Evolution and Probability

Probabilistic thinking is pervasive in evolutionary theory. It’s not a bad thing, just something that needs to be acknowledged and appropriately handled.

Denial

Some go so far as to deny it, but in my experience these people are ideologues. These are critics of ID who complain about the lack of any numbers being attached to the probability arguments of ID proponents, and their denial is perhaps rooted in their fear of a tu quoque.

Where are their own probability calculations?

Incredulity

Another reason for their denial could be that they also love to accuse ID proponents of making arguments from incredulity, while being unwilling to face up to the fact that they are guilty of the same thing. Does evolutionary theory depend on arguments from incredulity? Almost certainly.

Take for example the idea that all extant life shares a common ancestor. It is based upon the idea that it is simply too implausible that life should arise more than once and yet share common features such as the genetic code.

We can be very sure there really is a single concestor of all surviving life forms on this planet. The evidence is that all that have ever been examined share (exactly in most cases, almost exactly in the rest) the same genetic code; and the genetic code is too detailed, in arbitrary aspects of its complexity, to have been invented twice.

Dawkins, Richard. The Ancestor’s Tale: A Pilgrimage to the Dawn of Evolution


An argument from incredulity.

Probabilities are Important

The importance of probablity in evolutionary thinking might best be seen in the following text:

If there are versions of the evolution theory that deny slow gradualism, and deny the central role of natural selection, they may be true in particular cases. But they cannot be the whole truth, for they deny the very heart of the evolution theory, which gives it the power to dissolve astronomical improbabilities and explain prodigies of apparent miracle.

Dawkins, Richard. The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe without Design

Independence of Events

While having said all this, I’d like to focus on the idea that evolutionary events are not independent and that this somehow rescues evolutionary theory from being guilty of appealing to vastly improbable outcomes, aka miracles.

Consider a toss of the dice in a game of craps. The odds of double six is 1/36. Sure, we can roll a single die twice, and the odds of a six on each roll is now only 1/6 vastly more likely to occur by chance (not really). 1/6 x 1/6 is still 1/36. The probabilities are multiplicative because the events are independent events. The fact that if you have two dice and you roll the first die until you get a six and then you keep that (by cumulative selection) and then roll the second die until you get the second six and now you have two sixes doesn’t change the probabilities one whit. Doesn’t that demonstrate that cumulative selection is helpless in reducing probabilities?

Well, you might say, you need to roll BOTH dice until only one of them shows a six and then keep that one and then roll the second die. But what in evolution is analogous to that?

Sure, if you roll two dice trying to roll a six you have a better chance of a six showing on one of the two dice than if you roll just one. It’s like rolling one die twice in an attempt to get a six rather than just once. Of course the probability of the second six would still be 1/6. But why aren’t justified in adding a third die after our first six is rolled so that once again we are trying to get a six from two dice and not just one? And doesn’t this again demonstrate that it is not cumulative selection at all that is responsible for the reduction in probability but rather the number of trials we allot each attempt to roll a six?

Closing

The fundamental question is why aren’t evolutionary events independent and thus multiplicative?

The secondary question is what is the true role of cumulative selection in reduction from the miraculous to the mere appearance of the miraculous?

291 thoughts on “Evolution and Probability

  1. dazz:

    Phoodoo: I hope Allan and Jock..and Joe, don’t read your link.You are going to give them ulcers.

    Dazz: Like you read it. You stopped right after the introduction, didn’t you?

    I guess gastric symptoms would depend on one’s attitude to philosophy.

    I would say that all of Joe, DNA-Jock, and Allan respond to the unending repetition of anti-evolution arguments, almost always with patience and thoroughness.

    How they have the stomach for that is beyond me. But apparently they avoid ulcers while doing so.

  2. phoodoo: Its essentially a repeat of every criticism of fitness that I have made here.

    And despite those criticisms, fitness can still be defined, and measured. So your criticisms accomplish nothing.

  3. Rumraket,

    I guess you know better than the authors of Bruce’s paper then.

