THE MECHANICS OF THE CHROMOSOMES 



125 



in diploid/ that is the cross-over maps are of the same total length, 

 although the distribution of genes along the chromosomes is different in 

 the two cases, probably owing to competition at zygotene pairing. If 

 each cross-over determines a chiasma, there must be the same number 

 of chiasmata per chromosome in diploid and triploid organisms, that is, 

 the total number of chiasmata in triploids must be I times the niunber 

 in a diploid. This prediction has been verified for related diploid and 

 triploid plants.'^ 



4. Chiasma Interference 



Mather^ has pointed out that the normal linear relationship between 

 chiasma frequency and chromosome length could be explained if we 

 supposed that in every chromosome pair one chiasma is first formed 



CHROMOSOME 



I A 



inert region 



CHROMOSOME 



Fig. 61. The Distribution of Chiasmata and Crossing-Over in the Chro- 

 mosome. — ^The upper diagram expresses the hypothesis that the first chiasma 

 is formed at a certain average distance from the centromere [cm), occurring with 

 a normal distribution round the point A; subsequently a second chiasma may be 

 formed further distal ly. In the lower diagram the curve gives the total frequency 

 of chiasmata between any point and the centromere, and thus the cross-over 

 distance between that point and the centromere. Note how points equidistant 

 along the chromosome become crowded together in regions of the map where 

 chiasmata are rare. 



(After Mather.) 



^ Cf. Redfield 1930, 1932. 



2 Darlington and Mather 1932. 



' Mather 1936c, 1937. 



