I was taking “fecundity” literally, interpreting it as having more offspring, period, regardless of how many end up successfully reproducing.
It should be obvious by now that there is another, entirely different, yet sufficient reason why Kleinman is missing your point.
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Why? That definition is irrelevant to anything we’ve been talking about.
Thank you so much for mathsplaining to me what I had just explained to you. At least you’ve confirmed you now understand this, even if you refuse to admit you originally got it wrong.
Then anything else you write is suspect because you may know it’s wrong but be unwilling to retract it.
I see it. A small difference in reproductive fitness led to a vast difference in population size.
But you said there was a vast difference in reproductive fitness. You were wrong. You have repeatedly refuse to admit it.
Have a nice life.
P.S. This is wrong too:
Humans have. There are 14 billion extant copies of most human genes.
This is wrong too:
The probability of a particular recombination event occurring are obviously also dependent on a particular size. Feel free to calculate the probabilities for (a) a population of 2 and (b) a population of 2,000,000,000 with the same frequency of variants.
This is also wrong, and will continue to be wrong until you cease using the Texas sharpshooter fallacy:
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That’s not what you argue in the “Capturing Christianity” video you made. You made the dogmatic argument that “distance = rate x time” explains the genetic differences between humans and chimpanzees to laymen that don’t know how to question your claim. You don’t need to explain the points you make above to me, you need to explain these points to the layman that don’t understand the subtleties of this discussion. Neutral mutations aren’t what determine common descent, the adaptive mutations make that determination. Based on the mathematics of DNA evolution and adaptation, there is no way that humans and chimpanzees arose from a common lineage. You simply do not have enough replications (about a billion in the human lineage) to account for these adaptive mutations. As far as this idea of common descent goes, do believe as evograd believes that humans and E. coli evolved from a common ancestor?
In addition, as you are a medical school professor, you have a responsibility to teach medical school students the correct mathematics of DNA evolutionary adaptation because that explains how drug resistance evolves and why cancer treatments fail. With the correct understanding of how drug resistance evolves and why cancer treatment fails, better strategies and treatment protocols can be developed to deal with these kinds of medical problems.
So you think that Faizal_Ali’s sad story about squirrels dying in a landslide is an example of non-random selection? How about when Lenski removes 99% of the day’s bacterial growth leaving only 1% to start the next day’s growth is a form of non-random selection in that daily bottlenecking of his populations? Selection can be non-random when the selection process kills or impairs the reproduction of specific variants in the population due to the reproductive fitness of those variants to those selection conditions. But selection conditions can also be random such as with accidents or in examples such as Lenski bottlenecking his population. The selection pressure which lowers the reproductive fitness of chimpanzees is non-random, it is starvation, a selection pressure that humans have adapted to by farming, something which requires intellect which no chimpanzee has.
Fixation is neither necessary nor sufficient for evolutionary adaptation to occur. For a lineage to have a reasonable probability of taking a step on an evolutionary trajectory does not require fixation, it requires amplification (increase in number) of that variant to improve the probability of the next beneficial mutation occurring on that variant (lineage). I recommend that you carefully study the Kishony experiment that demonstrates this fact. None of the adaptive mutations for any of the lineages in that experiment are fixed in the population. If fixation is required in a DNA evolutionary process (such as the Lenski experiment that has a limited carrying capacity) it slows the DNA evolutionary adaptive process. This is a very common error that biologists make, they confuse evolutionary competition with DNA evolutionary adaptation.
It’s the number of offspring that survive to have their own offspring and whether the number of offspring exceeds the number of the members from the previous generation that is the measure of reproductive fitness. If you don’t find 7 billion humans vs 300,000 chimps as evidence of a difference in reproductive fitness, it is because it doesn’t fit your biases and beliefs. There is no environment where the hunter-gathering existence chimps live will give higher reproductive fitness than the human’s ability to do farming in that same environment and what that will do for human reproductive fitness. You know you have a problem with your argument when John Harshman agrees with something I’ve said.
I get your analogy, you think humans are lucky and chimps are unlucky and it has nothing to do with the human ability to farm. If you want to understand DNA evolution, study the Kishony and Lenski experiments where we know the particular history of each of the lineages in terms of all the factors that influence their numbers.
So, why don’t you use your quantum mechanical understanding of evolution and explain the Kishony and Lenski experiments? You won’t.
