FINITE POPULATIONS 55 



always be accompanied by a corresponding increase in the 

 same direction by the other character. 



If the genes affecting multiple-factor characters, however, 

 were not distributed at random between the chromosomes a 

 much wider recombination spindle would be possible. If 

 such genes were entirely on separate chromosomes for each 

 character we might hope to achieve a random sample of the 

 entire recombination square. Suppose, for instance, that 

 the leaf shape and pubescence of the pre\dous example had 

 each been due to many genes, that substantially all the genes 

 for pubescence were in 3 chromosomes, and that substantially 

 all those for leaf shape were in any other 3, then our recom- 

 bination spindle would expand to fill the entire recombina- 

 tion square, and all the recombination types of Fig. 9 might 

 be achieved if we raised enough hybrids. There is as yet no 

 published evidence showing that multiple factors can be 

 distributed in any such way, however, and it is generally be- 

 lieved among geneticists that the genes affecting any one 

 character are distributed pretty much at random. So much 

 for the hypothetical limiting case of all-linked. As has been 

 pointed out above the amounts of crossing over which we do 

 actually obtain are not very far, comparatively speaking, 

 from this actual limit. In each chromosome we shall have 

 the restrictive effects shown in Fig. 10. For the chromosomes 

 as a whole we shall have recombinations restricted closely 

 to the axis of the recombination spindle, except as nonrandom 

 distribution of multiple-factor genes between chromosomes 

 allows more extreme combinations. The resultant of these 

 combined effects will be the same kind of narrow recom- 

 bination spmdle running through the center of all imaginable 

 recombinations. Linkage, in other words, takes what would 

 have been a spherical mass of probabilities and draws them 

 out towards the original parental positions. We may think 

 of linkage in two ways, either as a negative force that keeps 

 new recombinations from appearing, or as a strong positive 

 force tending to bring the hybrid population back to some- 

 thing very like the original types. \Miile it operates in both 



