The method assumes that the loci have not been subject to recombination or to directional or balancing selection. For recombination, we used only those loci that showed no evidence of recombination by the four-gamete test [38
]. It is possible that this has missed some recombination since the time of common ancestry. Regarding natural selection, the study was limited to loci that had not individually been reported to show evidence of directional or balancing selection. However, it is possible that when considered together, and polymorphism and divergence from chimpanzees are considered under a common neutral model, that there is evidence of selection. An HKA test [39
] of the eight loci with estimates of divergence from chimpanzees () yielded a p
value of 0.054, which is nearly statistically significant. This test assumes, as do the models analyzed in this study, that all loci are sampled from the same panmictic population [39
], and it is possible that the differing geographic sources of the loci included in the study may have contributed some variation.
Information on Loci Used in the Study
The estimated posterior distributions are shown in . For the initial analysis, allowing for exponential population size changes, the posterior distribution for t yielded both a major and a minor peak (the curve for t with a high tupper, D). Given the mutation rate estimates (see ), the location of the major peak (t = 0.032) corresponds to 7,130 y, whereas the location of the minor peak (t = 0.27) corresponds to 44,400 y. Given the remote possibility of such an ancient time as the latter, analyses were also done with a smaller upper bound on t of 0.2 (identified as “low tupper” in ), which corresponds to 33,000 y. Analyses were done with this reduced upper limit for t for both models in , allowing for population size change and for the case of fixed population sizes. In the case of constant population sizes, the distribution for t shows a peak (t = 0.038) very near those for the analyses under population size change; however, the highest posterior density is found at the upper limit of t. When the constant population size model was run with a higher upper limit on t, the posterior distribution showed the same low value peak as well as a steadily rising curve for higher values of t (unpublished data).
Marginal Posterior Probability Densities
The archaeological portrait of early New World populations has largely centered around widespread Clovis sites that have an earliest estimated age of about 13,000 y before the present [15
]. The oldest generally agreed upon New World archaeological date is from the non-Clovis Monte Verde site in Southern Chile, which has been dated to about 14,000 y before the present [10
]. Clearly the time points associated with our estimates of t
are more recent than expected, given the archaeological estimates. However, these distributions do span the time periods that have been most discussed. For example, a time of 14,000 y has a relatively high probability in each of the analyses (E). Given that people have lived in the New World probably for only several hundred generations, it is noteworthy both that the posterior densities for t
do show clear peaks in the expected time period and that the probability estimates drop to zero as t
approaches zero. In other words, the data contain a clear signal of a nonzero, albeit recent, founding time of New World populations.
With regard to migration, each of the three analyses show nonzero peaks for both directions of gene flow. These may well reflect the occurrence of more than one episode of migration to the New World. For example, it has been suggested on the basis of mitochondrial DNA haplotypes and glaciation history that an initial migration along a coastal route may have been followed later by another migration, possibly through an ice-free noncoastal corridor [13
]. However, the posterior distributions shown here have little resolution, as all of the curves for m1
are broad, and all have high probability at the lower limit of resolution, indicating that zero gene flow is nearly as well supported by the data as are nonzero gene flow levels.
The ancestral population parameter, θA
, shows a relatively narrow distribution with a very consistent peak location across the three analyses. These attributes are partly to be expected, given that the very large majority of the variation in the samples is older than t
. In effect, more information is available for θA
than for the other parameters. The estimated effective size of the ancestral population is about 9,000 (), which is roughly consistent with previous estimates for Asian samples [44
]. The current Asian population parameter (θ1
) revealed broad distributions and estimates that are near those for the ancestral population. Although the estimates of current effective size in Asia vary among the analyses (), they are all fairly close to the ancestral size estimates, suggesting that there has not been much population growth in Asia since t
. Also consistent with the apparent constancy of population size is the distribution of s,
the splitting parameter, which shows a peak at 0.992, signifying that only a small portion (less than 1%) of the ancestral Asian population left to found the New World population.
In contrast to the Asian population, the New World population parameter (θ2) is much smaller, and suggests a recent New World effective population size of less than 1,000 (). However, given the estimate of the effective size of the founding New World population (about 70; ), the overall picture is of a nearly 10-fold growth in the New World effective size since t.
Estimates of Demographic Quantities
In order to gain a sense of how consistent the data actually are with the model and the parameter estimates, 500 simulated datasets were generated under the model in B, with sample sizes and true parameter values (see , column 3) that were the same as for the actual data. From each simulated dataset, the average number of pairwise differences between sequences were calculated within each population (Asia and the New World) and between these populations. The average of these values from the 500 simulated datasets, and the observed values from the actual data, are shown in . In general, the observed and expected values are similar; however, one consistent pattern of departure is that the data from the New World, for most loci, show more variation by this measure than were found in the simulated data.
Contrasting Observed and Expected Levels of Variation