Does neutral evolution explain the genetic differences between humans and chimpanzees

I can’t imagine what I have written that would suggest to you I do not consider that very likely.

Mutations, probably many if not most of which are beneficial.

Just statistically, chimps probably had about the same number of beneficial mutations over the same period of time. They just produced different benefits.

That did not address what I asked. It couldn’t, since he is speaking about the dynamics of a single population, not a comparison between two different populations of organisms.

Tell me this: Why do you think the number of of a given species of bacteria in your own body is vastly greater than the number of humans walking the earth? Is it only because they have more beneficial mutation? Or are there other factors that are more important?

Just off the top of my head, I would think the fact Kishony is introducing a strong selective pressure in the form of an antibiotic drug is a factor. Lenski’s bugs are like a herd of domestic cattle idly grazing on a farm. Kishony’s are more like wild deer who are being preyed upon by a pack of wolves who are relentlessly weeding out the slower runners. You can’t expect the evolutionary dynamics to be the same in both situations.

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Good. I’m glad that is settled. But something still isn’t right …

If the frequency of all the alleles in the population is 1, then the probability of the second variant combining with the first is 1. No waiting! However, the MRCA population certainly will not be clones. I’ll think on that.

This is a more realistic question, where not all allele frequencies are 1. It also means I may have vastly underestimated the numbers of potential combinations, but I think I made that point sufficiently. With this large number of combinations, most individuals in the population should represent a unique combination. Beneficial trait should emerge at a rate roughly proportional to the population size.

BUT now you are asking how fast allele mixing occurs? Didn’t Kimura answer that one already? In any case I think @T_aquaticus already covered this question, with Punnett squares, and this …

I started my clock at fixation because it doesn’t really matter which random neutral allele arrives in the population, evolution works with the ones it gets. I could loosen the fixation assumption to Hardy-Weinberg equilibrium, allowing some allele proportions to be less than 1, and the effect should be the same. Mixing will be a little slower, but there will be more to mix. What population parameters are you assuming that would prevent >90% mixing from occurring in … let’s say 50 generations of random mating? Pick other numbers if you like, those are arbitrary.

Oh no doubt. I had an example worked out for very small probabilities, but it was pedantic. My claim is that combinatorial mixing beats “very specific circumstances”.

And now, trivia! :slight_smile:

My old boss was an editor for Statistics in Medicine; he was a man named Klein! You missed him by a few years.

This paper is not exactly taking the world of evolution by storm. Six citations and 5 of those are self. I do not doubt this is useful in the world of antibiotic resistance, but people aren’t bacterial.

Wait. He finally got a citation? What was it?

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Hey, I notice that the paper was accepted the same day it was received. What kind of review process would even have been possible? What kind of journal is that?

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I actually do doubt that it is useful, as supported by the fact that only one other author (on a paper with no citations) cites it for that purpose. Of his self citations, only two are themselves cited. Of these, one (2015) is cited twice, first by a paper that evidently didn’t read it as they cite him for something not discussed, and then by a dissertation in a throwaway line noting him as an outlier. The other (2016) is cited 4 times, 3 of which are by little-known author A Kleinman. The remaining citation is a cancer paper which does not cite him for his model, but for his commentary on the lack of a particular type of model.

His sum impact on the science of evolutionary biology is exactly zero. No one even thinks he’s worth responding to. Even Behe is more respected.

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I’m, not sure about that! The initial inoculation certainly has more than 1 individual…

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What biologist understands the basics? Even the Lenski team of researchers that have performed an evolutionary experiment for over 30 years have yet to give the correct mathematical explanation between carrying capacity, mutation rate, population size, and natural selection for that experiment. They understand that competition slows adaptation, they see this quite clearly with their measurements. They just don’t know why. The reason they don’t know why is that they don’t know how to apply the laws of physics to their experiment. It takes energy to replicate and replication is the random trial for adaptation. If different variants are competing for the same fixed amount of energy, it will limit the number of replications for each of the different variants.

