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. 



