FINITE POPULATIONS 



53 



leaves resembling the Fi (2/2) would be 13 times as frequent 

 and would be expected 26 in 144 times, making up nearly 

 one fifth of the population. This is on the hypothesis that 

 there is no localization of chiasmata, in other words, that 

 crossing over between a and B is as likely to occur as between 

 B and C and that either of these is as likely as crossing over 

 between C and D. With such 

 localization the restriction upon 

 frequencies would be even 

 greater. Figure 12 shows the 

 expectations in a population 

 of 576, if crossing over be- 

 tween B and C were 4 times 

 as likely to occur as between 

 A and B or C and D. 



In other words, if we con- 

 sider the ' 'recombination spin- 

 dle" connecting the two ex- 

 treme parental types, the effect 

 of linkage upon frequencies is 

 to restrict the actual F2 indi- 

 viduals in any finite popula- 

 tion to a spindle. Any tend- 

 ency toward localization of chiasmata will restrict this inner 

 spindle still further, the force of the restriction depending on 

 the degree of localization. 



What kind of an F3 can be expected from this finite F2? 

 The exact answer will depend on the mating system, the 

 population size, etc. Let us take as an illustration a rel- 

 atively large population with no differential viability and 

 calculate the expectations if all the recombinations of Fig. 11 

 had actually occurred and each had contributed, by self- 

 pollination, 72 plants to the next generation. The results 

 are shown in Fig. 13. It will be seen that recombinations 

 outside the ' 'recombination spindle" of the F2, though the- 

 oretically possible, are in a small minority. For plants ap- 

 proaching the glabrous-obovate or ovate-hairy, there are 



Fig. 13. The drift in future gen- 

 erations. Expectations for an F3 

 of 10,368 plants if all the plants 

 of Fig. 1 1 had been self -pollinated 

 and each had contributed 72 seed- 

 lings to the next generation. 



