LINKAGE AND CROSSING-OVER 445 



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 Linkage 



Percentage Strength 



50 O 



40 20 



30 40 



20 60 



10 80 



o 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. 



In the plant, Primula sinensis, Gregory observed the occurrence 

 of linkage in a group of five characters, viz., 



Dominant Recessive 



1. Short style vs. long style (1) 



2. Magenta corolla vs. red corolla (r) 



3. Tinged corolla vs. full-colored corolla 



4. Green stigma vs. red stigma (s) 



5. Pale stem vs. full red stem 



Altenburg later determined the strength of the linkage existing 

 between three of these five pairs of characters, viz., 1,2, and 4 of the 

 above list. His results may be expressed in a linkage map as follows : 



- r s 



34 o 45-6 



The cross-over percentage between 1 and r was found to be 34.02, 

 between r and s, 11.62. The sum of these two, 45.64, is the total 

 (uncorrected) map distance. The observed cross-over percentage 