That’s right and the computation doesn’t use Newtonian mechanics. T_aquaticus came up with a value of 90,000,000 replications for the first beneficial mutation in an evolutionary trajectory. Do you want to try to come up with the number of replications necessary for the second beneficial mutation in that evolutionary trajectory? Hint: You don’t use Newtonian mechanics and you don’t use distance = rate x time.
It depends on the number of replications of the particular variant every generation, not just generations. In the Kishony experiment, it only takes only about 30 doublings (generations) of the founder bacterium of the colony to get the billion replications necessary for the next beneficial mutation to occur. I know this is hard for you to understand but the replication is the random trial for the next beneficial mutation and if the particular variant is able to do about 1/(mutation rate) replications, you will have on average one beneficial mutation for that variant on that particular evolutionary trajectory,
The Lenski experiment has taken over 5e12 replications to get about 100 beneficial mutations. And you don’t understand the difference between fixation and adaptation.
What ever they are teaching you, it doesn’t give you the capability of explaining the simplest evolutionary experiments. In fact, you are conflating evolutionary competition with evolutionary adaptation. What do your teachers teach you about evolutionary competition? Does evolutionary competition slow down or speed up evolutionary adaptation?
Dan, you are the one not getting it. Not every recombination event gives improved fitness. In the DNA evolutionary process, when the number of replications equals about 3/(mutation rate), a point substitution has occurred in every site of the genome in some member of the population. What that means is that if a gene is 500 bases long, there will be the original allele for that gene plus 500 mutant variant alleles for that gene and that goes for every other gene in that genome. The environment is testing every one of these alleles and the measure of that test is the absolute fitness to reproduce. If in all these possible genes and alleles for each of these genes, there are more fit variants, it is possible that sexual reproduction can take beneficial alleles from different genetic loci in different members of a population and recombine them in a descendent. But detrimental and less fit alleles can also be recombined and it is also possible that a beneficial allele will not be passed along to a descendent and that beneficial allele is lost from the gene pool. The probabilities of these recombination events occurring depending on the frequencies of the particular alleles. I posted an empirical experimental example where yeast was studied.
What the harsh environment is doing is selecting out the less fit varients increasing the frequency of the more fit varients which improves the probability that a recombination event will occur with beneficial alleles. This is the explanation for Darwin’s finches. The environment selects for specific beak types, those variants mate and the probability of a recombination event that selects for particular beneficial alleles increases. But those alleles first have to be created by the DNA evolutionary process. And since you continue having difficulty doing the math, I’ll tell what the correct distribution function is for recombination. If you are not familiar with the trinomial distribution, look it up and learn how recombination works.
If you think I’m ignoring relevant data, identify the data. And speculation is not data. Remember, I started this discussion because Dr. Swamidass made a video aimed at laymen claiming the common descent of humans and chimpanzees based on neutral evolution. The selective use of data that way is the classic Texas Sharpshooter fallacy. And that claim only appears to work with a claim that chimps and humans diverged at a particular number of generations ago. The problem with this claim is that it leaves virtually no time for any significant adaptation. Don’t invoke neutral evolution and ignore 7 billion vs 300,000. If you think that recombination somehow addresses this problem, present your mathematical and empirical data which shows how all the beneficial alleles in a population somehow end up in a single human lineage and it didn’t happen in the chimpanzee lineage. You won’t.
Why don’t you do the computation yourself and show us the equation you want to use? But first you should tell us the frequency of the different alleles in the population, we wouldn’t want you to leave out any relevant data.
Actually it is the argument I made in that CC video! 
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No. But in the context in which we are discussing, it is primarily fixed mutations we are talking about. Those will mostly account for the differences between humans and chimps as distinct species.
I don’t believer that is actually a requirement, but I’ll let the experts weigh in on that. I’ve already made myself look like a doofus enough in this discussion.
Yes, that has been clarified for me. Sorry for my misunderstanding.
Well, I have already provided several realistic examples in which drastic population differences can arise for reasons other than “reproductive fitness” in the sense you are using. Which, as far as I can tell, you are defining as the gross number of beneficial mutations that have risen (not even fixed) a population over the course of time. Or, perhaps more accurately, you are asserting that reproductive fitness cannot increase without this parameter also increasing.
You are quite wrong about that. But good luck to anyone who want to persuade you of that.
Nope. Rather, I am saying that our ability to farm does not necessarily entail that we have had more beneficial mutations than chimps in the time since we diverged from a common ancestor.
