A 'Modern Population Bottleneck?'

NPR has a story on the (almost) disappearance of modern humans here. It is not a hypothesis that I had heard of before. Robert Krulwich writes:

Once upon a time, says Sam [Kean], around 70,000 B.C., a volcano called Toba, on Sumatra, in Indonesia went off, blowing roughly 650 miles of vaporized rock into the air. It is the largest volcanic eruption we know of, dwarfing everything else...That eruption dropped roughly six centimeters of ash — the layer can still be seen on land — over all of South Asia, the Indian Ocean, the Arabian and South China Sea. According to the Volcanic Explosivity Index, the Toba eruption scored an "8", which translates to "mega-colossal" — that's two orders of magnitude greater than the largest volcanic eruption in historic times at Mount Tambora in Indonesia, which caused the 1816 "Year Without a Summer" in the northern hemisphere.

Although this is a provative hypothesis, it does not match modern genetic studies. Dennis Venema writes:

Studies based on SNP/LD approaches have now estimated ancestral population dynamics for various human groups over time in more detail than is possible with mutation-based estimates. African groups have a higher effective population size (~7,000) than do non-African groups (~3,000) over the last 200,000 years. This approach, though based on methods and assumptions independent of previous work, nonetheless continues to support the conclusion that humans, as a species, are descended from an ancestral population of at least several thousand individuals. More importantly, the scalability of this approach reveals that there was no significant change in human population size at the time modern humans appeared in the fossil record (~200,000 years ago), or at the time of significant cultural and religious development at ~50,000 years ago.

When the first mtDNA studies began to come out in the late 1980s and early 1990s, they all supported the recent African evolution of modern humans and they all came to the same general conclusion: that modern humans had originated in sub-Saharan Africa between 140 and 280 thousand years ago. The earliest fossil evidence we have for modernity in Africa are the Herto remains at 160,000, at the site of Bouri, in the Afar Triangle. These remains bear more than a passing similarity to the modern Skhul 4 and 9 remains from the Israeli site of Skhul (dated at around 100,000) and suggest a general northern migration of these populations.

The other problem is that this does not correspond to a die-out of Neandertals either. The Neandertals didn't go away until around 30,000 and interbred with the incoming moderns anyway. Indeed, it looks as if the incoming moderns simply swamped the Neandertal genome and assimilated them. It is hard to do this if you have a very small effective population size.

I have not read this book so he may have counters for all of these arguments but I would be really curious to know what they are.