effective size of the species. This estimate has a large variance (see below).

In the case of balanced selection, the population size required for the maintenance of a polymorphism is smaller. On the assumption of overdominance, with a heterozygote advantage on the order of 0.01, and 10-8 selected mutation rate per site per generation, the HLA polymorphism at the DRB1 locus requires a mean effective size of 100,000 individuals over the last 30 million years (Takahata et al., 1992). Computer simulations lead to estimates also on the order of 105 individuals as the long-term size of the ancestral populations leading to modern humans (Klein et al., 1990; Takahata, 1991, 1993a).

If we assume a mean population size of 105 individuals and a long-term generation time of 15 years, the expected coalescence for neutral alleles is 6 Myr, which is much less than the 30 Myr coalescence of the DRB1 alleles. Although the coalescence estimate has a large variance, it seems that either our ancestral population was even larger than 105 or, as assumed, balancing selection accounts for the long-term persistence of the MHC polymorphisms. The presence of balancing selection is supported by the analysis of the DNA sequences of HLA alleles. In codons specifying amino acids of the PBR, variation at the first and second positions is significantly higher than at the third position, and this observation is taken as evidence that positive selection acts on the first two positions (Hughes and Nei, 1988, 1992). Moreover, Hill et al. (1991, 1992a, b; see Miller, 1994) have shown that MHC polymorphism may increase resistance to Plasmodium falciparum, the parasite responsible for malignant malaria.

Estimates of the magnitude of the selection coefficient, s, that maintains the MHC polymorphisms vary from locus to locus, but range from 0.0007 to 0.019 (Satta et al., 1994). It seems unlikely that the selection coefficient would be in any case much larger than 0.01–0.03, but even large selection coefficients do not allow for the long-term persistence of polymorphisms except in the presence of large populations. For example, only 7 alleles can be maintained in a population of N = 1000, even with overdominant selection as unreasonably large as 0.3 (Figure 5; Klein et al., 1990).

Population Bottlenecks and the Origin of Modern Humans

We have concluded, assuming an overdominant selective advantage of 0.01, that the long-term effective population size of the human lineage for the last 30 Myr is 100,000 individuals or larger. When population size oscillates, smaller numbers have a large effect on the value of N, since



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