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 0, 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 ° 
49 20 
30 40 
20 60 
10 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. 
In the plant, Primula sinensis, Gregory observed the occurrence 
of linkage in a group of five characters, viz., 
Dominant Recessive 
. Short style vs. long style (1) 
. Magenta corolla vs. red corolla (r) 
. Tinged corolla vs. full-colored corolla 
. Green stigma vs. red stigma (s) 
. Pale stem vs. full red stem 
AP WN H 
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: 
1 r s 
° 34.0 45.6 
The cross-over percentage between | 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 