Can you cite where they have shown a correlation between population size and gross number of beneficial mutation?
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It’s not about assumptions. It’s about understanding the argument. It’s a silly argument, but you make it sillier by misunderstanding that little bit.
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No, you haven’t. You require enough generations to mutate the entire genome before you get a beneficial mutation. That is wrong. That assumes that there is only one mutation out of all of them that will increase fitness.
FALSE!!!
You still haven’t learned. Sexual reproduction allows for the combination of mutations.
False. Our family can marry into another family who had an ancestor that won the lottery.
SEXUAL REPROCUTION. Not recombination. SEXUAL REPRODUCTION.
You don’t know what that probability is? On average, how many possible beneficial mutations are there in the modern human genome? Is it 1? Is it 1 million? Is it 100 million? What is it?
If there are 100 million possible beneficial mutations how many offspring are needed to get one of those beneficial mutations? Do we have to mutate every base in the human genome in order to hit 1 of those 100 million?
Do those yeast reproduce asexually or sexually?
That’s false. Not all humans have the lactase persistence mutation, but it is still beneficial. A different mutation can happen elsewhere in the human pouplation and not reach fixation. A mother carrying one beneficial mutation and a father carrying a different beneficial mutation can have children, and those children can have both beneficial mutations. At no time did either of the mutations reach fixation.
Yes, you do. Every time you require all bases of the human genome to be mutated in order to get one beneficial mutation you are making that assumption.
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A point of misunderstanding here, my fault for being unclear. I am STARTING from fixation in the population. My understanding is that new alleles arrive at roughly the mutation rate (all mutations, not just single nucleotide replacement). Any negative selection has already occurred at the time of fixation, otherwise it wouldn’t be fixed. Positive selection means it fixes more quickly but is not relevant - I am starting my clock at fixation.
Of course not every recombination results in improved fitness. My point is there are a truly astounding number of possible recombination of allele pairs, allele tripletes, etc., which have the potential to create a new trait.
For example, let’s say that only 200 genes are relevant to the differences between human and pan, ignoring the other 99% of genes. I feel this is being conservative. Now let a single new allele become fixed. It is unlikely to be a beneficial trait all by itself, but consider the potential trait that are allow by recombnination. There are …
200 (200 choose 2) possible allele pairs that may generate a new trait,
19,900 (200 choose 3) allele triplets that may generate a new trait,
1,313,400 (200 choose 4) quadruplets that may generate a new trait,
~6.5 million 5 allele tuples,
~2.5 trillion 6 allele tuples,
and this continues to increase by roughly an order of magnitude for each additional allele for quite a while.
[EDIT Long after the fact: I’m off by a step here. The first paring has 200 combinations (200 choose 1) with the new allele. There are 200 choose 2 existing pairs to form triplets with the new allele, 200 choose 3 triplets to form quadruplets, etc… Dan]
Now add a second new allele to the population and repeat. I’m willing to allow that more complex traits are less common, but it is undeniable that there are a hell of a lot of them (it’s a simplification to assume a small but equal probability for all). The question becomes, out of all of these possible combinations, what is the probability that no beneficial new traits will arise?
I’m sure you know this math already, but I’ve explained it to others so many times before I made a thread for it. For a convenient rule of thumb, the limiting probability of an event X with probability 1/N and N trials (here allele combinations), the probability X will occur at least once in N trials is ~0.63 (=1-1/e). If the odds of X are 1 in a million, and there have been a million trials, there is a good chance X has happened already.
Now use whatever fixation rate, replication rate, and population size you like, and apply the proper recombination rate to the probability that at least one of those combinations is beneficial.
Thank you for the quote, this also makes my case.
Miscellaneous details:
- A single combination need not arrive at the final configuration of a new trait, it need only get “close enough” for positive selection to act. This will significantly increases the probability of arriving at beneficial traits, but it would be difficulty to calculate.
- Only considering single nucleotide replacement only makes the Sharpshooter Fallacy worse. There are also transposition, which don’t create anything new but may allow new combinations the other 99% of the genome I excluded from my example.
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Me: You’re trying to explain electrons with Newtonian physics.
You: Well how would you explain orbital mechanics with quantum physics!?
Your response to my criticism was to do the thing I criticized more explicitly. Like I said, you’re desperately confused.
Rate equations are used everywhere.
