Sorry it has taken me a while to respond; my fortnight of teaching has ended now,
I am glad to say and although I now have a backlog with my research group,
I hope I can give this discussion a little more time this week.[quote=“glipsnort, post:169, topic:37039”]
Given enough time, a complicated demographic history can produce all kinds of frequency spectra. In this scenario, though, the core problem is recovering diversity in a short time frame; there isn’t time for complexity introduced by multiple rounds of anything.
I agree, and this is the concern with your model that I am pointing to. I am not sure quite what time scale you are alluding to, as in your original models you covered a wide range of time spans. Are you currently referring to a 200,000 year timespan, or a longer one? Also, as we have already discussed, if the founder couple came from a highly variable population themselves, the issue is less about recovering diversity and more about their alleles at 25% and 50% frequencies drifting downwards.[quote=“glipsnort, post:169, topic:37039”]
There is no mating system in my model. The model assumes a pool of 2N genomes consisting of unlinked markers. For allele frequencies averaged over the whole genome, such details should not matter.
I am not convinced that such details would not matter. I would think that separate male and female sexes, and the complex breeding patterns that this generates in human populations through monogamy, polygamy, sexual selection etc would be bound to have an effect on allele frequencies.
I was thinking of Prado-Martinez et al 2013 Nature. I mentioned this to Dennis in my original email to him: “The average human has 3.1 million single nucleotide variants (SNVs), but the average chimp has 5.7 million (Prado-Martinez et al 2013 Nature). African humans approximately 1.1 heterozygous SNVs in every 1000bp, whereas central chimpanzees have approximately 1.75 (Prado-Martinez et al 2013 Nature).” If, for the sake of the argument, we assumed that the ancestral couple carried similar levels of diversity to chimpanzees, I imagine that would have an appreciable effect on the model. (Note for readers: please do not mis-read me as suggesting that modern day humans evolved directly from chimpanzees - I am just pointing out that present day great apes have higher levels of genetic diversity than humans (despite much smaller current census population sizes) and that it might not be unreasonable to think that our own ancestors had high levels of genetic diversity).[quote=“glipsnort, post:169, topic:37039”]
It would correspond to a spectrum with too many low frequency alleles (relative to a constant-sized population) and some much higher frequency ones, with a relative dearth in between.
But this seems to assume subdivision into just two populations, followed by a merger event. I am suggesting a more complex model which is more likely to reflect the actual population structure: one of multiple sub-populations, multiple migrations – some small, some large – and many mergers and splits. As we have already discussed, this could give smooth allele frequency curve, and the major criticism you have made of this idea is the time available, rather than the ability of complex demographic history to generate “all kinds of frequency spectra”.
I appreciate that it would be a lot of work, and would distract you from your valuable work on malaria. I respect that. I am also not in a position to give much time to this issue, and have to squeeze it into my evenings and weekends. I am grateful though that you are willing to share your code.
However, I have to admit that although I think that your arguments from allele frequency spectra could potentially make a good test of the Adam and Eve bottleneck hypothesis, I would need to see this worked through in considerably more detail before I was fully persuaded that it was an adequate test. I have been reading a bit more widely about site frequency spectra and the factors that can affect them in a few spare hours. In particular I found these recent papers helpful:
Harpak, A., Bhaskar, A., & Pritchard, J. K. (2016). Mutation Rate Variation is a Primary Determinant of the Distribution of Allele Frequencies in Humans. PLoS genetics, 12(12), e1006489.
Ferretti, L., Ledda, A., Wiehe, T., Achaz, G., & Ramos-Onsins, S. E. (2017). Decomposing the site frequency spectrum: the impact of tree topology on neutrality tests. Genetics, 207(1), 229-240.
Koch, E., & Novembre, J. (2017). A Temporal Perspective on the Interplay of Demography and Selection on Deleterious Variation in Humans. G3: Genes, Genomes, Genetics, 7(3), 1027-1037.
Gao, F., & Keinan, A. (2016). Inference of super-exponential human population growth via efficient computation of the site frequency spectrum for generalized models. Genetics, 202(1), 235-245.
These papers have strengthened my view that a wide range of complex demographic, phylogenetic, selective and mutational processes, together with sampling strategies, can influence site frequency spectra, and that I therefore cannot conclude from the models that you have run that a bottleneck of two in the history of the human lineage is not possible. To be convinced I would need to see more complex models run that try to incorporate these factors. I realise that this is beyond the scope of what you wish to do in the context of the present discussion, but I do hope that in the future others may wish to take up the idea.
OK, that is fair enough. I have to admit, I had thought you were doing them to bolster Dennis’s case.
OK, well it’s good to know that you don’t quite have the level of confidence against an ancestral bottleneck as Dennis. What about the existence of Littlefoot?
Thank you, this is a very helpful explanation of where you are coming from on this question and in this discussion. I hope that Dennis might perhaps send you a copy of his book, given the time you have invested in this discussion. I think that if you had read chapter three of Dennis’ book, and then read my blog on it you might have more sympathy with my critique of Dennis’ case, even if you agree with his final conclusions. I think you might feel as I did when I was flying to Tenerife from London a few months ago, and across the aisle a man said to his family “You can tell we are getting south, as the cabin is getting warmer”. I considered the man to be entirely correct in his conclusion about the location of the plane, but knew that the evidence he had given for it was based on a very partial understanding of physics, climate and aeronautical engineering. If I had had the time, I might have tried to explain to him that whilst I agreed with his conclusion, the reason he had given his children for it was not going to help their science education.
If you read Dennis’ chapter, it would remind you that it is this chapter - and not my blog - that raises the hypothesis of a bottleneck of two, and treats it as a hypothesis that has been raised, tested and disproven with a very high level of certainty.
I respect your view on this as you have a long track record in the analysis of human genetic variation. However, I know that you would not want me as a scientist to resolve this issue with a simple statement from authority. Until I can see the evidence and appropriate analyses clearly laid out in detail and clearly refuting the hypothesis, I can’t see it as decisively disproven.
Given that you do not seem to want to pursue this further due to time constraints, could I finally just ask you these questions (and these can be my final questions to you if you wish): Which published analyses in the literature do you see as most convincingly disproving a bottleneck hypothesis? Do you consider that analyses of the coalescence of different haplotype blocks within the human population could yield decisive tests of the bottleneck hypothesis?
Once again, I would like to say how much I have appreciated your contributions to this discussion. It has certainly moved my understanding of this area forward, and I now have clearer ideas about how the bottleneck of two hypothesis could be tested, which I am very glad about. I am sorry that this has not been as decisive as we might have hoped, but I certainly have learned a great deal. I hope in the future we will see some conclusive testing that can put this issue to rest.