A few questions for you - if we take as reasonable your suggestion that Zhao (2000)'s data coalesce to four haplotypes between 300,000 - 1,000,000 years ago, how does that help your case? In Adam and the Genome I consistently discuss humans as a species arising ~200,000 years ago. So, by your calculations, Zhao (2000) supports my case - human variation in this all region of the genome cannot be reasonably explained by a bottleneck to 2 individuals within human history, as I argue in AatG. Am I missing something here? I want to be sure I’m reading you correctly.
Also, I do think it would be helpful at this point to discuss common ancestry. Zhao (2000) explicitly depends on humans sharing common ancestors with orangutans and chimpanzees. This is how they estimate the forward mutation rate for this region. We’re a couple of professional biologists discussing a technical paper, so I was taking for granted that we both accepted that. I’m not so sure now, so I’ll ask it again: do you accept that humans share common ancestors with chimpanzees and orangutans? If you don’t that is going to substantially affect how you read and interpret Zhao (2000), so I’d like to know.
You have been appropriately pushed to present specific numbers, and you have. Thanks. I am going to work that out here for others to follow.
I should point out, however, that I think it is already clear that the Zhao 2000 does not demonstrate evidence against (1) a couple bottleneck that was (2) 500,000 years ago, where (3) there was heterozygosity in this couple. The reason why is actually much more straightforward.
In genetics, TMRCA is always to 1 allele. However, in your scenario, there was never just 1 allele, because it started with 4. We need to know the Time to Most Recent 4 Alleles (TMR4A). This is not a standard computed number in genetics. Provisionally, I think that on average TMRCA / 4 = TMR4A. So given Zhao’s estimate TMRCA of 1 mya, we could estimate that the TMR4A is about 250,000 years ago, matching y-MRCA of about 200,000 years ago and mito-MRCA of about 200 years ago. That is, of course, well within your 500,000 cutoff. So I think we already know (back of the envelope) that the data can be explained by your model.
Someone tell me if I’m wrong in my estimate (TMRCA / 4 approximately equals TMR4A).
This is a pretty classic mistaken regardless. Genetics is not genealogy. Just because genetics has not coalesced, does not mean we are not down to one couple. In fact, if the couple is heterozygous, we do not expect TMRCA to equal bottleneck time. That is fairly obvious, but equivocated time and time again.
However, there is value in working out the math for observers. Of course, if I have made an error (which does happen sometimes) please do point it out. I will fix it.
First off, if we are talking of a single couple bottleneck about 500,000 years ago, it will take time to get back up to 10,000 individuals, somewhere between 300 to 1000 generations (depending on growth rates). However, that is just a small effect on your estimate of 20,000 generations, which is actually a bit low any ways. So, let’s just say 20,000 generations.
Next, your estimate of 1.1x10-9 mutations / bp is reasonable. We can compute about how many mutations we expect in the whole population each generation. 10,000 individuals * 1.1x10-9 mutations / bp * 10,000 bp --> 0.11 mutations per generation in this region.
We can also compute the mutation rate in this region as a whole as 10,000 bp / region * 1.1x10-9 mutations / bp -> 1.1x10-5 mutations in region.
That means every about every 9 generations, one person in a population of 10,000 will have a mutation in this region. So this region would be mutated 0.11 mutations/generation * 20,000 generations -> 2,200 times. This matches @RichardBuggs’s number.
How many of these are going to be fixed?
Well, we know that that with random drift, it will take about 10,000 generations (the number of individuals), for a mutation to be fixed. But the variance is high here. Someone who knows better (@glipsnort?) correct me if I am wrong, but the variance is much higher. Regardless, we can expect about 1.1x10-5 mutations / region * 20,000 generations --> 0.22
mutations to fix during this time in this one region.
To be clear, there are few major simplifications in that last number. First, it assumes equilibrium, which is not the case. Remember, in the very first ~500 generations, the population is growing; so there are fewer mutations there. At the same time, when the population is growing, it is much easier for a mutation to be fixed.
