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THE AMERICAN NATURALIST [You LIV 



them is obviously impossible to obtain, on account of the 

 sterility of the females carrying both factors. 



Another prediction based on the solid models dealt 

 with the frequency of separation hot ween the factors 

 hairy and magenta, of Drosophila virilis. It had been 

 found by Metz that the per cent, of cross overs between 

 hairy and forked was 3.1 and between forked and ma- 

 genta 3.7 ; this would make the per cent, for hairy magenta 

 6.8 (or 0.6), if the factors were in a straight line. In the 

 solid model, however, the arrangement of these factors, 

 based on separate determinations of their frequencies of 

 crossing over with distant loci,— is shown as triangular; 

 and on the basis of this model Castle predicts that the 

 frequency hairy-magenta will be found to be 4 or 5. The 

 frequency has recently been determined by Weinstein, 

 who has kindly consented to allow its use in this connec- 

 tion. He finds it to be 6.6. 



It should be pointed out that Castle has endeavored 

 to protect himself, in these predictions, by saying that 

 they only hold, provided the relations given * ' have been 

 determined with sufficient accuracy"! 



8. One of Castle's specific objections to the linear 

 maps, on which he lays much stress, is that on them the 

 distances between the extreme factors is much more than 

 50 units, whereas factors which are linked must have a 

 separation frequency of less than 50 per cent. It is only 

 necessary to point out here that since, as we have seen, 

 the linear maps, unlike the models, do not imply a pro- 

 portionate relationship between the distances and the 

 separation frequencies, these distances of over 50 dtf not 

 connote separation frequencies of over 50 per cent. On 

 account of the progressive reduction in separation fre- 

 quency, due to double crossing over, that occurs with in- 

 creasing distance, even distances of 100 or 110 in the 



cies as high as 50 per cent. On the other hand, it should 



