162 GENETICS IN RELATION TO AGRICULTURE 
inconceivable thing, if viewed from a purely mathematical standpoint, 
unless a special biological mechanism exists which favors such mutations. 
The same difficulties are met with in the case of other systems of multiple 
allelomorphs the origin of which have been observed in pedigree cultures, 
consequently the situation in the above system is not unique. 
4, If a curve of linkage values be plotted in Drosophila for a consider- 
able number of known factors it will be found that the frequencies of 
different values correspond with one another until those displaying 
multiple allelomorphism (or complete linkage) are met with and these 
are far in excess of the number normally to be expected from purely 
mathematical considerations. They are not, therefore, merely the ex- 
tremes of ordinary cases of linkage. 
5. There are no very good reasons why only one sort of change should 
be possible in a given locus in the hereditary material. It is true the 
presence and absence hypothesis does hold that the only difference with 
respect to a given factor is its presence in the hereditary material or 
its absence from it, but there are many reasons why this view at present 
appears untenable. A factor in the hereditary material may well be 
regarded as a complex chemical substance of some kind which maintains 
essential relations with the other factors in the system such that to lose 
it entirely might well disorganize the entire system. But such a com- 
plex chemical substance might well change in many relatively slight ways 
which would modify the particular character in which it is concerned 
in various directions depending upon the specific manner in which the 
factor has been altered. 
When these arguments are considered and the type of cases to which 
it is applied are taken into account, it is apparent that the theory of 
multiple allelomorphism is a useful analytic tool in the solution of a 
certain class of peculiar Mendelian phenomena. Although some of the 
above cases may prove to be instances of extremely close linkage, never- 
theless for most of them the case is firmly established experimentally, 
and deserves careful consideration from that standpoint. 
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