And if 0.22 mutations are fixed assuming equilibrium conditions, and it takes 10,000 generations to fix a mutation, it is expected to see several mutations “in transit” during this time, and not fully fixed. As @RichardBuggs says, 78 is not a problematic number.
So, provisionally speaking, it does seem possible, maybe even likely, that in this scenario we could observe this 78 SNP variants (perhaps even at these distributions) in the population today from a primordial pair 500,000 years ago. For observers, it is critical to recognize that a couple at this point in history would not be a modern Homo sapien. This also does not explain all the data (if I am right) but just this single region. An effective model would have to explain all the data, not just this area. To be taken seriously, one has to refrain from claiming success in one area is the same as declaring success everywhere. Moreover, this is merely a qualitative analysis of the sequencing data (as I have not actually verified that only a few variants are required). A better analysis would do a quantitative analysis. Moreover, this does not take into account the linkage between all the variants.
Once again, this is consistent with the TMR4A number I computed above, so no real surprise if that can be trusted.
Notably, the same math that shows a bottleneck of one couple at 500,000 years ago fits this narrow component of this small part of the data, is the same math that gives strong evidence that we share common ancestry with the great apes. It is important to keep this in mind too.
What About Linkage and Recombination?
The analysis above ignores linkage, the adjacency in the chromosomes. We can do a similar analysis for recombination. My intuition here (for what its worth) is that this is not enough to make a definitive statement about a bottleneck of 2 at 500,000 years ago, but it’s difficult to know for sure from eyeballing. At issue here is the distance between variants (which is not included in the image).
The rate of recombination is approximately 1% per million bp, or 10^-4 recomb / individual in this region of 10,000. Eyeballing it, there about 20 variable regions, so we would say that the recombination between variants (assuming equally spaced) is about 5x10^6 / individual between adjacent variants.
Similar calculations as before follow. Expect there to be 10,000 * 5x10^-6, or 0.05 per generation. So every 20 generations, some individual somewhere will recombine betwixt one of the loci here. About 1 individual per generation will show recombination in at one of the 19 regions between variant loci.
How many of these are going to fix?
In the region, we expect 10^-4 recomb in whole region / individual * 20,000 generations --> 2 recombinations to have fixed. This is 10 times more fixed recombinations than the number of fixed SNP variants. That means we should expect more recombinations “in transit” to fixation than SNP variants themselves.
Notice, that is much faster than the mutation rate, but there is a twist. Not all of these times a recombination is detectable, because there really needs to be heterozygosity here for it to matter. Honestly (help me @glipsnort?) I’m not sure what the correction factor is here. My guess is that it would about 50% less than we observe because of an intuition from Hardy-Weinberg, and then an additional 50% less because of other factors, so 25% of that rate. This, however, is a major fudge factor that should probably reduce the estimates further.
As a simple (and wrong estimate), parameterized by the data itself may be possible. if we observe 78 SNP variants, we should also see 780 recombination variants too. With our fudge factor, maybe 200.
Though, really, no one should trust this analysis as anything more than qualitative (because of a lot of assumptions here). More care (as is done in published) work must be given to the distances between markers and considering several places in the genome. I’ve only worked this out here to demonstrate how some of the mathe works, and to show that we actually expect to see a lot recombination in this 10kbp region in 500,000 years. And I expect this computation to refined with more information about the data and better formulas, and also recognition of the actual sampling distribution (and past population structure).
Better theoretical analysis of this can be found here: http://www.pnas.org/content/98/24/13757.full For those that want a real treatment, look there, and references within. And ultimatley this is what whole genome wide LD analysis does, and such analysis does not detect any bottlenecks. TMRCA, ultimately, is not as important as effective population size estimates on the whole genome.
Allele Clustering is Unconvincing This Far Back
This argument, from the beginning, was quite weak, because clustering is notoriously subjective. Any data can be clustered, but how many clusters are in the data? That is much more difficult to determine from “eyeballing” the data as we done here.