An evolutionary trajectory is simply a sequence of genetic transformations. Each of these genetic transformations (steps on an evolutionary trajectory) can do one of three possible things. It can cause that new variant to increased reproductive fitness to the selection conditions of the environment, the new variant can have no change in reproductive fitness to the selection conditions of the environment, or the new variant can have a decreased reproductive fitness to the selection conditions of the environment. Not every mutation gives increased fitness to the new variant which is well demonstrated in the Kishony and Lenski experiments. That’s why the previous variant has to replicate 1/(mutation rate) times to give that probability that the particular beneficial mutation occurs at least one time.

??? You really need to think about how you calculated 90,000,000 replications for every possible base substitution for the mutation rate you specified. Then think about how many replications of each of those 90,000,000 members it will take to get the next beneficial mutation. That’s the fundamental math of DNA evolution. You think that if you superimpose sexual reproduction on the DNA evolutionary process that it significantly changes that math but you forget that it is DNA evolution that creates those new alleles that can recombine.

Sure, I have. But we are talking about more than Mendelian genetics. We are talking about populations that have a wide variety of different alleles at different genetic loci with different frequencies for the different alleles. What is the probability of two members with two different particular beneficial alleles sexually reproducing giving an offspring with both beneficial alleles? Mendelian genetics and Punnett squares do not give that answer. If you want to have a chance to understand this, put this into the context of a real situation. Consider the use of combination herbicides where some members of the weed population have a beneficial allele (call it A) for one herbicide and other members of the population have a beneficial allele for a second herbicide (call it B). The rest of the weed population has neither beneficial allele. What is the probability that an A member will sexually reproduce with a B member to give both beneficial alleles?

But that recombination process does not create new alleles. Creating new alleles requires DNA evolution. And you should know by now that a very large number of alleles are created by the DNA evolutionary process. How do you get any of the possible beneficial alleles among the millions of neutral and detrimental alleles to recombine in a single lineage?

The problem is that there are a huge number of potential mates out there. There is a reason why in many societies, the parents choose the mate for the child. The parents have a better chance of seeing beyond the sexual attraction the love-birds are experiencing.

The correct answer is that sexual reproduction does not create new alleles. Sexual reproduction can only change the phenotypic expression of existing alleles.

That’s the math, you did it yourself using a mutation rate you specified.

Try noticing this section:

Why do you think there was no difference in change in fitness in the standard medium (low selection pressure environment) while in the harsh environment recombination does give an improvement in fitness? Hint: The Punnett square doesn’t give the answer.

That can happen but only under very specific mathematical conditions and you haven’t figured out yet what those conditions are (yet).

Because there is absolutely no evidence that there are 100 million possible beneficial mutations in the human genome. In fact, everyone posting on this forum thinks that the vast majority of mutations in the human genome are neutral, except you now.

Perhaps it’s your sad story about squirrels dying in a landslide?

There are two ways to get all those beneficial mutations into a single lineage, DNA evolution and recombination. DNA evolution requires about 1/(mutation rate) replications for each beneficial mutation. Using T_aquaticus’s mutation rate That gives about 90,000,000 replications for each beneficial mutation or at best about 10 or 11 beneficial mutations in the first billion human replication. That’s pretty much a mathematical no-go. So you have the other mechanism of genetic transformation, sexual reproduction. Do you want to explain how one could breed all those beneficial mutations into a single lineage?

Kishony gets the same results whether he uses Ciprofloxacin or trimethoprim. Either selection pressure requires a billion replications for each evolutionary step.

And the reason why bacteria have a vastly greater population than humans is the carrying capacity of the environment. Absolute reproductive fitness is all about the energy available in the environment necessary for reproduction. It takes a lot more energy for humans to reproduce than for bacteria. We have more than enough energy in our gut to carry huge populations of bacteria. When a population reaches a size where there is no more energy available for reproduction, the population stops growing.

Not quite, most of the bacterial growth in the Lenski experiment are for lineages that ultimately go extinct in the competition and fixation process. Of the ~1.5 trillion replications in those 20,000 generations, only about 10-20 billion of those replications are for the lineage that accumulates the 10-20 beneficial mutations. Haldane recognized this in his “Cost of Natural Selection Paper”. Haldane’s estimate of 300 generations/fixation was also an accurate prediction of what happens in the Lenski experiment where they measure a fixation rate in a range of about 200 to 1000 generations.

