RECOMBINATION IN SEXUAL ORGANISMS 79 



length, then the crossover events would be distributed according to the 

 Poisson equation (p. 48). The same parts of similar chromosomes 

 would not cross over an identical number of times, but rather some 

 would not cross over, some would cross over once, twice, and so on. 

 For example, suppose that an average of one crossover event occurs per 

 meiosis between two genes that are actually 50 units apart. If the 

 crossover events are distributed at random according to the Poisson 

 formulation and their average number, m, is one, then in about 37 per cent 

 of meioses no crossing over will occur; in 37 per cent, one will occur; 

 and in 26 per cent, two or more will take place. Now only crossover 

 events give new combinations, so 63 per cent of the exchanges will 

 produce recombinant chromatids. But both single and multiple cross- 

 over events yield only 50 per cent recombinant chromatids; 63 per cent 

 X 50 per cent is 31.5 per cent. Thus, observation of the frequency of 

 chromatids carrying new combinations of genes so far apart as 50 units 

 would lead to a map distance of only 31.5. This error can be anticipated 

 and the observed distance corrected to approximate the true one by the 

 use of the equation: 



y = 1/2(1 - e-2^) 



which relates the frequency of recombinant chromatids y to map dis- 

 tance d. 



There is another way to avoid the error in mapping introduced by 

 multiple crossing over. Because all single and multiple crossover events 

 yield an average of 50 per cent recombination chromatids, genes very far 

 apart on the same chromosome can recombine with a maximum frequency 

 of 50 per cent. They behave in this way as if they were not linked. 

 The smaller the distance between two genes, the less likely is a cross- 

 over event to occur; the smaller this chance, the smaller, relatively, is 

 the chance of a multiple exchange. By mapping small distances, pref- 

 erably in three-point crosses, and by adding many of them together, the 

 large errors made in locating two distant genes can be avoided. Thus 

 distances exceeding 50 map units can be measured. 



But these methods involve assumptions about the constancy of the 

 chance of crossing over along the length of the chromosome and the 

 randomness with which different strands exchange with one another. It 

 is known that deviations from these random expectations take place; they 

 are called interference and are the subject of current investigation. If an 

 exchange in one position along the length of a bivalent decreases the 

 chance of a second exchange, then there is positive chiasma interference. 

 Positive interference would occur if the chromatids were rigid so that 

 one exchange inhibited other exchanges in close proximity, allowing 

 them to take place only some distance away. But as we will see later. 