No, that was for every possible mutation. Any mutation in a particular category is more likely than a specific mutation in that category.
Another 30k. This time definitely generations, since you are trying to force it in the same lineage. Obviously that’s not how reproduction actually works, but that just makes it worse for you.
I’m beginning to think you don’t understand what an analogy is.
If beneficial mutations happen at a particular rate, then rate x time (or events) is a useful approximation of how many beneficial mutations will occur in a given period of time (after a given number of events). But you’re ‘technically’ right, because you’re asking for the number of events, so the equation is replications = mutations / rate.
No it doesn’t for two reasons. First, it isn’t about any particular variant. This is another of your many gross conceptual errors. Second, we’re solving for when a beneficial variant occurs in the first place, and it can’t replicate until after it occurs. So the number of replications of a variant over the period in question is always necessarily zero.
A billion replications of E. coli would be ~500 beneficial mutations, not one. This is your primary misunderstanding. We don’t need to explain specific mutations, just any mutations.
This is why the rest of the paragraph is vapid nonsense.
The estimate is 240 fixed in the first 20k generations.
Either that’s projection, or you didn’t understand the sentence you quoted. Not sure which. Could be both. Probably is.
Whatever they were teaching you, it didn’t give you the capability of understanding the simplest evolutionary experiments. Which is why you are so painfully, fractally confused about every aspect of this discussion.
By the way, this is still not a response. It is incredulity resulting from your own lack of education on the relevant material.
Again, either projection or failure of reading comprehension.
This is such an odd question. Adaptation to what? To the competition? That’s a tautology. To everything else? No.
Anyway, I’ll take the fact that you didn’t respond to the first part of my previous comment as an admission that you accept all three corrections, although you still need to provide the math for the third point. Do you need help with that?
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Because you wouldn’t admit you were wrong even if I did, and everyone else already knows you’re wrong.
Can’t you work out the frequency of alleles is in a population of 2?
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At about 35:00 into the video, you make a passing reference to Darwinian evolution and positive selection and then you go on to discuss how everyone accepts neutral evolution (well, everyone except Joe Felsenstein who seems to have an understanding of the difference between neutral and adaptive evolution in determining common descent of humans and chimps) and this is your explanation for common descent of humans and chimps, and rats and mice. Why don’t you explain to these layman that neutral evolution is based on the assumption that these genetic changes don’t change reproductive fitness and this model doesn’t explain the population differences between humans and chimpanzees? There are a lot of subtle but very important assumptions you are making that you are not explaining to these laymen. But in a very dogmatic way, you use neutral evolution to explain the genetic differences between humans and chimpanzees and other life forms to explain common descent. What if you use Jeffery Tompkins’ estimate that human and chimp DNA is only 87% similiar? How does that change the time line for human/chimp divergence using your distance = rate x time model? Does that mean you change the time of divergence from say 5 million years ago to over 30 million years? You are the one doing the Texas sharpshooter fallacy by ignoring the data of adaptive evolution in your model.
And you didn’t answer my question. Do you believe that humans and E. coli evolved from a common ancestor? How far do you take your concept of common descent? I’d like to know as one of the viewers of that CC video and perhaps other viewers of the video would like to know.
Until you learn the difference between evolutionary competition and evolutionary adaptation, you will not understand the context. Until you learn that distinction, nothing you say will be relevant to this discussion.
Do you even understand the meaning of fixation?
Now watch the Kishony video. The drug resistance adaptation process proceeds without the elimination of the drug-sensitive variants. As long as the colony size can amplify (reach a population of about a billion), the next beneficial mutation has a high probability of occurring on one of the members of that colony. No fixation is occurring in that adaptive evolutionary process. I’d like to see an expert on the physics and mathematics of evolution say otherwise.
I appreciate that.
You are not paying attention. I used Kimura’s equation to define absolute fitness in a population and that equation has nothing to do with beneficial mutations. It is simply and equation that relates the change in population size from one generation to the next by a factor W. If W = 1, the population size remains constant from one generation to the next. If W < 1, the population size decreases from one generation to the next, and if W > 1, the population size is increasing from one generation to the next. That equation is simply a gross measure of the reproductive fitness of a population. This equation tells you nothing about the number of beneficial mutations.
