He’s assuming that you mean humans and E. coli are sister species. That’s not what [common ancestor] means.
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Oops, I meant “not what common ancestor means”. And of course, as this thread is in Slow Mode comments, once posted, cannot be edited. In spite of the little pencil icon being there.
@swamidass I didn’t realize that slow mode prevents editing (it doesn’t for mods). Is there a setting to adjust this?
Don’t think so…but you can ask on meta.
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Roy, you need to study the mathematics of compound interest because that is what is operating here. If you hadn’t heard this quote, you should read this one:
I won’t retract my claim because there are over 7 billion humans on earth and only about 300,000 chimps. What appear to you to be small differences in any given generation leads to vast differences over time that for some reason you can’t see.
I’m not making that assumption. If you understood the math that I’ve presented, you would know that I’ve taken that factor into account. Not only is a replication a random trial in the DNA evolutionary process, so is the mutation a random trial. The beneficial mutation rate will always be lower than the overall mutation rate because you multiply the mutation rate by the probability of the particular beneficial mutation(s) occurring. In the simplest case where each of the base substitutions has the same probability of occurring, the beneficial mutation rate will be 1/3mutation rate. If two of the possible substitutions improve fitness, then the beneficial mutation rate will be 2/3mutation rate.
It’s not the percentage of those members with the first beneficial mutation replicating for the next beneficial mutation occurring, it is the absolute number of members with that first beneficial mutation replicating that determines the probability of the next beneficial mutation occurring. Here’s an analogy that might help you understand. Let’s say that for your family to survive, your family has to win two lotteries. The probability of winning the first lottery is 1 in a million and the probability of winning the second lottery is 1 in a million. The probability that you win both lotteries is 1 in a million times 1 in a million, 1 in a trillion, a very low probability. But let’s say you win that first lottery, and because of that, you are very wealthy and you can raise a very large family. And as your family grows, each of your descendants buys a ticket to the second lottery. As soon as you have enough descendants, you will have a reasonable probability of winning that second lottery. That’s how random mutation and natural selection works.
Why do you think that DNA evolution works differently in bacteria and any other replicator? If you say recombination, read that link again about the evolution of yeast which does recombination, and how recombination can affect adaptation, and compare that with the math that I’ve published on recombination.
Of course, you don’t, it might happen on the first replication, but that probability is very low. This is a binomial probability problem, that is, does the beneficial mutation occur or does it not occur on replication. You should study up on the binomial distribution and learn how to calculate the variance and standard deviation of that distribution. It takes a lot of replications before the probability of a beneficial mutation starts to increase significantly.
I don’t have to. The mathematics for the accumulation of a sequence of single beneficial mutations is enough to crush the human/chimp common ancestor story. If a double mutation is required to improve fitness, using your mutation rate, the population size needed to give a reasonable probability for that outcome goes to over 10 billion. Bacteria, viruses, and cancer cells can achieve these kinds of populations, humans haven’t. That’s why combination therapy is needed to have any chance of a durable treatment for diseases like HIV, cancers, and other diseases subject to evolutionary adaptation.
It doesn’t matter when it comes to the math.
Have you read that paper on experimental evolution in yeasts that I linked to yesterday? That paper also substantiates the math that I’ve presented. If you haven’t read or can’t find the link, let me know and I’ll post it again.
I don’t know how you did it but you got it backward. The probabilities of beneficial mutations occurring in DNA evolution depend on the absolute number of replications of the particular variant (the sub-population size) while the probabilities of a particular recombination event occurring depend on the frequencies of the different variants, not the population size.
You have two errors here, the first is that fixation must occur before an adaptive mutation can occur. If the carrying capacity of the environment is large enough, the population size can become large enough for an adaptive mutation to occur without fixation occurring. That happens in the Kishony experiment. On the other hand, the carrying capacity of the Lenski experiment is not large enough to give the number of replications necessary for the next beneficial mutation to occur without fixation occurring first for that particular variant. And your second error is once again thinking that the frequency of a particular variant determines the probability of a particular mutation occurring. The first time I saw this claim was in the Haldane “Cost of Natural Selection” paper. Though his math is correct, that claim is wrong.
And I don’t make that assumption. Different beneficial mutations for a given selection condition certainly do exist but these different beneficial mutations are part of different evolutionary trajectories and each of these trajectories is constrained by the same law of physics.
Joe Felsenstein used this archiac term in one of his posts. Why don’t you ask him what he meant by this?
