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THE AMERICAN NATURALIST [Vol. LIV 



any two pairs of genes without stopping to reverse the relations 

 indicated by cross-over percentages. For example the following 

 linkage relations are shown by the genes of rats and mice 

 (Dunn). 



Albinism— red-eye, rats 1.8 (?) 96.4 



Red-eye— pink-eye, rats 18.3 63.4 



The strongest linkage here indicated is that between albinism 

 and red-eye in rats, next comes that between albinism and pink- 

 eye in mice. But albinism and pink-eye in rats show less linkage 

 than in mice. The three genes, albinism (c), red-eye (r) and 

 pink-eye (p) in rats are apparently arranged in linear fashion 

 thus : 



2(?) 21 



This kind of a diagram is what Morgan, Bridges and Sturtevant 

 (1919) have made familiar to us under the name of "chromosome 

 map." Not to prejudice the case for or against the chromo- 

 somes, we might perhaps call it a linkage map or map of a link- 

 age system. In its construction we use cross-over percentages 

 as direct measures of map distances, but in Drosophila at least 

 only distances relatively short have been found to be strictly 

 comparable. Beyond distances of about 5 units (cross-over per- 

 centages) it is found that double or triple cross-overs become 

 increasingly common and thus decrease the apparent number of 

 breaks in the linkage chain between two genes. So that long 

 map distances are based, not on directly observed cross-over per- 

 centages between the more distant genes, but on summation of 

 intervening short distances, it being assumed that the arrange- 

 ment is in all cases linear. While this latter assumption is not 

 to be accepted for all cases without proof, it must be admitted 

 that for Drosophila at least the evidence for a linear arrange- 

 ment is very strong and no insuperable objections can be raised 

 against it. 



Map-distances have been found in the "first chromosome" 

 linkage group of Drosophila exceeding 60, and in the "second 

 chromosome" group exceeding 100. But in no case does the ob- 

 served cross-over percentage between two genes, however re- 

 mote, of the same linkage group exceed 50. This means that 



