444 READINGS IN EVOLUTION, GENETICS, AND EUGENICS 



Accordingly the construction of maps on the basis of short distances 

 summated is justifiable, provided the arrangement is linear, as it seems 

 to be. But it must be borne in mind that the map distances do not 

 correspond with cross-over percentages (although they are based on 

 them) except in the case of very short distances. Map distances often 

 exceed 50, but cross-over percentages cannot do so, as already pointed 

 out. To get a distinctive name for the map units, Haldane has called 

 them units of Morgan or simply "morgans." Haldane has computed 

 a formula for converting cross-over percentages into "morgans" and 

 vice versa. He finds that the two correspond only for very low values 

 (5 or less) and diverge more and more as the observed cross-over per- 

 centages approach 50. Haldane's formula may be stated thus. If 

 three genes, A, B, and C, occur in a common linkage group, and the 

 cross-over percentages are known between A and B and between B and 

 C, we may predict with a probable error of not over 2 per cent, what 

 cross-over percentage will be found to occur between A and C. Call- 

 ing the cross-over percentage between A and B, m, and that between 

 B and C, n, the cross-over percentage between A and C will lie between 

 (m-^-n) and (m-\-n2mn). It will approach the former for amounts 

 of 5 or less, and the latter for amounts of 45 or over. In a useful table 

 Haldane shows the calculated map distances (morgans) for all cross- 

 over percentages between 5 and 50. This table is based on the rela- 

 tions of the genes observed in the sex-linked group of Drosophila, but 

 it applies equally well to the second linkage group of Drosophila, and 

 to a group of three genes in the plant, Primula. Provisionally it may be 

 considered to apply generally to linkage systems in animals and plants. 



TABLE IV 



A TABLE FOR CONVERTING CROSS-OVER PERCENTAGES INTO MAP DISTANCES 

 ("MORGANS") AND VICE VERSA (AFTER HALDANE) 



As an example of how the table may be used in predicting undeter- 

 mined linkage values, suppose that A is linked with B, and B with C 