And if you can’t understand that it is the ability of humans to produce food for its populations by farming is the reason why humans have much greater populations (and therefore reproductive fitness) than chimps who are hunter-gatherers, then I think there is no logic that I can present to you that you are able to find acceptable. The mathematical logic couldn’t be more trivial, more food => larger populations. Maybe you can understand this, the larger your family is, the more food you need to buy on each trip to the grocery store (or you could go to the grocery store more often). Check your receipts from the grocery store and see if this is confirmed.
So, what’s your explanation for humans having the ability to farm while chimps don’t? Why do humans have that intellectual capability and chimps don’t? Human population growth seems to coincide with the advent of farming. Do you think that is just some coincidence or there is a cause and effect explanation?
Certainly, and I’ve posted the links multiple times. I’ll post them again for you:
For the Kishony experiment, in particular, listen carefully to what Kishony says starting at about 0:50:
And for the Lenski experiments, there are many more accurate measurements but from Wikipedia, here’s a summary:
You have to do a little math to convert generations to number of replications. Lenski’s bacteria do about 6 1/2 generations (doublings) per day and in that one day, population increases from about 5 million to 500 million. So to convert 20,000 generations to number of replications use the following equation:
20,000 generations/6 1/2 generations/day * 500 million replications/day = total number of replications in 20,000 generations. If I did my math right, that puts you in the ballpark of about 1.5 trillion replications for 10 to 20 beneficial mutations with about 80-90 hitchhiking neutral mutations.
You should ask yourself, why does it about 3000 days for the Lenski experiment to get 10-20 beneficial mutations and only about 11 days for the Kishony experiment to get 5 beneficial mutations.
You are not paying attention to what I’m saying. It is not generations which determines the probability of a beneficial mutation occuring, it is the number of replications of the variant that determines that probability. And I’m not assuming that there is only one possible beneficial mutation for adaptation to a given selection pressure. What I am saying is that each of the possible beneficial mutations leads to a different lineage that takes its own particular evolutionary trajectory to improved fitness for that selection condition.
So, give us the mathematical explanation of how that recombination process works.
You could also marry into a family that is in debt.
How does SEXUAL REPRODUCTION create alleles that don’t exist? Do you think that with the proper breeding program for dogs that you could make a lineage of cats?
You should know by now that the environment determines whether a mutation is beneficial or not. For example, a sickle cell mutation is beneficial in a malaria endemic environment but in an environment without malaria, that mutation is at best neutral and might even be detrimental.
You didn’t read the paper! They can reproduce either way. And they measured something interesting about recombination. Go back and read the paper and learn something about recombination and evolution.
And DNA evolution does not require fixation of the variant before a beneficial mutation can occur on that variant. The variant simply needs to accumulate sufficient number of replications.
That’s not an assumption, that’s a mathematical fact of life. The number of replications necessary to give a reasonable probability of a beneficial mutation occurring also happens to be the same number of replications necessary for a mutation at every site in the genome. You did the simple form of the math yourself.
Ok, let’s start the clock at fixation but put it into context of the Kishony experiment (I know, E. coli doesn’t do recombination but some variants E. coli do conjugation so bear with me). The clock starts when Kishony innoculates a founder bacterium on the drug-free region of the plate. Because it is the only member of the population, the frequency of all its alleles is 1. Assume that this bacterium has a genome length of 5e6 and the mutation rate is 1e-9. After 200 replications, on average, there will be one member of that population that has a mutation somewhere in its genome. There will be one mutant allele in that population but every other allele in that population will be identical to the original founder. Another 200 replications will give another mutation on some member of that population somewhere in the genome. If this were a recombining population, by the 400th replication, there would be enough variation in the population for recombination to operate with a possible change in fitness for that offspring. In other words, there is a very small probability that the variant with the first mutation could conceiveably recombine with the variant with the second mutation to give an offspring with both mutations. But by far, recombination would be between variants that have identical alleles and therefore no chance for improvement in fitness. Now, continue this process and consider the number of replications required for each new allele and how the frequencies are changing for all the different alleles and tell us what you come up with.
Sure, there is a vast number of recombination possiblities in genomes with 20,000+ genes. But the particular alleles have to exist in the first place. And the probabilities of any recombination event depends on the frequencies of the different alleles in the population. Put this into context of the human/chimp divergence. When humans and chimps diverged, you have to assume that initially both lineages have the same alleles at the same frequencies in their populations. Any new alleles that occur in either population have to occur based on the mathematics of DNA evolution. My response above shows a simple way of approaching that math. The accurate way is to actually do the probability calculations. And I’ve already told you which probability distribution to use, the trinomial distribution.
