However, the simple growth model and archaeological evidences of past population sizes are contradicted by analyses of other autosomal systems. We are aware that the smoothed growth curve of this model could not reflect the detailed model of human population growth for all prehistory. Evidence of oscillating climate and dramatic habitat shifts across the Pleistocene shows that some areas were depopulated for significant periods, and so the history of the human population and its structure cannot be simple. However, there are some autosomal genes that indicate that there was no significant growth of the human population in the Pleistocene. These include single genetic loci such as ß-globin, dystrophin, and ZFX. Analysis of these autosomal systems combine a low average population size and positive values of Tajima’s D statistic. Therefore, their variation is not compatible with constantly increasing population size. In fact, they are not compatible with any population size increase of a magnitude greater than 50%, earlier than some 10,000 years ago; that is, at any time during the span of the Pleistocene (Hawks 1999 ).
The value of Tajima’s D for the human worldwide ß-globin data is 1.158, where significantly negative numbers are expected in cases of large past expansions. This statistic shows no evidence of ancient population expansion, nor do others (Harding et al. 1997 ). A similar situation is found for the human dystrophin locus, with Tajima’s D being equal to 0.962 for the worldwide human sample (Zietkiewicz et al. 1998 ). Likewise, the distribution of variation at the lipoprotein lipase locus (Clark et al. 1998 ), with a Tajima’s D statistic of 0.909, shows no evidence of expansion, although this sample is not as evenly distributed geographically as those for other loci. Hawks (1999) investigated the power of these loci to detect recent population expansions by simulations of different demographic scenarios. He found that while recent population expansions are unlikely to show significantly negative values of Tajima’s D, they are also highly unlikely to show positive values for this statistic. The observation of positive values of Tajima’s D at multiple autosomal loci therefore has great statistical power to reject hypotheses of population expansion. Using this observation, Hawks (1999) used simulation methods to test whether the observed pattern of autosomal diversity is compatible with recent population expansions. That study tested expansion times from 0 to 150,000 years and expansion magnitudes, from no expansion to 100-fold expansion. Unlike mtDNA, which could be interpreted as showing an expansion around 70,000 years (Harpending et al. 1993 ; Sherry et al. 1994 ; Rogers and Jorde 1995 ; Relethford 1998 ), the distributions of these autosomal loci apparently rule out population expansions of an order of magnitude or more earlier than 10,000 years ago.
Other autosomal data also show no signs of significant population expansions during the Pleistocene. Li and Sadler (1991) present a study of 48 human genes for which at least two human sequences are available. This data set shows no evidence of mutation-drift disequilibrium. Takahata and Satta (1998) , in a study of intraallelic variation among HLA haplotypes, also show no evidence of mutation-drift disequilibrium. Furthermore, Hey (1997) , in a comparison of a single X chromosome locus and mtDNA diversity, found disequilibrium in mtDNA that was not present on the X chromosome, an observation that is clearly inconsistent with population expansion. While these loci do not have sufficient resolution to detect recent population expansion events, none of them indicate any sign of population expansions and are consistent with the larger sets of data that reject them.
The problem is that these same loci determine a very small long-term average human Ne for the Pleistocene. Combined with the absence of evidence for population size expansions noted here, interpreting Ne as a measure of census population size means, effectively, that the ancestors of modern human populations did not first emerge from their homeland and expand significantly enough to be archaeologically visible until the beginning of the Neolithic. If these interpretations are valid, one must assume that a great replacement of indigenous populations around the world, including the far peripheries such as the Americas and Australia, took place at this time or later.
This is an unusual reading of human prehistory (and history), and we question whether there might be a better explanation of the genetic data. As we have noted, such observations on nuclear DNA call the assumption of mtDNA neutrality into question. They raise other questions because they are not compatible with archaeological data that suggest much earlier expansions through evidence of range and density increases (Klein 1998 ; Stiner et al. 1999 ). It is difficult to argue that these archaeological data can be dismissed as the record of behavior in other human species, because significant parts of it are African or are found in western Asia at times when the archaeological remains are associated with so-called "modern humans." Therefore, it would be these "modern humans" whose populations did not expand.
It is more reasonable to conclude that these autosomal genes are under selection. If so, the absence of evidence for recent expansion would be explained, but then these genes could no longer be used for valid Ne estimation (Caballero 1994 ; Rogers 1997 ).