First off, given recombination, wedo not even expect this to be four allele clusters from a primordial pair. We would need to look at smaller regions than 10,000 bp (and actually look at them across the genome) to discern 4 alleles in that way. We would need to look at region sizes much smaller to expect 4.
Second off, given drift, even in smaller regions we expect some of the primordial alleles to have drifted away early on. So some regions would have to 4 ancestral alleles, some to 3, some to 2, some to 1. The notion that is should be four either (1) assumes no recombination or (2) that this couple had infinite children. In this case (assuming no miracles), we might say they had 10 kids or so (but not 200). That is going to create a distribution over 1 to 4 of the number of ancestral alleles, that might in principle be detectable. How far back? I have no idea, but I imagine if done systematically over the whole genome on small regions, we should see that signature quite farther back than 200,000 years ago.
This should be a good reminder that population genetics is not-intuitive. It really does help to work out the math. Eyeballing clusters in data cannot be a substitute for actually modeling the data with simulations and more rigorous treatments…
Move On From Zhao 2000?
From that, can we now move on from Zhao 2000?
I think there is good reason that this single paper’s data (in isolation) can be explained by a primordial couple that is heterozygous at 500,000 years ago. Once again, @DennisVenema has already admitted this is not the strongest evidence. Moreover, he never even considered a couple 500,000 years ago.
It is not that the 4 allele cluster argument was correct (it was not), but the whole premise that TMRCA in one autosomal location tells you where a single couple bottleneck happens is flawed. It is a category error. Moreover, recombination is happening this area, and we do expect to see it in this region.
Ultimately, I agree that the totality of the evidence shows no bottleneck, but there is also value in delimiting exactly what specific points of data (like Zhao 2000 which only looks at one 10kbp region) do and do not tell us. This data, in particular, seems to allow for @RichardBuggs’s hypothesis. Unless, someone can point out the error in my math, perhaps it is time to grant that point and move on.
Of course @DennisVenema or @glipsnort can correct me if I made an error here (and I may have). If I made an error, it really should be fixed, and I apologize ahead of time.
@DennisVenema, in your defense, the question you laid out in Adam and the Genome was answered by your book. If “human” = Homo sapien, and we simplify the problem by ignoring the clear evidence of interbreeding, does that taxonomic category ever go to a single couple within the last 150,000 years? The answer, of course, is “no,” unless there was a lot of miracles or interbreeding. No one should be confused by that.
However, that is not the question being ask right now, and it appears it never was, at least not in this exchange.
Your are missing several critical things.
You have assumed without warrant that “humans” = Homo Sapiens. This is a minority position in the origins debate. Most YECs now day, for example, would say that Homo erectus is “human.” As we have seen recently, even OECs like @agauger are open to this position too.
Regarding Homo sapiens in particular, there is evidence of a large number of remains as anciently as 300 kya, not 200 kya. It is possible that Homo sapiens were around longer than to, say going back as far as 350 kya. So the short timeline of 150 kya is not really justified when considering Homo sapiens = “human” anyway. (This was discovered AFTER Adam and the Genome published, so @DennisVenema could not have included it in his book)
Also, there is very strong evidence that Neanderthals interbred with “humans,” as you define them. If that is the case, TMRCA estimates of Homo sapiens are going to be pushed back by that interbreeding event. So some sort of correction that excludes these parts of the genome is required. As I understand, no one has done studies like that in the literature.
Also, as I pointed out earlier, TMRCA tells us when things collapse to a single allele, not when they go down to 4 at the TMR4A. So using TMRCA’s on autosomal locations embeds the assumption that Adam and Eve were homozygotes and with identical genomes.
Neandertal’s Human or Not?
A fairly important question here to make sense of all this is if Neandertal are “human” too. If they are, there is a massive amount of additional variation that must be accounted for (pushing back estimates).
If they are not, some account has to be given for interbreeding. Do we accept it happened or not? How do we make theological sense of this in a way that avoids all the nastiness that so often arises in these conversations?