    And their references:

    “The Confusions of Fitness,” British Journal for the Philosophy of Science

    “What’s wrong with the received view of evolutionary theory? PSA 2, East Lansing: The Philosophy of Science Association,

    “Is the Theory of Natural Selection a Statistical Theory?”, Canadian Journal of Philosophy

    “The Two Faces of Fitness,” in Thinking about Evolution: Historical, Philosophical, and Political Perspectives.

    “Quantum indeterminism and evolutionary biology,” Philosophy of Science….

  4. Rumraket: And despite those criticisms, fitness can still be defined, and measured. So your criticisms accomplish nothing.

    There is a link at the end where you can contact the author for suggestions about how to do so.

  5. BruceS: respond to the unending repetition of anti-evolution arguments

    Well, there certainly are a lot, I will grant you that.

    Thanks for adding to that list.

  6. Yeah, remarkably ulcer free here. What phoodoo seems to argue is that, as we can’t anticipate the fitter of two types, traits that increase offspring numbers accruing to bearers cannot in fact increase in the population. If you can argue it a tautology, it magically ceases to have causal power. It’s a dumb argument, but of course that never bothers phoodoo much.

    If a trait increases the fitness of bearers, measured in terms of average numbers of surviving offspring, it can only tend to

    a) increase
    b) decrease
    c) stay the same

    in the population as a whole. Pretty obviously, it’s generally gonna be (a), though statistically b and c can occur with some frequency. Phoodoo must tick the box marked ‘none of the above’, go for a directionless ‘all of the above’, or insist that there is in fact no variation in reproductive effect for any trait.

  7. BruceS,

    If you are just saying that if two events are independent, then you multiply the probabilities, they of course you are trivially correct. But what does that have to do with evolution?

    If according to empirical science (Szostak) a randomly generated 70AA protein binding to ATP is 10^-11 what is the probability it can bind to a second molecule assuming it has the same binding probability as ATP?

  8. Allan Miller: If a trait increases the fitness of bearers, measured in terms of average numbers of surviving offspring, it can only tend to

    a) increase
    b) decrease
    c) stay the same

    in the population as a whole. Pretty obviously, it’s generally gonna be (a), though statistically b and c can occur with some frequency.

    Maybe you should read the paper. It will tell you all about what I have been arguing.

    If you can stomach it that is.

  9. phoodoo: Maybe you should read the paper.It will tell you all about what I have been arguing.

    If you can stomach it that is.

    Read it years ago. Perhaps you could address my point rather than hiding behind the words of others? They don’t say what you think they say.

    If a trait increases the mean fitness of bearers, what will be the general effect on that trait’s frequency in the population? Up, down, sideways or none of the above?

  10. Allan Miller: Yeah, remarkably ulcer free here. What phoodoo seems to argue is that, as we can’t anticipate the fitter of two types,

    then you can’t design by artificial selection.

    Fixed it.

  11. Allan Miller:
    petrushka,
    Indeed. And nor can resource competition in ecology actually work, either.

    Being unable to anticipate the consequences of change does not impede natural selection or drift.

  12. Puccio is now calculating the number of generations we need wait to have an 80% chance of having some sequence transmutate into another predefined sequence with 100 specific amino acids, in one go, *poof*. The guy is a fucking clown. Period.

  13. colewd: If according to empirical science (Szostak) a randomly generated 70AA protein binding to ATP is 10^-11 what is the probability it can bind to a second molecule assuming it has the same binding probability as ATP?

    This is a great example (it’s 80aa not 70aa, btw).
    I can say with some confidence that the probability it can bind to a second molecule is within the range 0.98 – 1.00
    I would try isoguanine 5`-triphosphate, 2`-deoxy-adenosine 5`-triphosphate, and Adenosine 5′-(gamma-thiotriphosphate) for starters. Pretty sure one of those will work.
    Not what you meant to ask. That just keeps happening.
    You want to know the probability that it will simultaneously bind a different unrelated molecule (of a similar level of complexity), and at a similar level of yield and avidity?
    In THAT case, the answer is: don’t know.
    It could be anywhere between 1 and 0.
    I suspect it might be somewhere in the 10^-1 to 10^-3 range.
    Perhaps you wanted to ask, “What’s the probability that my ATP-binder will also bind THIS specific molecule (e.g. ubiquitin)?”
    Post-hoc specifications, so much fun, so fallacious.
    Remember, though, once RV+NS gets its hands on any of these molecules, all bets are off.

