THE FUNDAMENTALS OF MENDELISM 



49 



(Tubby) was found which could not be placed in any of the haploid 

 number of linkage groups already known, it appeared to provide an 

 exception to this rule until it was shown by cytological examination 

 that these particular flies contained an extra fragment of chromo- 



some/ 



Fig. 16. The Equality of the Number of Chromosomes and Linkage 

 Groups. — There are four chromosomes in the haploid set of Drosophila melano- 

 gaster, and four groups of linked factors. A fly (on the left) was found in X-rayed 

 stock which showed several deviations from the normal (on right). It was called 

 Tubby; but the gene determining its appearance was not linked in any of the 

 known groups. Cytological examination was able to explain this apparent fifth 

 linkage group by showing that the fly contained an extra chromosome fragment, 

 which is indicated by the arrow in the metaphase figure shown. 



(From Muller and Painter.) 



8. The Additive Theorem of Linkage Values'^ 



The further development of the chromosome theory of linkage was 

 based on the discovery of the additive theorem of linkage values. If the 

 percentage of recombinations found in a double heterozygote AaBh is 

 defined as the recombination value (or Hnkage value) between the 

 loci A and B, then the additive theorem states that if A, B, and C 

 are three Hnked genes, the recombination value AC is the sum of the 

 values AB and BC (provided that the values AB and BC are small, 

 cf. p. 89). Morgan and his associates saw that this fundamental relation 

 could easily be accounted for by the hypothesis that the genes are 

 arranged in a single linear series along the chromosome, and that a 

 recombination is due to a chance breakage and rejoining between the 



' Muller 1930. ^ Morgan 191 1, Sturtevant 1913. 