Watch the video I linked to in the very first post of this thread.
Not that complicated except that most of the human population growth has occurred in the last 10k years, 99%. And you imagine that something bottlenecked the chimp population but not the human population? My arguement is that human population grew because humans have the intellect to do farming while all chimps can do is hunt and gather. And you don’t need a natural disaster to suppress the chimp population if that is how they supply their population with food. All humans have to do is compete for the chimp habitat, and starvation will bottleneck their population. That’s basic Darwinian evolution.
I know that, what Joe said was, “… But the question is: what is the chance that a change in junk DNA has a selective advantage or disadvantage large enough to be selected for or against by natural selection? …” Some definitions of “junk DNA” is DNA which has no purpose. I’d like to have a clearer meaning from Joe what he thinks “junk DNA” is.
Well, it is known that about 2% of the genome codes for proteins. If you know the proportion of the remaining 98% of the genome that does control and other functions, you should tell the people at NIH because they don’t know the answer.
So you claim that a only a tiny portion of the genome is necessary to control the differentiation of the zygote stem cell into a full grown human or chimp? Is there any portion of the genome that you know has no function whatsoever? If so, tell us how you know that.
I’m not the one making videos and telling layman that you can explain the genetic differences between humans and chimpanzees using a distance = rate x time neutral evolution model. I’m the one explaining to you the correct mathematics of DNA evolution and adaptation. So, why don’t you tell us how many of these genetic differences between humans and chimpanzees are neutral and how many are adaptive because you only have about a billion replications for any adaptation process for the human lineage and most likely fewer replications for the chimpanzee lineage when it is claimed these two lineages diverged from the primate progenitor.
You can’t even correctly explain the Kishony and Lenski evolutionary experiments. And until you do, you should think twice (perhaps more) before you put E. coli into your phylogenetic tree. Why don’t you ask some of your graduate school instructors to give the mathematical explanation for these experiments and see what happens? Have them explain the phylogenetic trees that are actually visualized in the Kishony experiment.
and
Not quite. What I’m saying is that based on the physics and mathematics of evolutionary adaptation, you can’t put humans and chimpanzees on the same phylogenetic tree let alone E. coli. Here’s the mathematical problem. Assume that the human and chimp genomes differ by 2%. That is about 60,000,000 bases. No one knows how many of these genetic differences are neutral or adaptive but we can do the math which determines the number of possible adaptational steps that a human lineage can take based on population size. I posted a link at the beginning of this thread that gave population size for humans throughout history. None have challenged that data. In that table, from the origin of the human lineage until 10,000 years ago, there were about 1 billion people or about 1% of the entire human population. At that point, the human population has rapidly increased. 99% of the human population that has ever lived has lived in the past 10,000 years. One should conclude that any genetic adaptation that would allow such an increase in population size would have to occur in that first billion humans. If one accepts the fact that adaptational mutations can only occur at slightly less than the frequency of the mutation rate, the population size of 1 billion will determine how many adaptational steps are possible.
I’ve presented two ways of computing the number of adaptational steps possible as a function of population size. One method consists of nested binomial probability problems (does the beneficial mutation occur or does it not occur on a replication) where each binomial probability problem is linked to the other by the multiplication rule of probabilities and the other method consists of a Markov chain process where the transition matrix includes the effect of population size on the transition probabilities. Both methods give consistent results with each other and with empirical examples of evolutionary adaptation.
Under the best of conditions where each adaptive mutation in a lineage can be accumulated sequentially and using T_aquaticus’s mutation rate of 1.67e-8, it will take 90,000,000 replications for each adaptive step on that evolutionary trajectory. That ideal evolutionary trajectory requires that each adaptive mutation in that sequence gives improved fitness at each step on that evolutionary trajectory. That gives about 11 adaptive mutations possible. Under very specific conditions recombination can increase this number slightly. Under less ideal circumstances, if it takes two particular mutations to give improved fitness at a given step on the evolutionary trajectory, the population size needed for that adaptive step goes to about 10 billion.
Another point, in your 2018 Fisher lecture, you are using the gamma distribution in your computations. The correct probability distribution to use for evolutionary adaptation is the binomial distribution, does the beneficial mutation occur on replication or does it not occur.
No, I merely intended to demonstrate that large populations differences between populations related by common descent can occur without there being any changes in the number of beneficial mutations fixed in there genome. It seems to me a very obvious point, but you seem unable to grasp it. I thought I could help with that. Oh well, at least I tried.