If we accept Neandertals interbred with “humans” (defined as Homo sapiens), then why would we think TMRCA would even give us a good estimate of “humans” in the past? It will always be giving us the sum total of Human plus Neandertal ancestors (and any other hominids Homo sapiens interbred with).
This is all to say, given the exceedingly strong evidence (including remains of a hybrid!) of Neanderthal + Homo sapien interbreeding, if Homo sapien = “human” the argument against a single couple origin of Homo sapien seems to weaken substantially. We would expect to see no single couple bottleneck, because population estimates are always adding in numbers from our Neanderthal ancestors.
The warrant of saying Homo sapien = “human” is very low any ways, so probably that is the part that should be dropped. But this is a big part of what is contributing to confusion about why @RichardBuggs and @agauger and many in the Church still have question after reading the book.
The case against a single couple origin (without interbreeding) has to be made in a way that does not assume Homo sapien = “human.” Honestly, the case against interbreeding with other lines is weak Scripturally, that very few people are going to insist on that any way.
Time to Most Recent 4 Alleles (TMR4A) and TMRCA
This last point about TMRCA and TMR4A is most interesting, and most likely to be abused. I’ve been thinking about this, but we should really see a distribution of TMRCAs of individual autosomal locations if there was a single couple origin.
A key overlooked parameters appears to be the NUMBER of OFFSPRING, that the first couple has. We will get very different distributions if they had 5, 10, 20 or 1000 kids (last on would clearly require miracles). However, in the very first few generations, some locations will very quickly drift to 3, 2, or 1 allele. The exact distribution will depend on precisely what happens in that moment, and even the degree of inbreeding, which will drive it lower. Someone needs to do the modeling here, but there may actually be a detectable variance increases in TMRCA measured in several locations.
The problem however, is that there is already high variance in TMRCA estimates. So if this shift in variance can be seen with any confidence, I am not sure. Regardless, this is a caution of applying my estimate that TMRCA / 4 -> TMR4A when the whole genome is considered (as in the later studies). Those studies would not enable such a facile computation, or at least I do not think so.
However, the really interesting thing is the population structure in the first few generations of a single couple bottleneck. That appears to be an overlooked detail by @RichardBuggs and @agauger, and I am curious what they are thinking about that. Basically, we expect large linkage domains of the genome to have only one ancestral sequence, because of drift in the early population. That seems to undercut a major source of variation, and also suggest that this bottleneck should have been detected by now.
Our Common Ground
I do, however, want to emphasize that a very recent common couple ancestor (with no miraculous biology or interbreeding), say within 100,000 years ago, does appear to be ruled out. It is not as if @DennisVenema has missed something so large as to call that conclusion into question.
For those that think Adam and Eve are real, in our recent past, and our universal genealogical ancestors, ask if interbreeding with other lines is a problem in your reading of Genesis. If not, a genealogical Adam could have been recent (as recent as 10,000 years ago). To understand how that can be possible, you have to understand the difference between genetics and genealogy.
Only when they are talking about fossil identification, because they deny any creatures, human or otherwise, were around 150,000 years ago. Every fossil has to be a modern human or a modern ape. So how is the YEC classification of homo erectus relevant to the discussion?
Just pointing out that “human” = Homo sapien is a minority position. It seems the scientific community has tipped towards “Homo” = “human” too, but even that is disputed and debated. “human” is ambiguous in the distant past.
Moreover, we see Homo sapiens as early as 300 kya ago. So the 200 kya date is not accurate any more.
Clearly, we see no single couple bottlenecks (or Homo erectus) in the last 10,000 years (and I do not think any one here is disputing this). However, the assumption that “human” = Homo sapien was central to Dennis’ question:
[taking my own advice and removing a distracting post]
So it is possible that: TMRCA / 4 approximately equals TMR4A. This may be a reasonable estimate where we are looking at (1) a single region and (2) that region is autosomal (not X, mito or Y chromosomes). For Y and Mitochondrial regions, we are still most interested in TMRCA, not TMR4A. And for X we would be interested in TMR3A.
