286 CHROMOSOMES IN HEREDITY: MECHANICAL 



with the values expected in a chromosome with its known crossing- 

 over frequency on the assumption of no interference between 

 successive chiasmata in regard to the choice of chromatids which 

 take part in them (Mather, 1935 a). 



This nearly random segregation of chromatids where two chromo- 

 somes, that have undergone crossing-over, pass to the same pole 

 at the first division, means that the segregation expected in tetra- 

 ploids will not always be in the simple proportions given by Muller 

 in 1914 for the assortment of chromosomes but will show a higher 

 proportion of recessives. It will be possible for both divisions to 

 be reductional in regard to a given part of a chromosome repre- 

 sented four times (Haldane, 1931 a ; Mather, 1935 a, 1936 a ; and 

 cf. Fig. 146, factors PPPp) . This random chromatid segregation will 

 only be expected when factors are at the unattainable asymptotic 

 distance where they show 50 per cent, of crossing-over with the 

 centromere. It is therefore strictly in accordance with this theory 

 that the chromatid type of segregation has been found in only a 

 small proportion of the cases investigated (Crane and D., 1932 ; 

 E. Sansome, 1933). 



Frequency. The total frequency of crossing-over per chromosome 

 in the triploid is the same as in the diploid, although the distribution 

 is different (Redfield, 1930). This should mean that the total 

 number of chiasmata per configuration is increased by half in the 

 triploid. Exactly the same increase is found in triploid plants that 

 have been compared with related diploids (Tulipa, D. and Mather, 

 1932 ; Hyacinthus, Stone and Mather, 1932). 



(iv) Structural Hybrids. Crossing-over in dyscentric hybrids 

 has already been considered. Observations of crossing-over in 

 interchange hybrids agree with expectations based on cytological 

 observation if crossing-over is supposed to be conditioned by 

 pairing of identical segments of chromosome at pachytene, as are 

 chiasmata. 



On this assumption, Dobzhansky's results (1931) show that the 

 amount of pairing is reduced in the neighbourhood of a break in 

 Drosophila heterozygous for a translocation or interchange. Where 

 the break has occurred near a median centromere of a chromosome 

 it usually leads to a reduction of crossing-over in both arms. Where 