    P.S. For those kind souls concerned re my gastric health, I concluded long ago that one commenter here appears incapable of formal operational thought. Specifically, the concept “propensity” seems beyond him. I’m not even sure about concrete operational…

    ETA : Note that, per Keefe & Szostak, there must be 10^93 different ways to bind ATP.
    That’s a lot of needles!

  14. phoodoo: Wow, that is quite a source you reference.For those who don’t believe in the concept of fitness that is.

    Its essentially a repeat of every criticism of fitness that I have made here.

    What you left out were from your list were the answers to the superficial circular critique of the concept of fitness, answers which are discussed in detail in that article.

    This article shows the openness and transparency of the philosophical community, mirroring that attitude in science, to considering all sides of difficult issues.

    That puts the lie once more to the repeated fantasy in anti-science groups that some kind of conspiracy prevents controversial ideas from being aired. Even ideas on central concepts, as in this case, where the challenge is to understand the nature of fitness.

    Of course, essentially all the philosophers participating in this conceptual analysis continue to believe in the science of evolution.

  15. DNA_Jock,

    That’s a lot of needles!

    Yet the haystack is 100 billion times larger 🙂 I know you see the problems w the theory so I won’t pound it in any more.

  16. dazz,
    I love it when IDists actually start working with numbers.
    In post 296,
    gpuccio shows his calculations, demonstrating that the time expected to obtain one specific amino acid mutation is ~110 days, and the time expected to obtain two is ~1,100 days.
    Now before I delve into his math, I will note that he must be looking for simultaneous mutations, since he doesn’t blanche at the “one takes 110, two takes 1100” result, which would be obviously wrong otherwise.
    He reckons 1e-10 mutations/nucleotide/generation, and requires that the mutation produce the desired amino acid (kinda goofy 1 out of 20, i.e. 5%, but we’ll let that pass arguendo) such that the P(desired mutation) is 1e-10 x 5% = 5e-12 per generation.
    He wants the probability of success to reach 80%, so he figures (using the binomial wtf?) that this will take 3.3e11 cell divisions. I used the Poisson and got 3.22e11. No matter.
    Now he gets suddenly conservative, and postulates a population of 1e9 bacteria dividing three times a day.
    I went for something a little easier to visualize: a human being, with 3.9e13 bacteria and (say) 30 generations per day. [Really, why is it that whenever we are building a flagellum, it has to be completed with high efficiency within 20 minutes, but now, when….oh, nevermind]
    That’s 1.1e15 doublings per day, rather than his 3e9. So rather than 110 days, it takes 24 seconds to get that mutation.
    But here comes the doozy:
    gpuccio reckons that the double change has a probability of 1e-10 x 5% x 5% x 2.
    Huh?
    No, the probability of the double mutation is (1e10 x 5%) squared.
    And, thus the time needed to see the double mutation in one human’s gut flora would be 150,000 years.

    [Across humanity, we’ll see the specified double mutation every 13 minutes.]
    Later, in #306, feeling perhaps that his 1,100 days result wasn’t impressive enough, he repeated the “forgetting the 1e-10” error to calculate time-to-get 3, 10 and 50 specific changes.
    He’s off by ~ 10^10 for every change he adds.
    It’s epic.

    I think what he is trying to calculate is how long before the cumulative probability of the single/double/etc having arisen in the population reaches 80%. But that brings us back to the 1 takes 110, 2 takes 1,100 disconnect. The cumulative Prob of BOTH specified mutations having happened reaches his 80% goal when the Prob of each individual hits 89%. That’s 154 days in his bacterial population, 33 seconds in one human’s.

  17. colewd: Yet the haystack is 100 billion times larger

    Actually the haystack has not changed size. You are arguing that the number of needles is only 10^93 / 10^11 = 10^82.
    You have no basis for this argument, and the number could easily be 10^91.
    and
    “Remember, though, once RV+NS gets its hands on any of these molecules, all bets are off.”