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Therefore you were employing a straw-man fallacy, one of many.
That is the definition used by scientists. Instead of pretending that Joe wrote something that he didn’t write, why not ask him?
[quote=“kleinman, post:127, topic:13271”]
Yes.
Deletions.
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If >99% of the mutations are neutral, then it is fair to say that the genetic differences can be explained in terms of rate x time.
“correct mathematics”? You can’t give the ‘correct mathematics’ for a theory you don’t understand with a model you refuse to apply properly. You have multiple gross conceptual errors with respect to evolution generally and population genetics specifically. ‘Wrong’ would be an improvement for your math. You’re ‘not even wrong’.
Nearly all of them.
A few in both lineages.
Good thing you only need about 30k, then, huh? And again, that’s 30k for your nonsensical misunderstanding of how population genetics works, the reality is closer to… 0. But you’ll misunderstand and misrepresent this the same as you have everything else said to you.
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Am I correct that this represents haploid reproduction, NOT diploid sexual reproduction? If so, then the binomial model is incorrect; sexual reproduction is combinatorial, as I noted above.
You continue to make the error of assuming that such differences in population can only be due to differences in number of beneficial mutations.
My sad story about the squirrels did not seem to impress you, so I will now try an even sadder one:
In March 2021 the COVID-19 virus undergoes mutations that not only renders it impervious to the current vaccines but also greatly increases its infectivity and lethality. By the end of the year, the human population is completely wiped out. We are no more.
Chimpanzees, however, are not affected.
In this scenario, what beneficial mutation occurring in chimpanzees in 2021 was responsible for their phenomenal growth curve, relative to the human population?
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Note that there are several definitions there, some of them mutually contradictory. But more to the point, all of them are wrong. Junk DNA is DNA without function. Lack of function can be estimated in a number of ways, but “we don’t know what it does” is not one of those ways. “It doesn’t code for proteins” is also not one of those ways. Ignorance can be excused, but refusal to learn cannot.
Of course Kleinman refuses to learn; witness his response:
Apparently they haven’t read the literature. It’s about 90%.
If you had read the literature on this subject, you wouldn’t have to ask.
They differ by 1.3%; that’s about 35,000,000 bases. There are about 5,000,000 differences that aren’t point mutations too. Around 99% of those are in junk DNA, but that’s an underestimate of the number of neutral differences, since most of the differences in functional DNA are probably neutral too. Your calculations are useless for other reasons, though. You don’t consider that different sites can evolve in parallel, you ignore standing variation, and you employ the Texas sharpshooter fallacy.
Oh, and you don’t understand what Joe was using the gamma distribution for.
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Incidentally, here:
Maybe you could send that link to NIH too.
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[quote=“kleinman, post:127, topic:13271”]
evolution.
That is a fair enough question. Regions of the DNA that do not code for either protein sequences or functional RNAs, and also are far from coding sequences, are most likely mostly junk, that is, mostly regions that contain no control sequences and carry out no structural function. Those regions have many sequences that are annotatible as “dead” copies of transposable elements. Every change of sequence must have some nonzero effect on fitness, but most such changes will have such small selection coefficients that they will evolve as if totally neutral.
The fallacy I am pointing out is thinking that just because most changes in DNA sequences, or most sequence differences between humans and chimps, are in those regions, those are the differences that are responsible for the observed anatomical, physiological, neurological, or behavioral differences berween humans and chimps.
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I get your point. You think that the difference between human and chimpanzee population is due to some unknown random selection process, but you miss the obvious explanation for this difference. It is simply the difference between the availability of food for either population that limits the growth of both the human and chimp populations. Chimps being hunter-gatherers can never achieve the population size that humans have because humans have changed the carrying capacity of our environment with farming. We do this because we have something in our intellect that enables us to do that which chimps don’t have.
That’s not sufficient to say that humans and chimpazees are related. If only 99% of mutations are neutral, that leaves 600,000 mutations not neutral. If 99.9999% are neutral, it would still require the accounting for 60 non-neutral mutations in only a billion replications. The math and empirical evidence is still against you in that circumstance.
Why don’t you give us the “correct” explanation for the simplest evolutionary adaptation experiments, the Kishony and Lenski experiments? Haven’t they taught you that math in your graduate studies in evolutionary biology? I doubt it.
How many replications necessary for a reasonable probability of a single beneficial mutation occurring?
How many is a few?
