GENETIC BASIS 41 



illustrates all the F2 genot>T)es that would be possible in an 

 F2 of infinite size. The Fi is furthermore considered to be 

 perfectl}^ fertile, and no structural differences affecting pair- 

 ing or crossing over have been assumed. 



Factorially, the 2 parental chromosome types are assumed 

 to be ai, bi, Ci, di, 61, fi and a2, b2, C2, d2, 62, ^2- The factors 

 in boldface type, b, d, and f, affect one character, and a, c, 

 and e affect the other. The species diagrammed in white is 

 supposed to have a minimum value for each of the 2 charac- 

 ters, and the species diagrammed in black is supposed to owe 

 its greater magnitude to the equal and additive effect of 

 each of the 6 genes for which it is homozygous. (These as- 

 sumptions are not necessary to the theory, but they make for 

 a simpler and more readily understandable diagram.) Each 

 dumbbell-shaped figure in the diagram denotes a single F2 

 genot^^e, black representing genes from the large species 

 and w^hite those from the small. As shown at the upper left 

 of the diagram, the upper half of the "dumbbell" represents 

 one of the chromosomes, the lower half the sister chromo- 

 some. The chromosome is diagrammatically represented 



in the compact zigzag arrangement \, / \a/ \f ^^ ^^^^ 



the 3 factors a, c, and e affecting one character are pushed 

 towards the top, and the other 3 (b, d, and f) are pushed to- 

 wards the bottom. The smaller species is given a base value 

 of for each character. The larger species, by definition, 

 will therefore carry 3 units of increase in each of its chromo- 

 somes, for each character, and its value on the diagram will 

 be 6 for each. 



The diagram is for a short chromosome which regularly 

 has one chiasma and only one, so that only single crossovers 

 are possible. If the 6 genes were in separate chromosomes, 

 64 types of gametes would be possible. Linkage (wholly 

 aside from its effect on frequencies) reduces the number of 

 kinds to 12. 



Even in populations of infinite size, therefore, the effect 

 of hnkage upon recombination types is very great. If scores 