  18. phoodoo: I guess you know better than the authors of Bruce’s paper then.

    If they claim fitness can’t defined or measured, yes. Of course, they don’t claim that, so you’re just blustering.

  19. phoodoo: There is a link at the end where you can contact the author for suggestions about how to do so.

    I don’t have to do that, multiple examples are given in the text. Perhaps you can contact them and tell them how it’s all wrong. Did you even read it, or just the titles?

  20. phoodoo: Maybe you should read the paper. It will tell you all about what I have been arguing.

    Maybe YOU should read the paper, if you can stomach it.

    I’m calling your bluff right here. You’ve read the titles only, and you think the article somehow concludes that fitness can’t de befind or measured. It does not do that. It is a discussion about different concepts of fitness, their various advantages and shortcomings. There is no overall conclusion that shows fitness to be an immeasurable or undefineable concept.

    It’s hilarious to see you flail around desperately like beached flounder. Dude, go back in your sea cave.

  21. BruceS: What you left out were from your list were the answers to the superficial circular critique of the concept of fitness, answers which are discussed in detail in that article.

    This article shows the openness and transparency of the philosophical community, mirroring that attitude in science, to considering all sides of difficult issues.

    That puts the lie once more to the repeated fantasy in anti-science groups that some kind of conspiracy prevents controversial ideas from being aired.Even ideas on central concepts, as in this case, where the challenge is to understand the nature offitness.

    Of course, essentially all the philosophers participating in this conceptual analysis continue to believe in the science of evolution.

    Let’s not even kid around here, he read the titles only, perhaps the first section under each title in which the issue is defined, then stopped reading thinking the whole thing was one big argument against fitness, as opposed to what is common practice in both scientific and philosophical publications, to define and discuss the problem and it’s history first, and then to give examples of how such problems have been addressed before, or to suggest your own modifications or solutions.

  22. Rumraket: Maybe YOU should read the paper, if you can stomach it.

    Some papers aren’t fit to read. phoodoo is waiting to see if it survives first.

  23. phoodoo: And their references:

    “The Confusions of Fitness,” British Journal for the Philosophy of Science

    “What’s wrong with the received view of evolutionary theory? PSA 2, East Lansing: The Philosophy of Science Association,

    “Is the Theory of Natural Selection a Statistical Theory?”, Canadian Journal of Philosophy

    “The Two Faces of Fitness,” in Thinking about Evolution: Historical, Philosophical, and Political Perspectives.

    “Quantum indeterminism and evolutionary biology,” Philosophy of Science….

    Of which you have not read even a single one.

  24. BruceS: If you are just saying that if two events are independent, then you multiply the probabilities, they of course you are trivially correct. But what does that have to do with evolution?

    I ought to be trivially correct, but some people can’t even seem to grasp that.

    Are there truly no independent events that occur in evolution? So are we never justified in multiplying the probability of two events?

    Say you have a polypeptide and a single change to an amino acid has no apparent effect but if there is a change to two of them it can all of a sudden bind to some other molecule. Why wouldn’t we consider the two amino acid changes to be independent events each with their own probability of taking place and thus the probability of them both would be the product of the individual probabilities?

  25. dazz: Now compare that with “this or that is so complex that NS+RV couldn’t have possibly done it”. There is NOTHING there except for mere assertion.

    Oh please. Goddidit is more parsimonius than RV+NS did it.

  26. DNA_Jock,

    Actually the haystack has not changed size. You are arguing that the number of needles is only 10^93 / 10^11 = 10^82.

    The haystack is 20^80 or 10^104. Haystack= total sequence space. That works out to 10^93 x 10^11.

  27. Mung: Are there truly no independent events that occur in evolution? So are we never justified in multiplying the probability of two events?

    Well, the trick here is to re-express your events as conditionals, and calculate the conditional probabilities. Good luck.

    Mung: Why wouldn’t we consider the two amino acid changes to be independent events each with their own probability of taking place and thus the probability of them both would be the product of the individual probabilities?

    Because they are not. Do you not understand probability?

  28. Mung: Oh please. Goddidit is more parsimonius than RV+NS did it.

    given that RM+NS has been demonstrated to exist, your statement re parsimony is incorrect. “Linda is a bank teller” incorrect.

