Various apologetic arguments claim that the scientific estimate of the minimum human population is some value such as 2,000, which is not supported by the actual scientific literature; in this post we'll look at where some of those numbers seem to be coming from.
An actual study
The above graph is from a study published in Nature (Li and Durbin 2011). It was derived from the sequenced genomes of 6 individuals: two West African (YRI1, YRI2); two European (CEU1, which happens to be Craig Venter, and CEU2); and two East Asian (KOR and CHN). The method used produces an estimate of past effective population sizes over time from each genome independently, but loses accuracy outside the range 20,000 years to 3 million years.
(I chose this study to focus on first because unlike prior studies it has detailed estimates over a time range rather than a single estimate, and because it produces some of the smallest reported population sizes of any study using nuclear DNA methods.)
So we can see from the graph three major features: a bottleneck in all populations about 500k to 800k years ago (this predates the first known anatomically modern humans, for whom the oldest fossil evidence is about 200k years old) at which the effective population size was somewhere around 7,000; a later bottleneck (size given in the paper as 5,700 at 50k years ago) in the ancestors of the West African samples; and a much narrower bottleneck of as low as 1,200 at 40k-20k years ago in the non-African samples only.
(Estimates for the ages of MEve and YAdam currently fall in the 100k-250k year range, give or take; so according to this paper the effective population size at that time was around 10k to 14k. This isn't really significant, since what matters for apologetic purposes is the smallest bottleneck at or before the time of MEve and YAdam; the apologist can simply argue that MEve is just some descendant of the Biblical Eve since the "MEve" label moves over time anyway as lineages die out.)
The fact that we get such a small bottleneck for the non-African populations (which presumably reflects an "out of Africa" migration event) implies that this method would, assuming we can trust it at all, detect any comparable size bottleneck in the African population had one existed. So the fact that the African population shows no bottleneck below 5,700 is quite good evidence that no such event occurred (at least within the last 3Myr).
(There's some uncertainly about the horizontal scale on this graph. The model used actually gives ages in units of the inverse mutation rate, so scaling to chronological years relies on an estimated average generation time and average mutation rate, as shown on the image legend. But variations in these parameters don't change anything except the age scale, and the model has been tested (using simulated data) for robustness in the face of variable mutation rates, recombination hotspots, and other artifacts.)
So where are Craig and other apologists getting estimates of 2,000 from? There are a number of possible sources.
Craig references Faz Rana at Reasons to Believe (Hugh Ross's old-earth creationist group). Rana in this article cites Zhivotovsky et al 2003, which gives a number of figures for ancestral effective population sizes. However, while that paper gives population sizes of ~1,700 for some non-African populations at 17-25k years ago, broadly consistent with the study above, the estimate it gives for its African hunter-gatherer effective populations is from only 4.3k years ago, too recent to be relevant in this context. The paper even points out that its attempt to estimate an ancestral effective population size does not give a consistent result; Rana's claim that the study “concluded that humanity originated from a single point of origin (apparently Africa), from a small population (~2,000 or less)” is a complete misrepresentation.
Another apologist who gives a 2,000 number is Catholic writer Dennis Bonnette, in this article: “Effective population size estimates can vary from as high as 14,000 (Blum 2011) to as low as 2,000 (Tenesa 2007), depending on the methods used.” But Tenesa 2007 does not give a figure of 2,000 anywhere; their final results are 3,100 for the non-African population against 7,500 for their African samples, consistent with every other study that shows a smaller out-of-Africa bottleneck.