Alas, not so. Exponentially expanding populations have been the norm only since the industrial revolution, and occasionally during colonisations of new landmasses. Apart from that, populations have been relatively stable, with slow growth, no growth or sometimes even shrinkage (e.g. black death, or volcanic winter).
I’m not sure how else to get you to see that Jeanson’s approach is seeing the tree as a regular old genealogical male-line tree, which you can do if the mutation rate is at least 1 AFAIK. I’m trying as best I can. As I said before, it made more sense for me to look at the dots as men, not genes - so the connections are how many sons a man has. Obviously a man will have to come from the previous generation. So they join together in the previous generation if they have the same father.
I don’t know how a y-chromosome coalescent tree looks like when the mutation rate is less than 1, but my assumption is that mutations are closer together (because you’re losing men) and then farther apart when the population is growing, as you’re saying.
Point of order: “Exponential growth” is rapid if the coefficient is positive, but slow when the exponent is negative. It doesn’t always mean “very fast.”
What is the chance two genes come from the same copy in the previous generation? Surely you had some rationale for connecting genes between one generation and the next?
And FYI it doesn’t matter in this case if you think of them as genes or men. Every gene will have a different coalescent tree and the Y-chromosome is but one of many.
Also to be clear this is what a coalescent tree looks like for a population undergoing a bottleneck. Jeanson would mistakenly interpret this as some exponential expansion.
The bottom trees are from exponential population growth. Jeanson’s method would likewise misintrepret those trees as well.
From Hein, Schierup, and Wiuf 2005 Gene Genealogies, Variation and Evolution: A Primer in Coalescent Theory. Oxford University Press.
Well, if the father had two sons. As the population expanded I had to connect more than 1 man to the previous generation. So the probability is related to average population growth in this case.
So close but no.
If you take two genes from the population at random what’s the chance they are derived from the same copy in the previous generation, let’s say out of a population of 100.
Well in a stable population I would think it would be 1/100 because it can’t be less than 1. But populations aren’t stable and mating isn’t random.
What is the math for an expanding population?
Just checking to make sure because I still don’t know if I have an affirmative on this: With a mutation rate of at least one, a distanced-based tree will look like Jeanson suggests - yes or no?
No. A mutation rate of one (assuming you mean per Y chromosome) in no way suggests that every Y chromosome will have a mutation.
This is about as basic as probability gets.
OK right 1/100.
So now what if the population is only 10 what’s the chance?
Right. I should have said “at least one occuring per generation.”
You already explained this in the video. It’s one out of 10. You didn’t comment on what I commented about random probabilities earlier. I copied it again below. Also I really am curious about the math in an expanding population.
OK so for a population of 100 the chance that two genes come from the same copy in the previous generation is 1/100.
For a population of 10 the chance that two genes come from the same copy in the previous generation is 1/10.
So based on what you just told me which population would be expected to have the shorter coalescent times (and thus shorter branch lengths). Big population or small population?
Of course: a small population or I wouldn’t have had a reason to make the point that humans act like they’re in a small population.
But again, when we talk about the tips of the tree we’re talking about a recently rapidly expanding population that will act like many small populations. And it would be nice if you’d address that point.
Sharing these quotes in case they have contributed to some confusion on my part:
We compared these mutation accumulation predictions to the branch lengths derived from the data in Karmin et al. (2015). Since the published tree in Karmin et al. was given in time units rather than in units of base pairs, we redrew a tree from the Karmin et al. data. First, we converted the online supplied VCF file3 to FASTA format with PGDSpider software,4 after applying appropriate sample names and labels to each individual based on the online metadata (see Supplemental Table 10 for details of relabeling).5 Though the tree in the main text of Karmin et al. contains over 300 individuals, the metadata file contains labels for only 297. Then we drew a midpoint-rooted neighbor-joining tree (see Supplemental fig. 3 for rectangular display, Supplemental fig. 4 for topology-only display) with MEGA7 (Kumar, Stecher, and Tamura 2016) software, selecting the “Pairwise deletion” option for treatment of gaps/missing data. Branch lengths were extracted manually from the tree and deposited in Supplemental table 11).
So are you saying the tree he redrew and/or the trees in the book aren’t distance-based trees?
If they are distance-based trees, I see two options: either his mutation rate is wrong, or how you’re saying coalescent trees would act in this situation is wrong. I do not see how he could be wrong about how distance-based trees would look in this situation.
What actual mutation rate would be the minimum required for that?
So you see how you’re just fabricating evidence to accommodate your desired conclusion, not starting with the evidence?
The point is that Jeanson’s method of counting branches to infer population size doesn’t work WITH ANY SORT OF TREE.
You came to this logic yourself, or so close, when you basically acknowledged that shorter branches should be found in SMALLER populations not large populations. That observation throws an enormous wrench into Jeanson’s approach.
I will say this however. Right now you know way more about the coalescent and population genetics than Jeanson.
Yeah, I think I don’t and didn’t. However, I did read this blog a few days ago, and I think it and another video helped clear up some of my worst misunderstandings about trees. Bringing alleles back together: applications of coalescent theory – The G-cat
Also, it made me realize I probably would have done what Jeanson did if I had a simple tree, a short timeline, a high mutation rate, and a genealogical hypothesis about a recent bottleneck, and it was easy to check if it worked. Coalescent theory seems like it was made for long timelines and complicated or static population scenarios. Also, what I’m seeing is that short branches arise inside the bottleneck if the population after the bottleneck is stable or grows very slowly. But if the population grows rapidly afterwards, then genes could coalesce before it. It seems like the theory is helpful for making inferences, but it’s very hard to know how accurate those inferences are.
I also noticed y-chromosome coalescent tree from Karmin could look like it does if human history had frequent migration plus rapid growth - bottleneck rapid growth bottleneck rapid growth, etc. A young “pruned” tree that grew exponentially looks very different from an old lightly pruned tree that grew exponentially. (At one time I had called Jeanson’s hypothesis a “genealogical bottleneck”; later I was trying to figure out drift and trees. That made me think of pruning so I started to use the word “drift” only to describe it. But after thinking about trees some more, I realized the imagery confused me - “drift” is not specific enough - a population bottleneck in this case is, of course, tree pruning. I particularly like the pruning metaphor.)
As far as your recent comments to me and others elsewhere in the forum about keeping faith and science separate, my brain just doesn’t put things in separate compartments like that - I skips around. For example, trees are my favorite biblical imagery. So I have had a worshipful appreciation that this tree is like a regular tree - long, sturdy ancient branches with short populated branches at the tips. It would look weird the other way around. And that made me think of necessary pruning, and that made me think of the philosophical “problem of evil” in quite a new way: combining the reality of what this science describes historically and how fruit trees remain healthy.
And my life currently as a mom of 3 little kids mixes a lot of sweetness and poop (literally and figuratively) often. I wish I could separate it out sometimes, but just not possible. So I will happily enjoy it all together.
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