Hi @Swamidass, thank you for such a quick response. It looks as if you had a busy Sunday!
I felt an obligation to give a response in that: (1) it is a loose thread that needs to be tied up, and (2) it is a public blog that mentions my name in the title and (3) because I said I would and (4) because it is interesting. I also feel obligated to continue to reply and deal with the four papers that @DennisVenema references in the blog, even though you have already dealt quite effectively in their conceptual content within this discussion forum. If Dennis were to formally retract the blog, I would not need to do this, but otherwise I need to do this for the sake of completeness.
I think that you and I are essentially in agreement, and where we appear to differ it is mainly because we have different interpretations of what @DennisVenema was saying in his blog, or you are making additional comments that complement mine, or you have misunderstood what I was seeking to say.
I think you are saying the same thing as I was my statement:
“The loss of alleles via the sampling effect of the bottleneck will not show up as coalescence events in a coalescence model. These are two separate effects of a bottleneck.”
When you say this, do you mean (1) any lineage, or do you mean (2) a lineage that has a mutation that makes it a different sequence (allele) to other lineages?
I agree, and I agree that my figure shows that. That was not unintentional!
I am not sure what conditions you mean. Yes, I deliberately showed three lineages going through the bottleneck, two in a heterozygote and one in a homozygote. I tried to illustrate as many processes as I could in the figure.
I agree: three identical alleles in three different individuals coalesce into a single identical copy in a one parent.
I think we are misunderstanding one another here. There is no reduction in number of alleles from g1 to g0. There is a reduction in the number of copies of alleles (= a reduction in the number of lineages) but not a reduction in the number of alleles. By an allele here I mean a DNA sequence that is different in nucleotide sequence to the other alleles - as I explained in the text describing my figure, I show different alleles in different colours. There are three alleles in generation g1 (one red, one blue and one yellow, with copy number 1, 3 and 2 respectively) and three alleles in the g0 generation (one red, one blue and one yellow, with copy number 1, 1, and 2 respectively)
I agree. In the text that accompanied this second figure I wrote:
“How would coalescence to one lineage occur after a bottleneck? Figure 2 shows a scenario in the minimum possible number of generations.” The figure does not claim to show a single coalescence - it claims to show the most rapid possible coalescence back to a single lineage that passed through a bottleneck of two. (The significance of this is that it was the nearest thing I could think of that would to some extent correspond with what Dennis seemed to be writing about in his blog. A problem here is that Dennis’ blog was so off the mark that it is hard to reinterpret it in terms of actual coalescent scenarios.)
I think you are misunderstanding what I am seeking to do here.
I agree that this could be developed into that, but my aim here was simply to show how unlikely it is that three lineages would be lost after a bottleneck of two, leaving just one of the four allele copies that was present in the parental pair.
I agree that coalescence analysis is normally done with a sample, not the whole population. This is why I wrote: "Similarly, if we only sample a subset of the lineages, the probability of all of our sample coalescing at the bottleneck is slightly higher than the probability of all lineages coalescing, but again, this will not make a huge difference. For example, if we sampled four individuals in generation g2 the probability of all sampled lineages coalescing in the bottleneck would be 0.000977. "
I agree. Coalescence and fixation are completely different things.
That was not my case. There seems to have been a degree of misunderstanding in your reading of my blog.
I don’t dispute that, but the number of extant lineages in a coalescent analysis is simply our sample size. Every sample we take is a lineage. It doesn’t matter if they differ in their nucleotide sequence (i.e. are different alleles) or not.
I agree. This is a point I have been trying to make all along in this debate.
In summary, Joshua, I am glad we agree on the big picture, but I think you have misinterpreted some of what I was trying to say, especially (a) the distinction between lineages and alleles, and (b) what I was seeking to show in figure 2 and the calculations accompanying it.