This competition and fixation process is what slows the adaptation process. Those less fit variants are using the energy resources that the more fit variant could use to replicate and do their random trials for the next beneficial mutation. If Lenski were to run his experiment with 100ml of broth instead of 10ml (increasing the carrying capacity of his environment), the evolutionary process would occur more rapidly. Competition slows DNA evolution, the carrying capacity of the Kishony experiment is much larger than that of the Lenski experiment reducing competition in the Kishony experiment. Each of the more fit variants has a new unpopulated niche where their colonies can rapidly grow to a billion members (about 30 doublings of the new more fit variant), where the next beneficial mutation has a high probability of occurring in a colony of that size. It takes about 5 billion replications for a lineage in the Kishony experiment to accumulate their 5 beneficial mutations. The carrying capacity of the Kishony experiment allows for that kind of population growth.

By the way, in the 100 trillion or so bacteria in your gut, don’t be surprised if there are single drug-resistant or multi-drug resistant variants already in that population even if these bacteria have never been exposed to antibiotics. Even a trillion replications is sufficient to create variants that have some degree of resistance to two drugs. But don’t worry, 100 trillion replications is not enough to give variants with some degree of resistance to 3 drugs. That’s why 3 drug therapy gives a durable treatment of HIV. For a mutation rate of 1e-5, it will take about 1e14 replications to get a variant with 3 beneficial mutations.

That’s right, fixation isn’t necessary for DNA evolutionary adaptation to occur. But in some instances, fixation will occur in a DNA evolutionary process such as the Lenski experiment where the carrying capacity of the environment limits population size forcing competition and fixation in order for the more fit variant to get sufficient replications for the next beneficial mutation.

You are not thinking about this clearly. In the first 200 replications of the bacteria, you will have only 1 member with a single mutation, the other 199 members will be exact clones. Recombination for exact clones will not change the genotype.

How can you get more realistic than a real evolutionary adaptation experiment? I’m trying to get you to understand how a Markov chain random walk changes the frequencies of alleles from an initial founder. I understand this is a haploid example but you need to understand that as populations grow, mutations are accumulated in different lineages. But by far, the original alleles remain at the highest frequency by far, very close to 1. The mutant variants are at a very low frequency in the population. The magnitude of the frequencies of the mutant variants is of the order magnitude of the mutation rate. The vast majority of the recombination events will be with alleles from the original founder. And the probability of two mutant variants recombining will be extremely low and that’s without a guarantee that these are variants with beneficial alleles recombining.

This is not Mendelian genetics. This is a trinomial distribution problem where you are randomly selecting two variants from a population to calculate the probability of an A+B recombination event. What I’m trying to demonstrate is that the vast majority of the population are C variants that have neither the A or B alleles. Most of the recombination events will be C+C, you will get a few A+C, and B+C recombination events and very few if any A+B recombination events. Only if A and B variants are at high frequency in the population will you have a reasonable probability of an A+B recombination event. The yeast example demonstrates this. The harsh environment killed off the C variants, this increased the frequencies of the A and B variants which in turn raised the probability of an A+B recombination outcome. The standard broth didn’t kill off the C variants so the probability of an A+B recombination event was low and recombination didn’t give improved fitness.

This is nowhere near an equilibrium process. As the population grows, new alleles are being generated by mutation but by far, the alleles with the highest frequencies for the different genetic loci will be those of the founder’s alleles. The frequencies for those alleles will be very close to 1 and the frequency of the mutant alleles will be very low. The only thing that will significantly change this is if some selection condition bottlenecks the population and kills off the variants with the C alleles as the harsh environment did to the yeast population in that experiment.

Only in your dreams, I’ve given you an experimental example that demonstrates the math that I’ve presented. The math I’ve presented also explains why recombination doesn’t cause HIV 3 drug therapy to fail. Why don’t you present an experiment or some empirical evidence that demonstrates your math?

