LINKAGE AND CROSSING-OVER 445 



and that between A and B there are 10 per cent of crossovers. What 

 will be the cross-over percentage between A and C ? Converting the 

 observed cross-over percentages into map distances with the aid of the 

 table, we find the distance AB to be 10.3 and the distance BC to be 

 15.9. On the linear theory the distance AC will equal either the sum 

 or the difference of AB and BC, that is will be either 26.2 or 5.4. 

 Converting these distances into cross-over percentages by interpola- 

 tion in the table, we find that the cross-over percentage between A and 

 C should be either 23.7 or 5.1, according as the linear arrangement is 

 ABC or ACB. 



Measurement of linkage. It will be observed that as the strength 

 of linkage increases, the cross-over percentage decreases. With a 

 cross-over percentage of 50, there is no linkage. With a cross-over 

 percentage of o, the linkage is complete, two characters so related 

 behaving as allelomorphs. Accordingly we depend upon the observed 

 cross-over percentage both for the detection of linkage and for the 

 measurement of its strength. But unfortunately the linkage strength 

 varies inversely as the cross-over percentage. This makes the cross- 

 over percentage directly considered, a rather poor measure of linkage 

 strength. It is really the amount by which the cross-over percentage 

 falls below 50 that measures directly the strength of linkage. Thus 

 with cross-over percentages of 50, 40, 30, 20, 10, and o, we should 

 have linkage strengths of o, 10, 20, 30, 40, and 50. We should then 

 have a standard for measuring linkage strength directly, on a 

 scale of 50. But as we are more accustomed to grading on a scale of 

 100, it seems preferable to double the values indicated above. We 

 then have grades of linkage strength on a scale of 100, as follows: 



Cross-over percentage 50 40 30 20 10 o 

 Linkage strength o 20 40 60 80 100 



Accordingly, to estimate the strength of linkage in a particular case, 

 we multiply by 2 the difference between the observed cross-over per- 

 centage and 50. 



But suppose the observed cross-over percentage were greater than 

 50, what then? Such an occurrence would not indicate linkage, a 

 tendency of characters to remain grouped as they were, but an oppo- 

 site tendency, to assume new groupings. No such tendency has been 

 observed. If it should be, it would need a different name and method 

 of measurement. 



We may now consider some further examples of linkage. 



