I know you were being a little bit facetious in elements of your previous post, but when one writes a paper on human history, like this one on reconstructing Indian population history or the one on Neanderthals that I had mentioned, it seems that societal reaction cannot be neglected. Indeed the reason for interest in human history is exactly because it tells us where we came from; the most compelling stories are often the ones of our own past. As such, I think authors may feel an even higher burden of statistical certainty than they otherwise might, though of course one should always maintain high standards of proof for scientific statements.
When I was at Janelia Farm, I had gone to a lunchtime presentation about statistical methods for experiments involving multiple comparisons. It was interesting in its own right, discussing techniques that I myself have used for motif detection, and something that our father has some recent interest in. The other interesting thing, however, was the strong emphasis on ruling out null hypotheses. When classical statistics are used for scientific investigations, the use of controls and the notion of null hypotheses seem to be a huge deal. On the other hand, in traditional applications of statistical signal processing there seem not to be any privileged hypotheses. Since you are more closely involved in the statistics and statistical signal processing communities than I am, perhaps you have more insight into this philosophical distinction. I know you’ve done some work on detection in settings where false alarms are much more troubling missed detections (and not just referees that swallow whistles).
Anyway, let me come back to the Neanderthal paper, as you had asked me to. Rather than recapitulate the main results of the paper, which have been well-described by many other commentators, let me focus on a couple interesting little pieces. The first is phenomenon of unidirectional gene flow and the concept of gene surfing. As Green et al. say, “we detect gene flow from Neandertals into modern humans but no reciprocal gene flow from modern humans into Neandertals.” Now this seems very puzzling: how can gene flow not be bidirectional? They go on to explain this by essentially invoking facts about population dynamics: “it has been shown that when a colonizing population (such as anatomically modern humans) encounters a resident population (such as Neandertals), even a small number of breeding events along the wave front of expansion into new territory can result in substantial introduction of genes into the colonizing population as introduced alleles can ‘surf’ to high frequency as the population expands. As a consequence, detectable gene flow is predicted to almost always be from the resident population into the colonizing population, even if gene flow also occurred in the other direction.” So it is all about detectability. Moreover, “another prediction of such a surfing model is that even a very small number of events of interbreeding can result in appreciable allele frequencies of Neandertal alleles in the present-day populations.” So rare events can have huge impacts on what is observable.
Another piece that you might find interesting is found in the online supplementary material, and in particular part 14 on Date of population divergence between Neandertals and modern humans. The goal is to put an absolute time scale on evolutionary events such as splits in the tree from the genetic data itself. I won’t go into the details, but surprisingly, parameters such as mutation rate and generation time are not required because they cancel out; only one calibration date is needed. (Obviously the disembodiment of life implied by artificial insemination and the dissociation from physical time and space that it allows are not considered).
In closing this post, let me just say that I find it very hard to imagine what it would be like with several hominid species walking the earth simultaneously. Not just the Neanderthals, but also the hobbits Homo floresiensis (if they are actually a separate species), and others. [As you had pointed out, interpreting archeological evidence is difficult, so it is unclear whether H. floresiensis is distinct. Brain size and scaling laws are the basis for several of the arguments both for and against.] Would there be positive social interaction or would there be deep mistrust? Would interbreeding result from acts of war? Perhaps each would see the other as a curiosity. Hard to know.