I’m sure he would have liked my papers, the other editors and peer-reviewer did. They even liked my paper on recombination.
Random recombination and evolution of drug resistance

The field of biology is like the Titanic, very hard to turn and they haven’t figured out yet that they have hit a mathematical and empirical iceberg. And look how mainline biology treats those who don’t buy into their dogma. And what makes you think that DNA evolution works differently for bacteria and humans? Oh, that’s right, humans are diploid so you have to multiply the number of genome replications by the ploidy and sexual recombination. Read the paper above and learn how to apply the trinomial distribution to recombination in a population.

Of course, he did, but you should be familiar with the term CFU, if not, it means “colony-forming unit”. Do you think the mathematics for one CFU works differently for another CFU? If so, explain the difference and show your math.

And John Harshman seems to be claiming that you believe that E. coli and humans arose from a common lineage and you have said nothing to refute that. Is John Harshman speaking for you? It is quite possible he is because like you, he believes that doubling population size doubles the probability of a beneficial mutation occurring. This, of course, is a fundamental misunderstanding and error of the mathematics of adaptive evolution.

This is the good old Bait and Switch on top of Texas Sharpshooter. We discuss the probabilities for neutral alleles and you swap in the probability for a beneficial combination. I suppose it is possible for a single allele to single handedly allow a beneficial trait, but highly unlikely*. A single allele may generate many (combinatorially MANY) traits, most neutral but some negative and positive. It is the balance of those combined traits which determines if a trait is beneficial or harmful. A new allele isn’t “born” beneficial*, it becomes beneficial when new combinations are discovered.

'* (a/except) the vanishingly rare case.

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For Jiminy Crickets, can we get back to diploids and sexual mixing already?

And in diploids, lineages mix.

And I am starting my clock at fixation …

[Once the frequency of the allele is at 100%, i.e. being the only gene variant present in any member, it is said to be “fixed” in the population](Fixation (population genetics) - Wikipedia).[1]

… but as already noted beneficial combination may have already occured prior to fixation (or equilibrium). Can we now end this silly game of Bait & Switch?

Bait & Switch.

But is it a Bait & Switch. Equilibrium just means we don’t nee to wait for 100% fixation.

Are you actually trying to make a case that, because beneficial traits are rare, it is impossible for new alleles to enter the population? When a new allele enters the population at any frequency new traits are immediately possible. MORE new traits are possible as the allele spread through the population by sexual mixing.

The math you present solves entirely the wrong problem.

People has been saying that about evolution for 150 years. Would you care to make a small wager? If not, please inform me when your Nobel Prize is awarded.

I’m not a big gambler - my standard offer is a $20 gift certificate for a claim that can be clearly arbitrated and claimed within the next two years.

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Clearly more than one thing isn’t right! :wink:

“That’s why the variant has to replicate 1/mutation to exist in the first place”

What are you even trying to say, and why do you refuse to use normal language to say it?

Fewer, obviously, since the first calculation wasn’t for the first beneficial mutation!

See that ‘particular’? That’s why your math is wrong.

When one lineage loves another lineage…
I mean, we don’t actually need to explain this to you, right?

So you’re saying that the beneficial qualities of individuals is sometimes apparent and influential in mating success? Huh, I wonder if that’s relevant.

You just got a simple division problem wrong by 6 orders of magnitude, and you’ve been in here complaining about everyone else’s math?

100m beneficial would still leave ~99% of the possible mutations. I don’t know how you define ‘vast majority’, but even with ~9% harmful you’ve still got 90% (nearly) neutral.

You should be familiar with the term CFU, because between the time the single unit formed the colony, and the time the colony was picked to use as an inoculant, the thing replicated a bunch! So if the plate gets inoculated with 1000 cells from that colony, then there are (using your math) already 5 variants present.

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Neither comment even remotely addresses the criticisms I made. I’ll let the issue drop. The point has been made.

Exactly. There are factors other than the number of beneficial mutations occurring in a lineage that can explain population variations between lineages. I’m glad we could finally settle that rather trivially obvious point.

