What I find interesting is the fact that neither Gauger nor Buggs discuss how many generations it would take to produce the observed genetic diversity in the human population after a bottleneck. Is it 100,000 years? Is it 1 million years? All we get is vague assertions like this one:
"Buggs goes on to discuss the relative genetic diversity of chimpanzees at 5.7 million SNPs (single nucleotide polymorphisms) and humans at 3.1 million (Prado-Martinez et al 2013 Nature). He makes the point that if a pair of chimpanzees were moved to an isolated region where rapid population growth was possible, the new population would have similar levels of genetic variability to modern humans."
They also tend to focus on heterozygosity vs. homozygosity which really misses the boat. The evidence for a lack of a bottleneck is the number of alleles at each locus. For example, for some of the HLA genes there are thousands of alleles.
Gene: # of alleles
If we start with just 2 people that is a max of 4 alleles for each of these genes. I just don't see how you can go from 4 alleles to 4,000 alleles in just 6,000 years, and have those alleles spread so evenly across the globe.
They also use a bit of misdirection:
"Effective population size is very hard to determine. In fact, in some situations the effective population size cannot be determined (On the Meaning and Existence of an Effective Population Size P. Sjödin, I. Kaj, S. Krone, M. Lascoux and M. Nordborg (2005) Genetics 169: 1061–1070). So any estimates concerning effective population size should be taken a bit skeptically."
To use an analogy, that is like saying it is difficult to accurately measure the orbit of an asteroid, therefore you can not claim that asteroids orbit the Sun. Even with limited accuracy we can still rule out many scenarios, and that is the case with a drastic bottleneck in the recent history of the human population.
What they need to do is use the standard equations from population genetics and show that the observed levels of human genetic diversity could be produced in such a short time. Without such a demonstration they are just blowing smoke.