284 CHROMOSOMES IN HEREDITY: MECHANICAL 



would give 50 per cent, crossing-over. Its total genetical map is 

 therefore still in doubt, and the possibility that it is really 50 units 

 long cannot be dismissed. 



In Zea Mays we can now compare the maximum possible 

 crossing-over lengths for each chromosome with the lengths already 

 observed in the study of linkage in this plant. We assume that 

 every chiasma is equivalent to 50 per cent, of total or corrected 

 crossing-over, since it means crossing-over between two of the four 

 chromatids taking part in it (Fig. 142) . The linkage studies can never 

 provide a complete map of the chromosomes, because gene-differences 

 will never be found between all the end particles of all the chromo- 

 somes. These studies are limited by the number of gene and structure 

 differences available for experiment, and only a fraction of the 400 

 known genes have so far been mapped. The linkage limits should 

 therefore always lie within the cytologically predicted limits. They 

 show such a margin (Fig. 94) : this margin will decrease with the 

 increase of linkage data. 



It is in a derivative of a Zea-Eiichlcena hybrid that Beadle (1932) 

 has succeeded in performing the experimentum crucis of comparing 

 the chiasma-frequency with the crossing-over frequency in a pair 

 of given recognisable segments. Between two such segments there 

 was 12 per cent, of crossing-over while there was 20 per cent, of 

 association at diakinesis and metaphase, which means this same 

 frequency of chiasma-formation, and therefore agrees closely with 

 the expectation of 24 per cent. 



(iii) Polyploids. Distribution among the Chromosomes. In 

 non-hybrid triploids and tetraploids the chromosomes pair at 

 random and form chiasmata at random, i.e., any one chromosome 

 may pair at different points with any of the other chromosomes 

 with which it is homologous and form chiasmata with them (Newton 

 and D., 1927). Similarly, crossing-over is at random amongst 

 corresponding chromosomes in triploid Drosophila (Bridges and 

 Anderson, 1925), and tetraploid Primula sinensis (de Winton and 

 Haldane, 1931). 



Structural Units. Gametes produced by triploid Drosophila with 

 three homologous chromosomes have one or two of these ; and 

 when they have two they are sometimes identical in one part. 