Yes. The larger the population, the more mutations that will occur, and the greater the likelihood that a given mutation will occur. Thanks for reminding us of yet another trivially obvious point.

It may be less trivial and obvious, but not by much, that increased selection pressures increase the likelihood of a beneficial mutation being fixed. This is illustrated in my analogy to a herd of deer being preyed upon by wolves who will exert a selective pressure on the slower running deer. And Kishnoy’s study involves selective pressures that do not exist in Lenski’s.

//By the way, in the 100 trillion or so bacteria in your gut, don’t be surprised if there are single drug-resistant or multi-drug resistant variants already in that population even if these bacteria have never been exposed to antibiotics.//

I am well aware, but thanks. That’s one of the reasons I don’t go running off to the doctor for antibiotics every time I have the sniffles. I want the deer in my body to be slowpokes for when I have to set the wolves on them.

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I missed that. Statist Med is a statistics journal (of course), not a biology or genetics journal. I witness thorough statistical review in the past, but can’t comment other review (if any).

Completely Fouled Up?

Yes they do.

The probability of getting an individual with both alleles from two heterozygous organisms each of which has one of the alleles is 1/4.

The probability of those specific organisms being the parents of a specific individual in the next generation is 1/(nn) where n is the population size.

The overall probability that a single reproductive event within a population containing only one heterozygous organism of each new allele is will produce an offspring with both alleles is 1/4nn.

This is Mendelian genetics.

Since you haven’t specified any assortive mating or zygosity, 1-(1-2ab)^n, where a and b are the proportions of the two beneficial alleles in a population n.

Again, basic Mendelian genetics and basic probability.

Which is, of course, Mendelian genetics (plus a bit of high-school probability).

Yes - if the first generation has allele frequencies a,b and c, the second generation (unless there’s assortive mating) will have allele frequencies aa, 2ab, bb, 2bc, cc and 2ac. If a and b are small, 2ab will be correspondingly smaller (but not zero unless 2ab < 1/n).

This is the Hardy-Weinberg equation as derived from Punnett squares and Mendelian genetics, so your repeated assertion that this isn’t related to Mendelian genetics or Punnett squares is bizarre.

‘High’ is vague. Presumably it’s somewhere between ‘vast’ and ‘small’.

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Dan, the mathematics for recombination of neutral alleles is the same as the mathematics of recombination for beneficial alleles. And I’ve shown you how to do that math using a trinomial distribution using 3 different alleles, A and B beneficial alleles, and C neutral alleles. If you want to say there are many different types of C alleles, you can break down the C subset of neutral alleles into C1, C2, C3,… neutral variants subsets. Why don’t you try to do the math for that case? And, of course, I know that the environment determines whether an allele is beneficial, neutral, or detrimental. Likewise, you can breakdown the A and B alleles into subsets and compute these probabilities as well. What you will find is that those probabilites of a recombination event will be proportional to the product of the frequencies of those variants doing that recombination.

There is a problem-solving technique that engineers are taught and which I learned in my engineering training that you should try to understand because this principle is very useful for understanding how evolution works. That problem-solving technique is called superposition. The way the superposition problem-solving technique works is to break down a complex empirical problem into simpler, easier solve components and then superimpose (recombine) the simpler components to get your final solution. So, for example, many years ago, before I entered my medical studies, I did engineering work on the Space Shuttle. One of my tasks was to estimate the heating patterns in the shuttle structure based on reentry heating. The reason why this was important was not just that over-heating the structure could weaken the structure but that temperature changes cause changes in length in the structural components inducing stress in the structure. Different re-entry trajectories give different heating patterns, a steep, rapid re-entry trajectory gives higher heating loads for shorter periods of time and shallower and slower re-entry trajectories give lower heating loads for longer periods of time. Each different trajectory caused different structural loads. The data I generated on these heating patterns were used by the structural engineers to calculate the stress in the structure. I had my equations based on the laws of thermodynamics and the structural engineers had their equations based on the laws of structural mechanics.