Let’s say that all the alleles necessary to make humans and chimpanzees already exist in the founder population and the divergence of the two populations is simply a breeding process. The implication of that is that a breeding program for chimps could produce humans. I don’t think anyone would accept that. So, let’s take your number of 200 genes and new alleles for those 200 genes to evolve a human lineage. If it takes only 1 particular mutation in each of those genes to produce that human lineage, how does recombination get those 200 particular alleles into one human lineage? Aside from the number of replications necessary to get those 200 particular mutations, it would require the mating of correct members of the population with those alleles to have any reasonable chance of recombination putting all those alleles that are scattered around in the population into a single lineage. Explain to me the mathematics for that.
I read your thread on this subject. The “at least one” rule gives a probability equation of the forn P(X)=(1-(1-p)^N). If we set the number of trials N=1/p, we get the value ~0.63. If N increases beyond 1/p, P(X) increases approaching 1. That’s why I keep saying that it takes 1/(mutation rate) replications for the beneficial mutation to occur. It also happens that with 1/p replications that every other site in the genome will have some member of the population having a mutation at that site. This is a fundamental equation for random mutation and natural selection. I wrote a paper based on this a few years ago:
The basic science and mathematics of random mutation and natural selection
Note that the joint probability of mutation B occurring on some member that already has mutation A is computed using the multiplication rule. Microevolutionary changes don’t add, they are linked by the multiplication rule. Also note, this paper predicted the behavior of the Kishony experiment before that experiment was run. It also simulates and predicts the adaptive component of the Lenski experiment and any other DNA evolutionary process to a single selection pressure.
Dan, I’ve never said that recombination can’t give improvement in fitness. What I have said is that only under very specific circumatances can recombination do this. There is a mathematical explanation for why recombination gave an improvement in fitness in the harsh environment while it did not in the low selection pressure environment. See if you can figure out what that mathematical explanation is.
Yes.
You did not seem to understand that I was questioning your assertion that “to have a reasonable probability of taking a step on an evolutionary trajectory… requires amplification (increase in number) of that variant to improve the probability of the next beneficial mutation occurring on that variant (lineage).”
If there is a single copy of a gene in a genome, and a single mutation to this gene provides a selective advantage, then it represents a step on what you call the “evolutionary trajectory.” I see no reason that amplification is necessary for this to occur, unless I am missing something. If so, I’m sure some of the people here who actually understand the basics will point it out.
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Then you would make a very large mistake, as Tomkins’s estimate is nonsensical, as has been discussed here and elsewhere before. And if it were sensible, we would have to redefine the rate of change, since the nature of the changes would be quite different from the point mutations that @swamidass references.
Adaptive evolution can be ignored because it involves only a tiny fraction of the differences between humans and chimps and as such doesn’t significantly affect the calculation.
Of course we did. Why do you think otherwise?
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False. It is the number of possible beneficial mutations in the genome (as well as the mutation rate) that determines how many offspring it takes to get a beneficial mutation.
Have you seen Punnett squares?
That’s avoidance. Do you understand that the family doesn’t have to win the lottery twice, they only have to mate with another lineage that has a lottery winner as an ancestor?
It combines alleles so that the alleles don’t have to evolve independently in multiple lineages.
Answer the question. If there are 100 million possible beneficial mutations in the human genome would we have to mutate every base in the genome before getting a beneficial mutation?
So what did they find when there was sexual reproduction?
I did notice this section:
Or mate with another individual who has the beneficial trait.
That’s completely false. If there are 100 million possible beneficial mutations in the human genome why would I have to mutate every base before getting 1 beneficial mutation?
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I am curious about this, too. I understand that most evolution-deniers do not accept universal common ancestry. But your question, @kleinman, seems to suggest that you do not believe everyone who accepts the standard theory of evolution understand UCA to be part of that theory. Is that really what you think?
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Tomkin’s 84% figure is a result of his inability, unintentional or deliberate, to find the average.
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For the Lenski experiment, you’re only counting beneficial mutations that have reached fixation. For the Kishony experiment, you’re counting beneficial mutations that haven’t reached fixation.
Also, the Kishony experiment has a range of environments, so there is scope for mutations that are beneficial for only part of that range. The Lenski experiment doesn’t.
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