I hasten to add that this shortcut does not work for reducing estimates of Y-Chromosome Adam and Mito-Eve, because we only expect one genome of each in the primordial pair (unless we go to the mosaic hypothesis which is a massive miracle). Moreover, this short cut may not work when considering the whole genome (several places in the genome at once).
Moreover, this is only provision. It needs a lot more careful thought to be sure. There is certainly some assumptions buried here, and I do not have a solid decision on how much I trust this yet.
A few comments: the paper that suggests Homo sapiens back at ~300,000 years ago came out after AatG was published, but I don’t see how it really affects things. I don’t see any evidence of a bottleneck in our lineage for the last 1 MYA or more. Even Zhao (2000) has a range of TMRCA/4 values (if we want to go with that) that easily pushes back past 300,000.
(Of course, we need to look at the distribution of TMRCA values across the genome as a whole - not just at one 10kb region, as you’ve noted.)
Also, those fossils are not uniformly accepted as Homo sapiens. They have some features that are decidedly different than Homo sapiens at 200,000 years ago. This is to be expected. Our species becomes a species as a gradient biologically. With a “perfect” fossil record over the last 2MY, we presumably would have a smooth gradient between early H. erectus all the way to modern humans in the present day. As such, it will become more and more difficult to “draw the line on the gradient” - as I discuss in the book- as we get a more complete picture of the fossil record. We’re a chronospecies.
I still think pushing an “Adam” back that far is strongly at odds with the scriptural account. Even for the concordists among us, Genesis is clear that one generation after Adam is farming, and a few more generations are doing metal working. How does that work if Adam is at 300,000 or 500,000 years ago? I just don’t see the appeal. YMMV.
I talk about interbreeding in the book. It (as far as know so far) only applies to non sub-Saharan Africans. Yes, it increases the difficulty of “finding Adam” because there are more human ancestors than those within our own species. I don’t avoid this in the book.
Yes. But my assessment of his sensitivity has been tempered by his practice of consistently ignoring various simple, easily answered, questions from those he is supposedly most concerned about assisting. Several people (including myself), have put very basic questions to him, the answers to which would help us assess the relevance of this complex scientific discussion, to our beliefs or those of others who feel affected by the subject. Those questions have been phrased consistently respectfully and graciously, with full acknowledgment of his time constraints.
However, those questions have been ignored. Note that this is not even a case of Dr Buggs responding to these questions with “I understand your concern and note your questions, but regret I cannot address them within my current time constraints”, it is a question of him completely ignoring them and not acknowledging them in any way at all. Perhaps now you have asked a couple of these same questions, he may feel more inclined to answer them, but at this point it really does look like his main concern is “taking down” Dennis in the name of ID and the Discovery Institute, rather than actually addressing the personal concerns of rank and file Christians.
No one has attempted to dismiss or ignore his question on the basis of its source, or claim that it is invalid on the basis of its source. The point being made is that his question has not arisen on a scientific basis; it has not arisen from a need to find a scientific solution to a scientific problem. It is an apologetic argument which has arisen on a theological basis, and this needs to be both acknowledged and stated explicitly. When someone’s interpretation of the science is affected by their theological constraints, it is important to identify this and examine how it affects their interpretation of the science. When this is swept under the carpet, and discussion of it is discouraged, red flags should fly.
He has also made the claim that there have been no scientific bottleneck studies which have ruled out a bottleneck of only two people. I believe Dennis has already shown that this is simply not true, and has listed a number of them. If Dr Buggs had mentioned these other studies and explained why he thought they didn’t support the conclusions of their authors, that would have been fine, but instead he has given the impression that they don’t even exist. My surprise at this claim of his was matched only by my surprise that Dennis was able to show easily that they do exist.
There is nothing wrong with Dr Buggs challenging Dennis over Dennis’ representation of the science. However, I don’t think Dr Buggs has been accurate in his representation of the science, and it is clear to me that he really does believe it is about the science, not simply Dennis’ representation of it.
