The Behavior of tlie Chromosomes as Studied through Linkage. 235 



these genes may be arranged in a linear series, using the strength of 

 the linkage between various allelomorpliic pairs as a measure of their 

 distance apart. By this method it becomes possible to predict with more 

 or less accuracy the linkage in any untried combination, after the genes 

 involved are once located in this linear series. My earlier paper was 

 intended only as a preliminary report, and the subject was then, ad- 

 mittedly, only verj' imperfectlj' investigated. There is now available a 

 much more extensive series of data, involving several new genes, and 

 enabling us to extend to one of the autosomes the conclusions already 

 reached for the X chromosome in Drosophila ampelophila. I shall first 

 present all the available evidence on this subject, and shall then in the 

 second part of this paper discuss the question of the role of the chro- 

 mosomes in heredity. 



When two pairs of genes, let us say A and a, B and b, show 

 linkage, each doubly heterozygous individual, AaBb, produces more 

 gametes of the sort that united in its formation than of the sort result- 

 ing from a shifting of these genes. Thus, if a gamete AB unites with 

 ab, an individual AB ab is formed. This individual produces more 

 gametes AB and ab than Ab and aB. But a union of Ab and aB gives 

 AbaB, wliich produces Ab and aB in larger numbers than AB and ab. 

 On Morgan's view these rarer combination must be due to an inter- 

 change of materials between homologous chromosomes (such as has been 

 observed by Jaxssexs '09). Moug.vn has called this process of inter- 

 changing "crossing over". The resulting gametes are then "cross-overs". 

 In order to get the simplest measure of the amount of crossing over it 

 is necessary, as pointed out by Baur ('lib), to mate doubly hetero- 

 zygous individuals to double recessives. Thus, if we suppose A and B 

 to be linked so that the ratio of cross-overs to "non-cross-overs" ("gametic 

 ratio" of Bateson) is 1 : n, the mating results as follows : 



ABab — gives gametes, nAB lAb laB nab 

 ab ab — gives gametes, ab ab 



nABab — phenotypic characters, AB 

 1 Ab ab — „ „Ab 



1 a Bab — „ „ aB 



nab ab — „ „ ab 



The amount of crossing over may then be calculated directly from 

 such a "back-cross". The same result is obtained in the case of sex- 

 linked genes (where the male is heterozygous for sex), by mating a doubly 