  29. DNA_Jock: But here comes the doozy:
    gpuccio reckons that the double change has a probability of 1e-10 x 5% x 5% x 2.
    Huh?
    No, the probability of the double mutation is (1e10 x 5%) squared.

    Oh, true, I missed that. No idea where he gets 1e-10 x 5% x 5% x 2 from.

  30. Mung: Oh please. Goddidit is more parsimonius than RV+NS did it.

    Pretty sure parsimony only applies to competing hypothesis. Goddidit isn’t a scientific hypothesis at all as it has no explanatory power

  31. Mung: Oh please. Goddidit is more parsimonius than RV+NS did it.

    You are confusing parsimonious with sanctimonious.

  32. colewd,

    That’s right! You are finally getting the hang of exponents!
    At the observed frequency of 10^-11, with a sequence space of 10^104, there must be 10^93 ATP-binding needles in the haystack. Good work! I explained this to you in February.

    In a delightful goal-post shift, you are now trying to claim that, for a doubly functional protein, the frequency is 10^-11 times 10^-11, and thus there are only 10^82 needles in the haystack. You are, as ever, WRONG. There are considerably more than 10^82 double-functional needles.

  33. DNA_Jock: Because they are not. Do you not understand probability?

    I don’t get it either I have to say. Why aren’t they? What is the probability that G will mutate to T at position 94 in the gene? And why does that mutation happening, affect the probability that A will mutate to G at posion 26 in the gene some time later(or in the reverse order)?

    I can sort of imagine at least abstractly that the G-to-T mutations has some epistatic interactions in the cell internally, that in turn has some biophysical effect of making other mutations in the genome more or less likely, but is that it? I get the impression that’s not what you’re saying, that there is something fundamental with probability involved. I don’t get it.

  34. BruceS: What you left out were from your list were the answers to the superficial circular critique of the concept of fitness

    You mean what YOU left out? Show the answer to these problems then. Has a cat got your tongue? Must be the same cat that has Rumrakets tongue.

    Perhaps some cats have found a new use for their extra digits, they use it for erasing the concept of fitness. Or maybe they are using it for eating evolutionists brains and preventing them from typing coherent solutions.

    I am calling your bluff, show where the paper finally shows what the definition of fitness is. Because as soon as you do I will show you where they also challenge each definition, and where they give multiple qualifiers for why the definitions are problematic.

  35. DNA_Jock: given that RM+NS has been demonstrated to exist

    What a complete nonsense statement. What does it mean to say “natural selection” exists? You mean life exists? Death exists?

    Saying natural selection “exists” is like saying expediency has been shown to exist. Laziness has been shown to exist (maybe that’s what you are showing).

    Good triumphs over evil has been shown to exist!

    The road less traveled makes all the difference. Its been shown to exist!

    Good things come to those who wait. Its been shown to exist!

    A stitch in time saves nine. Yep, its is so!

    Nothing ventured nothing gained! It exists!

  36. Rumraket: What is the probability that G will mutate to T at position 94 in the gene? And why does that mutation happening, affect the probability that A will mutate to G at posion 26 in the gene some time later(or in the reverse order)?

    I agree that any physical interaction between nucleotide 26 and 94 is so tiny that we can ignore it.
    So we will stipulate that the probability* of G94T is independent of whether we have A or G at 26, and vice versa.
    * that’s the probability per replication.
    The issue is the number of shots on goal. Think linkage disequilibrium. If 94 is 10% T and 26 is 10% A, you CANNOT conclude that 1% of the gene copies will carry T and A. The history of the gene will distort this calculation; thus the nucleotides that you observe at any location are not “independent” of the nucleotides that you observe at any other location. None of these idiots are actually observing mutations as they occur; they are observing diverged sequences and assuming that every divergent change is independent. No, they are not.

  37. phoodoo: Saying natural selection “exists” is like saying expediency has been shown to exist

    Then we agree. See, that was easy. My refutation of Mung does not rest on RM+NS being able to achieve any given outcome, just that it exists.
    Thank you for your support.

  38. DNA_Jock,

    When it rains it pours!

