unit distance 

 represents one crossing over per lOO gametes (the "Morgan," a name 

 not in general use). 



The additive theorem of linkage is only true when the linkage 

 values are small. The number of recombinations between two genes 

 which lie far apart on the chromosome is less than the sum of the 

 linkage values for the separate intervals into which the intervening 

 part of the chromosome can be divided. The explanation of this can be 

 found in double crossing-over; two simultaneous cross-overs, one in 

 the interval AB and the other in the interval BC, will remove B from 

 between A and C but leave A and C in their original association. The 

 total number of recombinations between A and C should be compen- 

 sated for this according to the formula AC = AB + BC — 2AB.BC, 

 since the chance of a cross-over simultaneously in AB and BC is 

 clearly AB.BC, and each double cross-over must be counted twice. 



This theoretical compensation is not exactly correct in practice, since 

 it is found that the occurrence of a cross-over at one place lessens the 

 probability that another will happen in the immediate neighbourhood 

 (interference). 2 There are therefore less than ^5.BC double cross-overs 

 and the formula becomes AC = AB + BC — 2 AB.BC. I, where / 

 (the coincidence) is an empirically determined constant, usually less 

 than I. The coincidence varies considerably from place to place within 



^ General reference: Mather 1938. 2 Muller 1916. 