I don’t think that Dennis has conceded this, or that Dennis has overstated the science. I am still wondering why Dr Buggs has not contacted Zhao et a, if he is so concerned that their analysis of the data is wrong.
I think this wrongly suggests that Dennis is acknowledging some kind of failure on his part which weakens his case.
It is NORMAL to quote historical and easier to understand references when engaging the public on established science. Dennis did nothing wrong here. The fact that he used weaker references ends up strengthening the case, because there is so much data out there that makes it clearer that our ancestors do not dip down to a single couple (at least within the last several 100,000 years).
Btw, I think the strongest evidence against a bottleneck in the last 6 million years is trans-species variation, which does not even appear to be on the “menu,” as it were. Trans-species does not have the same horizon problems as does allele frequency spectrums and LD estimates. Nor is it subject to as much uncertainty from population structure (though interbreeding can explain it away too).
To me, that seems to be exactly right. The fact that Zhao 2000 does not make the case with the strongest data is not really a big problem. There is so much more data. Even if a single couple bottleneck at 500,000 years ago, provisionally, can fit Zhao 2000, does not mean the same will work for all the rest of the data. I want to see how far we can go.
It is not really expected to give the best references in a book like Adam and the Genome. The field is huge. There is just so many papers out there, I doubt any of us have read absolutely all the relevant studies. None of the conclusions Dennis presented are disputed in mainstream science either. So he is not so much “making the case” but explaining what others have found. The evidential standards are just much much lower for that type of activity. He did not thing wrong by quoting a selection of papers.
Taking him to task on that is really beside the point. That is why I think we should move past a referendum on @DennisVenema. He has already basically admitted his references are not the best evidence. There is no reason, also, to think his references should include all the relevant evidence, because there is so much here, and historic papers actually make sense in this context.
[taking my own advice and removing a distracting post]
Hi @Swamidass thank you for contributing some substantial and substantive posts to this discussion in the past few days. Sorry that I have not acknowledged your presence here sooner. Because my time available for this discussion is very limited, I have had to prioritise responding to Dennis as he has invested more in this discussion than anyone else. I have therefore been making a lot of the use of the website function that allows me to only see Dennis’s posts, so many of the other posts I have not even read, let alone had time to engage with (though I would like to have done, were there not so many demands on my time). However, your posts have now come to my attention and I will just make a few comments. I will try to restrict myself to your points most narrowly focused on the points I have raised, as I don’t have time to comment on everything you have said. Many of your comments and observations I agree with, and I appreciate the peaceable nature of your contributions, and your occupation of the middle ground between Dennis and myself.
This is exactly my point. Thank you for stating it so concisely. To my mind, the way ahead would be to write a programme that computes the TMR4A for each haplotype block of the human genome, and work out a reasonable time frame using data from all blocks. Until that has been done, I do not think we can say that the bottleneck hypothesis has been rigorously tested.
I am glad that you agree with my back-of-the-envelope calculations, and my conclusions from that. I am interested that when you add in recombination you get a potentially shorter time to a primordial pair. I would also be glad to hear what you think of the rest of my post, where I suggest that if the population continued to expand from a single couple up to 7 billion individuals, then the time to a primordial pair could be lower than 500,000 years. All in all, it seems to me that the jury is still out on a minimum bound for a bottleneck.
I agree that more rigorous treatment is desirable. However eyeballing the data can be a useful heuristic in illustrating a point and deciding what ideas to follow up. The clustering that I did of the Zhao et al (2000) sequences shows that one can reasonably place them into clusters, and that not every possible combination of the variants are found in that data. If you prefer, here is a haplotype network for the whole Zhao et al (2000) dataset:
Looking at this - “eyeballing” again! - there are clear clusters with fairly recent common ancestors.
Agreed. So not every haplotype block in the human population today would have its TMR4A at the bottleneck (if one occurred) - some would have them at a more recent date, due to earlier loss of ancestral haplotypes. Just looking at such blocks in isolation would give a misleadingly young age for a bottleneck.
