DISTRIBUTION OF CROSSING-OVER 293 



with lower crossing-over in others. Such a negative correlation 

 between the frequency in different chromosomes of one nucleus has 

 since been shown by chiasma studies in numerous plants. This can 

 be done in two ways : either using a correlation table, where the 

 frequencies of the different chromosome types, such as the large 

 chromosomes and the fragments in Secale, can be recorded (D., 1933 ; 

 Mather and Lamm, 1935) ; or by finding out whether the variance 

 as between nuclei is less than the absence of interaction between 

 bivalents would require (Mather and Lamm, 1935 ; Mather, 1936 ; 

 Lamm, 1936). The first method requires dissimilar chromosomes 

 within the nucleus, the second uniform chromosomes, at least as to 

 part of the complement. Mather's extensive analysis shows first 

 that negative correlation may occur in all or a part or none of the 

 chromosomes of different species, and secondly that it may occur in 

 some individuals of a species, those with a higher chiasma frequency, 

 and not in others. Interference between crossing-over in different 

 chromosomes begins therefore above a certain threshold frequency. 

 How it works will be considered later (Ch. XII). 



(c) In Relation to Position ("Map-Distance"). In some 

 organisms the number of chiasmata formed in a bivalent is a direct 

 function of the length of the chromosomes paired. This is so in 

 Vicia Faba {v. Fig. 96), where the M chromosome with a mean 

 chiasma frequency of 7-1 is a little more than twice as long as the 

 m chromosomes with a frequency of 3-4 (Mather, 1934). This is 

 true of many organisms with complete pairing, and having a size 

 range of less than i : 4 {e.g., Allium macranthum, Levan, 1933 c). 

 It is not, of course, true of those like Fritillaria Meleagris and 

 Mecostethus which have locahsed pairing and in consequence the 

 same or even a higher chiasma frequency in the shorter chromosomes. 

 The proportionality with complete pairing may be shown in the 

 many organisms where new very small fragments have appeared. 

 These, as we have already seen, fail to pair in such a proportion of 

 nuclei as may be predicted from the chiasma-frequency of the 

 ordinary complement (Ch. V). Frequently, however, relatively small 

 chromosomes form part of the normal complement. We then find 

 that their regular pairing is not made possible by an increase of 

 chiasma frequency all round, but by an indirect proportionality. We 