This is why I continually try to get the posters on this thread to think in those terms so that they can get a handle on the overall mathematics of evolution. DNA evolution, evolutionary competition, and recombination are distinct physical processes with distinct mathematical behavior. The Kishony experiment is primarily a DNA evolution process, the Lenski experiment is a DNA evolutionary process superimposed on an evolutionary competitive environment. This paper shows how I use superposition to model the Lenski experiment:
Fixation and Adaptation in the Lenski E. coli Long Term Evolution Experiment

You should make an attempt to understand what happens if you superimpose recombination on a DNA evolutionary process. But you will need to understand how recombination works first. And the simplest model for random recombination is formulated using a trinomial distribution.

No, because you are not ready yet. First, understand the mathematics of how haploids generate new alleles. When you demonstrate that you understand that, I’ll go on and discuss how diploids create new alleles and the sexual mixing of those alleles.

And you still haven’t demonstrated that you understand how lineages mix. That mixing process depends on the frequencies of the different alleles in the gene pool. And to understand how to compute the frequencies of the different alleles in the gene pool, you have to understand how DNA evolution works to create new alleles.

Stop speculating and tell us how you compute the frequencies of the different alleles at each of the genetic loci in a genome starting with a single male and female founders. As the founders mate and have their offspring, tell us how the frequencies of every allele change from the original frequencies at the start of this population growth and tell us how many new alleles appear as mutations accumulate in the genomes. When you try to do this, perhaps you will understand why I tell you to understand how this works in a haploid population first without recombination.

I am not Dan! I’m trying to get you to understand that a new lineage, consists of a small number of members (the limiting number for a haploid clonal replicator is 1 and for a diploid sexually reproducing replicator is 2). The initial frequencies for all the possible alleles at all the genetic loci for the haploid founder are 1. The maximum frequencies for the particular alleles in the diploid replicator are 1 if both members are homozygous at the given locus and have identical alleles in both members. The minimum initial frequency for any genetic locus is 0.25 if both members are heterozygous at the given locus and none of the alleles are identical. As the population grows, the allele frequencies will slowly change but the appearance of new alleles will be rare occurrences, occurring at the frequency of the mutation rate. Do the math!

Dan, just because you can’t or won’t do the math, don’t accuse me of bait and switch. The probability of any particular recombination event occurring depends on the frequencies of the particular alleles in the population. You need to do two things to understand this math. You need to figure out how to compute the frequencies of the different alleles, and you need to figure out how to do the mathematics of recombination in a population with different variants. It is time for you to fish or cut bait.

No, I’m trying to get you to understand how DNA evolution creates new alleles and then for you to understand how to compute the frequencies of all the alleles in a population because that gives you the statistical information for computing the probability of any particular recombination event occurring. Once you know the frequencies of each of the alleles and the probability distribution, you can compute the probability of any recombination event occurring, beneficial, neutral, or detrimental.

What do you think that yeast experiment is demonstrating, the fermemtation of alcohol? That experiment is demonstrating when recombination can give an improvement in fitness. And it does that by using a harsh environment to select out the weak variants in the population which then increased the frequency of the more fit alleles and voila, you get a recombination event that gives improved fitness.

Edward Tatum explained the fundamentals of DNA evolution in his 1958 Nobel Laurate Lecture. All I have done is put some mathematical muscle on the bones that he described.

Las Vegas and the other gambling houses is not gambling. You play there long enough, you will leave everything you own there. It’s not very smart to gamble when the games are set up such that the odds are always against you. There was a time you could learn to count cards while playing blackjack and shift the odds in your favor but the people that run those houses stopped that fairly quickly.

So what do you want to wager? Do you want to wager that biologists suddenly understand the physics and mathematics of evolution? That’s not likely, they are way too entrenched in their mathematically irrational dogma. I think it’s going to take a long time for the field of biology to correct their errors in the understanding of evolution. I think the correction will start with people trying to deal with the problems of drug-resistance, herbicide-resistance, pesticide resistance, and targeted cancer treatment failures. And last I heard, weeds and insects reproduce sexually.

