Xo. 032] SHORTER ARTICLES AND DISCUSSION 



265 



one in the egg, the other in the sperm, then oftener than not 

 they will be found apart, in different gametes formed by the 

 cross-bred individual. 



Where no linkage exists between two genes, A and B, it will 

 be wholly a matter of chance whether they go together or not, 

 no matter what their previous relation was. We say that they 

 "assort independently," as genes do in ordinary Mendelian in- 

 heritance, such as was known to Mendel. In such cases change 

 of relation occurs in the long run in half (or 50 per cent.) of all 

 cases. Such change of relation is called ' ' crossing over. ' ' Link- 

 age evidently will be shown by a falling below 50 in the per- 

 centage of cross-overs. The more cross-overs decline below 50 

 per cent., the stronger will be the linkage indicated, until when 

 no cross-overs occur, we call the linkage complete or perfect. Ac- 

 cordingly and 50 per cent, will be the limiting values for cross- 

 overs indicating linkage. But it is conceivable that cross-overs 

 might occur in excess of 50 per cent. What would their signifi- 

 cance be? Not linkage, not a tendency to maintain relations 

 previously existing between genes, but a tendency to change 

 those relations, to go apart when previously together, and to get 

 together when previously apart. We are not acquainted with 

 any such tendencies as these, and it is difficult to imagine how 

 they might arise, but it is certain that they would be the opposite 

 of linkage and would need a different name, if observed. 



It is evident that the strength of linkage increases, as the cross- 

 over percentage decreases below 50. As a measure of the 

 strength of linkage, we might then take the difference between 

 50 and the observed cross-over percentage, as I have elsewhere 

 suggested ( Castle, 191 9) . This would give us a numerical grade 

 of linkage strength on a scale of 50. But since we are more ac- 

 customed to grading on a scale of 100, it will perhaps be better 

 to double values thus obtained. Our grading scale of linkage 

 strengths will then run thus : 



By this method we can compare the linkage strength between 



