evolve independently twice, let alone five times, in different regions and at different times (Dobzhansky, 1963). The candelabra model is, moreover, contradicted by fossil (Aiello, 1993; Spuhler, 1993) and molecular (Takahata, 1993a, pp. 13, 19) evidence.

The African replacement model proposes that modern humans first arose in Africa somewhat prior to 100,000 years B.P. and from there spread throughout the world, replacing elsewhere the preexisting populations of H. erectus or archaic H. sapiens (Stringer, 1990, 1992; Stringer and Andrews, 1988). One extreme version of this hypothesis (the Noah's Ark model) proposes that the transition of archaic to modern H. sapiens was associated with a very narrow bottleneck, consisting of only two or very few individuals who are the ancestors of all modern mankind.

The Noah's Ark model is supported by an interpretation of mitochondrial DNA analysis showing that the diverse mitochondrial DNA sequences found in modern humans coalesce to one ancestral sequence, the "mitochondrial Eve" or "mother of us all," that existed in Africa about 200,000 years ago (Cann et al., 1987; Stoneking et al., 1990; Vigilant et al., 1991). This conclusion has been challenged on grounds concerning (1) whether the coalescence is to Africa, (2) the time of the coalescence, and (3) the inference of a population bottleneck (e.g., Templeton, 1992). The actual date of coalescence depends on assumptions about evolutionary rates. Based on a time of divergence between humans and chimpanzees of 6 Myr, the time to coalescence for mitochondrial DNA polymorphism has been recently estimated at 298,000 years B.P., with a 95% confidence interval of 129,000–536,000 years (Ruvolo et al., 1993).

The inference that a narrow bottleneck occurred at the time of the coalescence is based on a confusion between gene genealogies and individual genealogies. Gene genealogies gradually coalesce towards a unique DNA ancestral sequence, whereas individual genealogies increase by a factor of 2 per generation: an individual has two parents in the previous generation, four ancestors in the generation before that, and so on. (The theoretical number of ancestors for any one individual becomes enormous after some tens of generations, but "inbreeding" occurs: after some generations, ancestors appear more than once in the genealogy.)

As we pointed out above, assuming an effective population of N individuals, mean coalescence is 4N generations for nuclear polymorphisms. Mitochondrial DNA is haploid and maternally inherited; hence, the mean coalescence is 2Nf, where Nf is the number of mothers. If we assume 20 years for a human generation throughout the Pleistocene, 298,000 years to coalescence implies an effective mean population size of 7450 mothers or an effective population size of 14,900 humans. The 95% confidence time estimate of 129,000–536,000 years yields 6,450–26,800



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