I know now, sadly squirrels can die in landslides. And only chimps have accidents, humans never do. You do need to work a bit more and learn something about the 1st law of thermodynamics. It’s the quantity of food that limits population size. Humans produce far more food than chimps. That’s the reason for that 7 billion to 300,000 population differential. Some people think that evolution explains this. These are the same people that think the E. coli and humans evolved from a common lineage but can’t explain and want to ignore two very important evolutionary experiments, the Kishony and Lenski evolutionary experiments. What do psychiatrists call it when someone loses contact with reality?

Sure, that is what evolutionary competition is all about, it’s about increasing the frequency of the most fit variant in a population. And if the intensity of selection increases, it will kill off the less fit variants more rapidly. But that competition process slows evolutionary adaptation. That should be obvious to you now.

You should ask yourself why the use of single drug antimicrobial therapy doesn’t immediately select for drug-resistant infections and under which circumstances it will do that.

How about 100% of the alleles in the descendants will be from the founders of a lineage. Only when DNA evolution introduces new alleles by mutation will that math change. The frequency of that new allele will be 1/(population size). You do that math for the creation of new alleles using Markov chain random walk DNA evolution. Try doing the math yourself and find out why. Hint: You don’t do the math with Punnett squares or the Hardy-Weinberg equation. Try advancing your science beyond the Hardy-Weinberg model.

Yes. Now, why is that?

You think it is because humans have experienced more beneficial mutations in our genome than have chimps. Or perhaps you just believe this is what must have happened if evolution is true.

Everyone else here seems to reject this, and accept that the difference can be accounted for by the specific nature of the mutations, rather than their raw number. In our case, they gave us a big brain that allowed us to develop agriculture. In the case of chimps, they caused other adaptations but not that one.

Not really seeing the problem, sorry.

Well, maybe you could explain the Kishony and Lenski how their experiments have shown that we are not related to bacteria. Or explain it to us, at least. So far, all you have shown is you do not understand those experiments, nor evolution as a whole, very well.

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Bait & Switch. Traits are beneficial, not the alleles themselves. Benefit is determined by the traits they enable.

Here is a bit of wisdom from my own profession: It’s hard to get the right answer by asking the wrong question.

I haven’t answered because it’s a Red Herring. You are arguing that a beneficial allele must first appear creating a new trait, and then mix to the greater population. This is possible but (as you say) unlikely. FAR more likely is that a new neutral allele appears, and a beneficial trait arises as that allele mixes to the population. Your implicit assumption is that neutral evolution does not happen, which is wrong. I don’t need mathematics to know that you are asking the wrong question.

I am a statistician, if you hadn’t noticed. :wink:

I was referring to this statement …

The field of biology is like the Titanic, very hard to turn and they haven’t figured out yet that they have hit a mathematical and empirical iceberg.

As simple and verifiable wager is that one of your relevant articles is noticed and cited in publications or prominent journals marking a turn in the “mathematically irrational dogma” within a few years. We could hash out specifics for how many citations, which sort of journals, and arbitration date, if you like. The real point is not to take your money, but to make you commit to a well defined claim. Do you REALLY think the theory of evolution is on the verge of being overturned? Are you so certain that you would take the risk more than words?

BUT don’t get me wrong - I commend you for getting your ideas published for consideration by others. This is the proper way to question science. I just don’t think this is the forerunner for the downfall of evolution. It’s more likely your papers will simply fall into the dust pile of forgotten hypotheses. No shame in that; this is the fate of most hypotheses.

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Shouldn’t he publish in journals that deal with evolution if he wants that to happen? Of course he wouldn’t get past the reviewers for any on-topic journal.

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If there are 100 million possible beneficial substitution mutations then we would get 100 million beneficial mutations after those 90 million replications, or around there. If there are 50,000 beneficial substitution mutations possible then we will get 50,000 beneficial mutations after 90 million replications.

Do you agree or disagree?

Having two beneficial alleles does not require a step-wise process because the two mutations can happen in two independent events and then be combined in a single individual through sexual reproduction.

Beneficial mutations increase in number over time.

The condition is the parents have the mutations.

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