LENGTH AND CHIASMA FREQUENCY 295 



femur-rubrum (Hearne and Huskins, 1935), Yucca flaccida (O'Mara, 

 1932) and y. recurvifolia (Sato, 1934) and in species of Agave 

 (Doughty, unpublished). In none of these species is there evidence 

 of localisation. 



It would appear, therefore, that here chiasma frequency is no 

 longer a direct function of length, and that this indirect propor- 

 tionality and localisation are genetical adaptations necessary to 

 the regular pairing of the short chromosomes. Such adaptations 

 must be alternative to a general increase in chiasma frequency, and 

 are to be expected wherever the chiasma frequency is low and 

 considerable differences occur in length (Fig. 97). 



The evidence of the behaviour of new fragments in always failing 

 to show this adaptation is sufficient to show that proportionality is 

 the simpler and original condition from which non-proportionality 

 is derived. Further evidence is provided by White's observation in 

 species of Locusta, Schistocerca and Stenobothrus that the non- 

 proportionality which is characteristic of them at normal tempera- 

 ture is reduced or disappears when the chiasma-frequency is 

 increased at higher temperatures. This suggests that the indirect 

 proportionality is due to a partial failure of pairing of the longer 

 chromosomes like that found with localisation, but near the centro- 

 mere instead of away from it. Such a failure might be concealed in 

 short intercalary segments by the development of relational coiling. 



The possibility of testing an analogy to these observations in 

 crossing-over frequencies is not yet available, but there are a few 

 indications that similar departures from simple expectation occur. 

 The X chromosome of Drosophila melanogaster is less than two-thirds 

 the length of the longest chromosome, yet it has two-thirds of the 

 map-distance length measured in crossing-over units. This is a 

 departure in proportion in the direction expected from the analogy 

 with Stenobothrus. A second indication is inconclusive ; the 

 X chromosome in Drosophila Willistoni (Metz, 191 6) is twice the 

 length of that in D. melanogaster, but its map length is only one-fifth 

 greater. 



Finally, the group of observations already referred to show that 

 wherever there are special conditions affecting crossing-over, the 

 distribution of crossing-over is affected relative to the centromere. 