I think we are planning to come on to linkage disequilibrium in this discussion, one we come to the Tenesa et al paper.[quote=“Swamidass, post:254, topic:37039”]
Is this conversation assuming common descent?
Absolutely[quote=“Swamidass, post:260, topic:37039”]
Btw, I think the strongest evidence against a bottleneck in the last 6 million years is trans-species variation,
I agree. I am assuming we would come to this in detail at some point.[quote=“Swamidass, post:260, topic:37039”]
None of the conclusions Dennis presented are disputed in mainstream science either. So he is not so much “making the case” but explaining what others have found. The evidential standards are just much much lower for that type of activity. He did not thing wrong by quoting a selection of papers.
Here I disagree with you, sorry! Most mainstream papers have not tested the bottleneck hypothesis. As you have said, the “Time to Most Recent 4 Alleles (TMR4A)… is not a standard computed number in genetics”. To test a bottleneck of two hypothesis, this is what is needed. There is quite a lot of interpretation going on by Dennis. Take the Zhao et al paper: Dennis is not making a point that the authors are making. This is to a greater or lesser extent the same for the other papers he cites in Adam and the Genome, as I have shown in my blog. Also, and this is just a minor point, the Zhao et al paper was not cited in Adam and the Genome: Dennis has cited it in this discussion to back up a passage which has no citations in Adam and the Genome. I would also note that thus far, no mainstream scientist has disputed my blog which has been read by many scientists.
Thanks again for your input. The time I can give to this discussion today is up. It is 10pm my time and I need to wake my baby son to have his final feed for the day!
I don’t see this. Dennis is making the point that there’s no evidence for a two person bottleneck in any of the studies he has cited. I don’t think that’s a matter of interpretation. Your only argument is this.
None of the studies above set out to explicitly test the hypothesis that humans could have passed through a single-couple bottleneck.
But you haven’t demonstrated that this hypothesis needs to be tested in a special way which hasn’t already been tested by previous studies. The fact is that previous studies have consistently arrived at the conclusion that a bottleneck of only a very small number of people is just not credible.
Genetic variation at most loci examined in human populations indicates that the (effective) population size has been approximately 10(4) (i.e., 10,000) for the past 1 Myr and that individuals have been genetically united rather tightly. Also suggested is that the population size has never dropped to a few individuals, even in a single generation. These impose important requirements for the hypotheses for the origin of modern humans: a relatively large population size and frequent migration if populations were geographically subdivided. Any hypothesis that assumes a small number of founding individuals throughout the late Pleistocene can be rejected.
There is no evidence for an exponential expansion out of a bottlenecked founding population, and an effective population size of approximately 10,000 has been maintained.
Note that this paper states specifically that there’s no evidence for “an exponential expansion out of a bottlenecked founding population”, which is precisely the model you are proposing. So this study has tested this specific aspect of your hypothesis.
This study likewise specifically denies the severe bottleneck of your hypothesis.
On the other hand our results also deny the hypothesis that there was a severe hourglass contraction in the number of our ancestors in the late middle and upper Pleistocene. If humans were descended from some small group of survivors of a catastrophic loss of population, then the distribution of ascertained Alu polymorphisms would show a pre-ponderance of high frequency insertions (unpublished simulation results). Instead the suggestion is that our ancestors were not part of a world network of gene flow among archaic human populations but were instead effectively a separate species with effective size of 10,000-20,000 throughout the Pleistocene.
This study also specifically tested the hypothesis of a very small bottleneck.
Moreover, the ancient genetic history of humans indicates no severe bottleneck during the evolution of humans in the last half million years; otherwise, much of the ancient genetic history would have been lost during a severe bottleneck
All of these studies are clearly testing exactly what you claim has never been tested. They say there’s no evidence for a bottleneck down to a small handful of people, and no evidence for an exponential population expansion after such a severe bottleneck. This is not a matter of Dennis’ interpretation, this is what the studies state explicitly. If you want to claim these studies are inadequate, you have to address their contents and explain their deficiencies.
I don’t see how this is relevant. Have you attempted to submit this for peer review?