Is that what they are teaching you in your graduate studies in evolutionary biology? No wonder the medical field has such a problem with drug-resistant infections and failed cancer treatments.
The empirical examples I use happen to be DNA evolutionary adaptation in haploid populations because those are the replicators used in those experiments. If you want to apply this math to a diploid (or polyploid population for that matter), you have to multiply the number of replications by the ploidy of the population to correctly account for the number of random trials on each member replication but the probability distribution remains a binomial distribution. These are models of DNA evolution, not recombination which is a distinct evolutionary process. You can superimpose recombination on the DNA evolutionary process, and you are partially correct about recombination. Recombination is a combinatorial process but also includes a sampling process combined. You should try to derive the probability distribution for recombination but you have to start with the DNA evolutionary process to create the beneficial alleles for the recombination process. Let me show you how to set up the sample space for recombination.
Using T_aquaticus’s mutation rate, the DNA evolutionary process will create every possible point substitution in the genome in 180,000,000 genome replications (90,000,000 diploid replications). Let two of these mutations (A and B) create two beneficial alleles call them the A and B alleles such that if a descendent gets both alleles, that descendant will have an increase in fitness for a given environment. An empirical example of this would be one subset of a weed population has a beneficial mutation for one herbicide at one genetic locus (the A allele) and another subset of the population has a different beneficial allele for a different herbicide at a different genetic locus (the B allele). What’s the probability of a recombination event of one parent with the A allele mating with another parent with the B allele giving a descendent with both A and B alleles at there particular genetic loci.
To construct the sample space for this recombination process, you need to identify the different subsets in the population. For example, you have some number of females with the A allele, some number of males with the A allele, some number of females with the B allele, some number of males with the B allele, and some number of members of males and females in the population that have neither the A nor the B allele. You now sample from this population for the possible recombination outcomes. It should be clear to you that sampling an A female and a B female won’t work, likewise, an A male with a B female won’t work. I suggest you start with a slightly simpler model to get an upper limit on the probabilities by considering only three subsets, A allele subset, B allele subset, and C allele subset (those with neither A nor B alleles) and that sampling any of those members leads to a successful recombination event. If you can derive the correct probability distribution then you can try to derive the probability distribution for the more complex case. I’ll even start you here with the mathematics for the simpler case.
nA+nB+nC=n where nA is the number of members in the subset of the population with allele A, nB is the number of members in the subset of the population with allele B, nC is the number of members in the subset of the population that has neither allele A nor allele B, and n is the total population size. What is the probability distribution for this sampling process? Don’t forget to take into account the different permutations possible in the sampling process. One more hint, this is a probability distribution of two variables P(X,Y).
You’ve got me wrong, my heart goes out to the poor squirrels in your story. But the reason why it doesn’t impress me as an explanation for the population differences between humans and chimps is that we are talking about fecundity over thousands or hundreds of thousands of generations and the value for reproductive fitness I computed using Kimura’s equation is an average over these generations.
And what if I told you that COVID will have very little reproductive effect on the human population? There’s already plenty of evidence that COVID is a relatively mild infection in most children (before child-bearing age). COVID is much more lethal to the elderly who are beyond child bearing age and have already had their children. Perhaps there will be some kind of infectious agent that will be lethal to humans and drive the human population to or close to extinction. So far, small pox hasn’t done it, the black plague hasn’t done it, cholera hasn’t done it,… What I can tell you, if you want to make a population far more susceptible to disease, starve the population and you will see disease run rampant. I think that chimpanzees that don’t have the capability to farm are far more susceptible to disease than well fed humans. Despite human’s ability to farm, far more people die of starvation than from COVID in the world.
[quote=“Joe_Felsenstein, post:135, topic:13271, full:true”]
And I agree with that point. Neutral mutations are not the way to account for the genetic (and phenotypic) differences between humans and chimpanzees, you must do the accounting for adaptive mutations to explain the phenotypic differences between humans and chimpanzees and you only have about a billion replications to do that math.
@kleinman, it seems you made several points that we all agree with, but you seem to think we disagree with, which is making this debate dip into the absurd.
- You argue that there are important differences between chimpanzees and humans, both genetically and functionally.
We agree entirely, and never did disagree.
- You argue that it is exceedingly unlikely that all these important distances appeared simultaneously in a single individual before they were enriched for by natural selection.
We agree entirely, and never did disagree. We just don’t think they need to appear simultaneously in a single individual to be selected. Nor do we think these specific and precise mutations are the only ones that produce the same functional effect in the end.
