28 
GENETICS: W. E. CASTLE 
lations, for a cross-over percentage greater than fifty is absurd. If A and B 
assort wholly independently, without any linkage whatever, just as they 
would in ordinary Mendelian inheritance where no linkage exists, cross- 
overs and non-cross-overs will be equal, 50% each. Any cross-over value 
consistently less than 50% shows linkage. A cross-over value greater than 
fifty cannot exist. For there must be either linkage or no-hnkage. But 
no-linkage means 50% cross-overs, and linkage means less than 50% cross- 
overs. Hence a value greater than 50% cannot occur.^ As an alternative 
to the hypothesis of linear arrangement it is possible to suppose that the 
arrangement of the genes is not linear, that the nearer genes are not directly 
in line with the more remote ones. 
If the arrangement of the genes is not linear, what then is its character? 
This query led me to attempt graphic presentation of the relationships indi- 
cated by the data of Morgan and Bridges^ but finding this method unsatis- 
factory I resorted to reconstruction in three dimensions, which has proved 
very satisfactory. The data used consist of the experimentally determined 
cross-over percentages between twenty genes of the sex-chromosome of 
Drosophila, as given in Table 65 of Morgan and Bridges. The only hypothesis 
involved in the reconstruction is Morgan's fundamental one that distances 
between genes are proportional to cross-over percentages. The secondary 
hypothesis, that distant genes are really farther apart than indicated by the 
experimental data, is rejected for the reason already explained, that impos- 
sible relationship are thereby entailed. Taking the data, then, exactly as 
they stand, we find it possible to make a very complete and on the whole 
self-consistent reconstruction of the architecture of the sex-chromosome 
from the linkage relations of its genes. A small ring of wire is taken to rep- 
resent the locus of a gene. Two genes are placed as far apart (in inches) as 
there are units in the cross-over percentage between them. Thus between 
yellow-body and white-eye there is shown by Morgan's data to be a cross-over 
value of 1.1%. Consequently the rings which represent these genes in the 
reconstruction are joined by a wire 1.1 inches long. Between white and ver- 
milion the cross-over percentage is 30.5. Accordingly the connecting wire in 
this case is made 30.5 inches long. Proceeding in this way the reconstruction 
shown in figures 1 and 2 is obtained. It indicates an arrangement of the 
genes not by any means linear, but rather in the form of a roughly crescentic 
plate longer than it is wide, and wider than it is thick. It is shown in side 
view in figure 1, and in edge view in figure 2. 
That the arrangement of the genes can not by any possibility be linear is 
shown by two critical cases, the loci for hifid and abnormaL Bifid (Bi, figs. 
1 and 2) is shown by a series of over 3,600 observations to be at a distance 5.5 
from yellow. It is almost the same distance from white, viz., 5.3, as shown 
by 23,595 observations. Yet white and yellow are distant from each other 
only 1.1 units, as shown by 81,299 observations. Therefore bifid can lie 
neither above nor below yellow and white, in the line which joins them, but 
