TABLE 1 Minimum population size at a bottleneck



Alleles through bottleneck 

s 
R 
N 
40/50 
60/70 
0 
— 
— 
270–300 
458–490 
0.01 
— 
— 
292–302 
454–462 
0 
1.1 
10,000 
460–470 

0 
1.1 
5,000 

750–790 
0 
1.05 
5,000 
980–1010 

0 
1.01 
10,000 
1540–1560 

0 
1.01 
5,000 

2120–2180 
0.01 
1.01 
5,000 

2140–2180 
The two columns on the right give the minimum number of individuals required for passing either 40 (out of 50) or 60 (out of 70) alleles, with a 95% probability. The initial bottleneck is always 10 generations. In some cases it is assumed that the population grows at a rate R per generation before reaching the equilibrium size N. The selective value due to overdominance is s. Each value is based on 300 computer simulations. 
N_{b}/t_{b}, which if smaller than 10 will have drastic effects in reducing genetic variation (Takahata, 1993a). Thus a bottleneck of 100 individuals would substantially reduce genetic variation if it would last 10 or more generations. Balancing selection facilitates the persistence of polymorphisms through a bottleneck. But because alleles behave as neutral whenever Ns < 1, if the selection is weak, such as s = 0.01, N has to be correspondingly large, at least 100, for selection to play a role. The persistence of HLA polymorphisms over millions of years requires that the size of human ancestral populations be at least Ns = 10 at all times (Takahata, 1990). If s = 0.01, the minimum population size possible at any time would be N_{b} = 1000. The minimum number must have been in fact much larger, because human population bottlenecks cannot last just a few generations, since many are required for a human population to grow from 1000 to the longterm mean of 100,000 individuals.
We have explored how small the population bottlenecks would be by computer simulations (Table 1). If a bottleneck lasts 10 generations and we ignore the time required for a population to grow back to its mean size, the smallest bottleneck that allows the persistence of 40 allelic lineages, out of 50 present before the bottleneck, with a probability of 95%, is 270–300 individuals. If the number of alleles passing through the bottleneck is 60 as in DRB1 (and assuming 70 alleles before the bottleneck), the minimum population size is 458–490. When we take into account the time required for the population to recover to its average size, the minimum population size at the bottleneck becomes substantially larger. For example, if we assume a rate of population increase of 1% per generation (which is 50 times greater