36 INTROGRESSIVE HYBRIDIZATION 



species. Gene by gene, or chromosome sector by chromo- 

 some sector, the cohesive effect of long, threadUke germ- 

 plasms is not very great. If we were to consider only three or 

 four genes, the cohesive force imposed by protein chains is 

 only of the order of 2/3 of the recombining that might occur 

 without any such restraint. Species differences, however, 

 are not matters of one or two genes; they are based upon a 

 great many gene differences — certainly scores of them, per- 

 haps hundreds, scattered all along the length of the chromo- 

 somes. The total cohesive effect of chain proteins in a species 

 cross, therefore, becomes 2/3 of 2/3 of 2/3 of 2/3 • • • . If the 

 number of genes is large this reaches a staggering sum. As 

 we shall show below, the total effect of these forces on the 

 aggregate of all the differences in the germplasm is enor- 

 mous. Its magnitude will vary with the number of genes 

 concerned, with the frequency of chiasmata, and with the 

 number of chromosomes, but it must always be high. We 

 can grasp its general comparative magnitude if we consider 

 two hypothetical limiting cases. Let us suppose that we 

 have 2 species, orientalis and occidentalism whose essential dif- 

 ferences are due to 100 genes. If these genes were all ag- 

 gregated in one big chromosome, with such strongly localized 

 chiasmata that there was no effective interchange at meiosis, 

 we could then have only 3 kinds of hybrid offspring, those 

 with 2 chromosomes of orientalis, those with 2 of occidentalis 

 and those with 1 of each. As our other limiting case, let us 

 suppose that the genes were in 100 separate chromosomes. 

 The possible number of hybrid gene recombinations would 

 then be 3^^^ 



These are the two hypothetical limiting cases. Neither 

 is realized in nature. The male Drosophila is, however, very 

 close to complete linkage. There are only 4 chromosomes, 

 and there is in the male no effective crossing over within any 

 one of the 4. In other organisms more recombination is 

 achieved. The larger the number of chromosomes, and the 

 greater the number of chiasmata per chromosome, and the 

 less localization there is in the points at which chiasmata are 



