Adam, Eve and Population Genetics: A Reply to Dr. Richard Buggs (Part 1)

[Swamidass (Peaceful Science)]

@RichardBuggs

This is just going to be a rather brief holding response as I have only got part way through my first read of the ARGweaver paper, and a series of mini-crises in my lab are taking up much of my time now, so it may be a while before I can give you a fully considered response. I don’t want to leave you waiting for too long, so here is a quick reply, with all the shortcomings that this necessitates.

No problem. Believe it or not, I have my own fires I’m putting out in my lab this week. I also have 4 public events I’m doing next week, including one with Hugh Ross. So a lot is going on here too.

Take your time in responding, but there is a lot you’ve written here I want to echo.

@RichardBuggs

I agree with you that the ARGweaver results, given the assumptions and simplifications behind its analyses, does appear, on your further analyses of its graphs, to give a reasonable bound of a bottleneck of 420 kya +/- 100 Kya.

Thanks for offering your public thoughts on that too, as hopefully that should put some criticism to rest.

@RichardBuggs

To be perfectly honest, I am quite surprised at how low this figure is. If you had asked me to guess beforehand I would have probably suggested a higher figure.

I agree. This was surprising for me too. I would have guessed a different number. It is still important to caveat that this is just a subset of the data, and subject to revision to a more ancient data with more evidence. It is hard, however, to imagine it being revised more recent than 300 kya.

In particular, I would point to two pieces of evidence that are not considered here:

1. Genetic evidence of interbreeding with Neanderthals/Densiovans seems to put a bound on a single couple bottleneck back to the Homo sapien common ancestor with them, perhaps 400 kya to 700 kya ago. This analysis of TMR4A used the median, and would underestimate that date because interbreeding with them only affects the minority of the gnome (it seems).

2. Interspecies variation will always put an asterix on these results. Though on re-looking at the literature, it is very sparse. In contrast with population genetics estimates of population size, there are only a handful of papers that address this. I have not been able to find definitive evidence of >4 alleles at a single locus with interspecies counterparts. However, that maybe just because no one has looked at enough of the Chimp data (which very sparse). Nonetheless, I’m less convinced now than when I started that this will be (at least in current form) definitive evidence against a couple bottleneck. Still, we have not taken it into account here.

@RichardBuggs

Having said that, on my rather shallow reading of the work so far, I would be slightly cautious,

@RichardBuggs

I think I would therefore have more confidence in your lower bound than your upper bound.

The phrasing here is difficult, but it sounds like you are saying you have more confidence in bound on single-couple bottlenecks of 520 kya than 320 kya. I’d agree with you here too.

@RichardBuggs

That is because every method (that I know of) would need the population size to remain constant for at least a few generations before it could estimate an Ne of 2. Thus, I think we can safely say that when effective population size is defined by an equation based on genetic data, a single generation of census size two does not have an Ne of 2, but of a higher number (exactly what I don’t know - I guess it would depend on the size of the pre-population bottleneck and the rate of population expansion afterwards

That is correct, and I have been working out the math on this, and planning some experiments. It looks like the key variables for Ne is (1) how many generations are at a single couple (just one in our case), (2) the number of offspring they have and degree of exponential growth in the few subsequent generations (which we can assume here is very high), and (3) how distant this is in the past (as the averaging window for Ne increases in the past). Keeping mind that #2 is essential a free parameter, #1 and #3 are such that the farther back we go in time the much less a single couple generation affects Ne. So, therefore, a single couple bottleneck can be entirely consistent with a very high Ne in the distant past (say at 500 kya)

Once again, this is just an informal description, but there are some interesting details in the math. Sufficiently interesting, I’m nearly convinced its worth turning into a publication in its own right. Interesting stuff.

@RichardBuggs

just having 4 lineages left in a population does not mean that those 4 lineages are all found in just two individuals, as I think you have already pointed out. Demonstrating that only four alleles are left in a population is a necessary pre-requisite of a bottleneck of two, but is not in itself evidence that a bottleneck of two actually occurred. For the four alleles to coalesce to the point of being in the same human bodies may take quite some while and could add a bit to to the timing (This depends on effective population size, of course, as has been frequently noted in the discussion above).

This is an important caveat to emphasize.

This is not evidence for a single couple bottleneck but evidence that population genetics will be unable to detect a bottleneck in the distant past. It is an argument that such a bottleneck would be hidden in the shadows, and not clearly seen in the data.

Moreover, median TMR4A, as you suggest, may be too generous a cutoff. My instinct is that we should probably use a CDF cutoff of about 70 to 80% instead of 50%, which would put TMR4A at about 525 kya. Though, I cannot be certain on instinct. The right way forward is to determine this cutoff from simulations, which I am nearly convinced are worth the effort to embark on. There seems to be good theoretical reason to think that detection power will correspond relatively tightly with some cutoff on the TMR4A CDF. Once I get around to doing those experiments, we’ll have a much better bound.

@RichardBuggs

In the ARGweaver paper, in a footnote to Table 1 the author’s write “Model allows for a separate Ni for each time interval l but all analyses in this paper assume a constant N across time intervals.” It sounds to me as if they use a constant Ne. I have to admit that I find the paper rather confusing on the point of effective population sizes, but you have spent longer than I have working out exactly what they did, so I look to you for enlightenment.

They are not clear in the paper. But the code itself is clear. The only way they seem to use Ne is to set the prior, and the prior (if anything) pulls TMR4A downwards. However, the influence of the prior on the joint likelihood (just 5%) is very low, so I’m not really concerned about this. There is no plausible reason I see to doubt the results of this study because of their use of the prior. As I have explained, the prior thinks mediant TMR4A is at about 200 kya, but we compute it at about 420 kya. So the data is pulling the estimate upwards, and there is sufficient data to totally overwhelm the prior.

@RichardBuggs

I think the most important take home message for me from your ARGweaver analyses is that (as far as I can see) you have shown nicely that genome-wide allele counts do not provide evidence that a bottleneck of two has not happened in the human lineage.

To be clear, I agree that “genome-wide allele counts” alone are not very good evidence. Moreover, their overall diversity do not provide evidence against a single couple bottleneck after about 400 kya_ (subject to revision). They do, however, provide evidence against a more recent bottleneck, as you have already affirmed.

As many people have noted, for most people, this is a fairly disturbing challenge to theology. Perhaps some will find solace in an ancient Adam that was not Homo sapien. At the moment, that seems to be an outlier position, though perhaps it will grow, especially as it seems we are beginning to come to a consensus here.