- You argue that neutral evolution alone can’t account for all these functional differences.
We entirely agree, and never disagreed.
- You argue that the evidence of neutral evolution in human-chimps doesn’t explain how all the functional mutations arose.
We entirely agree, and never disagreed. Neutral evolution does, however, give strong evidence of common descent, without ruling out the idea of God inspiring particular mutations or sets of mutations.
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There’s another major problem. Selection isn’t random.
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OK, that seems like a reasonable guess.
It has nothing to do with how many beneficial mutations were fixed in the respective lineages, though, does it?
I don’t know that we have any evidence that we have been more fecund (ie having more offspring per individual) than chimps over that time scale,
I would say you were getting bogged down in the specifics of the analogy, and missing the point.
It is not uncommon for populations of organisms to go thru population crashes due to epidemics of infectious diseases. So say the trout in a particular lake all perish due to some lethal bacterial infection. Does that tell us they had fewer beneficial mutations than the squirrels in my first example over the time since their divergence from a common ancestor? I really don’t see how.
There are more humans than chimps on earth at this moment. OK, fine. Why is that? The answer would be obtained by understanding the particular history of each lineage in terms of ALL the factors that would have influenced their numbers. Genetics as a whole is only one factor among these, never mind the specific genetic parameter of number of beneficial mutations fixed.
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Of course we do: there are more of us, and having, on average, more offspring (that survive to breed themselves) is the only way for that to happen. Of course the big increase is fairly recent. But I would suppose that we started increasing in population size as soon as some of us got out of Africa.
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Then you don’t understand the meaning of the words used.
Several things wrong here:
First, the fixed divergence between humans and chimpanzees is about 40m, with ~35m SNV and ~5m indels. Assuming this is equally distributed between the two lineages (a little higher in chimpanzees, but more or less accurate), that is 20m mutations per lineage, not 60m. So 200k and 20 beneficial fixation events per lineage for 99% and 99.9999% respectively.
Second, you’ve ignored the existence of ancestral polymorphism at the time of divergence. That is, variants that were neutral when they occurred, but were beneficial under changed selective pressures. Which is why I said the number of mutations needed after divergence was 0. It was a hint, you missed it. This is easily enough to explain 20 fixed variants per lineage, and plausibly enough for 200k (although I doubt 1% of variants were adaptive).
Third, you gave numbers but didn’t show the probabilities of those numbers. This is a massive oversight since you’re claiming these numbers to be unlikely. With a beneficial rate of 1E-4, you have a ~95% chance of at least 60 beneficial mutation at 730k replications, so the low end of the range looks easily manageable. I’ll leave it to you to calculate the 95% mark for 600k, and the 95% estimate for mutations with 1b replications.
Thank you for demonstrating my point about you not understanding the theory or the models. It’s like I said you were using Newtonian mechanics to model electrons, and your response was ‘Explain orbital mechanics, then!’
Like I said, you’re not even wrong. You’re just horribly confused.
I feel like we’ve already done this…
That’s for generations in a single lineage not replications in an entire population for an arbitrary number of generations, but same difference.
200 to 20k, depending on where you put the actual rate of beneficial mutations. This is a separate question from the number of fixed adaptive variants in each lineage because of standing variation at the time of divergence.
No, they definitely aren’t teaching your nonsensical math, because it has no relation to actual population genetics as it pertains to the divergence between humans and chimps. Unless you mean the ‘0’, in which case yes they do cover actual population genetics in my program. If the math confuses you, as it clearly does, I’m sure we can help.
Also, this isn’t a rebuttal, it’s a nothing. I’m not shocked that this is the best you can do. But I do hope that, as you read it back, you feel whatever facsimile of embarrassment you’re capable of to have said it in the first place.
Try harder.
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Here we have it - the point where the Texas Sharpshooter draws the bullseye around the bullet hole. My emphasis added. It’s not the probability that two allele will come together to create a particular new trait. It’s the probability that no combination of new alleles will come together to allow a beneficial trait. [edit: sorry, the complement of that, was in a hurry. it should read …]
It’s the probability that at least one combination of new alleles will come together to allow a beneficial trait.*
AND my comment I thought was in this thread is in another, which would explain why you are missing my point here, and why nobody cares in the other thread. 
I should start a new thread for this, but don’t have time tonight. The short version is that combinatorial growth in the number of new combinations will quickly outpace simple A+B recombination. .
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