    Life is what happens to you while you’re busy making other plans!

    Yesterday is history, tomorrow a mystery and today is a gift. That’s why we call it the present. Fact!

    Everything happens for a reason. True story!

    There are no atheists in foxholes! Look it up!

  39. phoodoo: You mean what YOU left out?Show the answer to these problems then.Has a cat got your tongue?Must be the same cat that has Rumrakets tongue.

    Oh look, the title-only reader is back. Meanwhile fitness continues to be a concept that can be defined, and measured.

    Perhaps some cats have found a new use for their extra digits, they use it for erasing the concept of fitness.Or maybe they are using it for eating evolutionists brains and preventing them from typing coherent solutions.

    Coherent solutions to what? You want a defined and actual measure of fitness used in research practice? Here’s one: Comment On The Use Of Selection Rate Versus Relative Fitness.

    I am calling your bluff, show where the paper finally shows what the definition of fitness is.

    Nobody claims it “finally shows what the definition of fitness is”. It discusses multiple different definitions, each with their own advantages and shortcomings.

    Because as soon as you do I will show you where they also challenge each definition, and where they give multiple qualifiers for why the definitions are problematic.

    Problematic doesn’t mean can’t be defined or measured. So you’re not demonstrating anything by flailing your limbs desperately in the direction of that article. Fitness is defined and measured in practice, every single day, by hundreds of thousands of people all over the world. What is it you think you are accomplishing here?

  40. Rumraket: It discusses multiple different definitions, each with their own advantages and shortcomings.

    No fucking kidding. Ha, why don’t you reference a different paper which claims a different definition of fitness. Oh wait, you already did that.

    Rumraket: Problematic doesn’t mean can’t be defined or measured.

    How about you come up with a definition for absurd. Can we use your post as an example.

    Did you know its better a witty fool than a foolish wit. Measured and shown. Ask Jock!

    And there are no atheists in foxholes! I guess atheists are draft dodgers.

  41. Here is a paper by Lenski discussing and evaluating experimental methods in an arena where fitness is comparatively easy to measure, when compared to long-lived organisms – in bacteria. Now, if I read phoodoo correctly, it should not even be possible to mix bacterial strains and evaluate which has the higher rate of increase. That there is, in fact, no such thing as a differential in rate of increase, in which case everything must have the same rate of increase, which seems a bit unlikely. He seems to claim support from philosophers on this, so scientists better tread warily!

  42. phoodoo: You mean what YOU left out?Show the answer to these problems then.

    Um… what do you think links are for…?

    If you go to the SEP site, you will find exactly the same conversations regarding concepts like space, time. And of course there is no philosophical consensus on what quantum theory tells us about reality.

    When you ask about what fitness is, you are asking a philosophical question. A good one. But the same types of questions are asked about the fundamental concepts in most successful science: what are they telling us about reality?

    These philosophical questions tell us nothing at all about the science. The theory of evolution, just like those of QM and GR, is one of the most successful sciences we have.

  43. One often hears the phrase “moving the goal posts” to describe what the speaker thinks is an invalid argument in a discussion. That phrase at least implies both participants are playing the same game.

    But what do we call situations where one side thinks they are criticizing the science, when in fact they are saying nothing at all about science, but rather (inadvertently?) making an argument in a totally different domain of knowledge.

    – phoodoo’s philsophical concerns about the concept of fitness

    – Mung’s literary concerns about Dawkins arguments in his popularizations

    – EricMH’s mathematical arguments about the nature of a definition and of complexity (Eric never followed up on his “this should be easy” commitment to Joe regarding Joe’s biological test of Eric’s math)

  44. Mung: I ought to be trivially correct, but some people can’t even seem to grasp that.

    Are there truly no independent events that occur in evolution? So are we never justified in multiplying the probability of two events?

    Say you have a polypeptide and a single change to an amino acid has no apparent effect but if there is a change to two of them it can all of a sudden bind to some other molecule.

    Of course, by “trivially” correct, I meant you are correct because that is the definition of independent events.

    I have no idea what biochemistry would say about the independence of two mutations related to the amino acid you name.

    But only talking about the two amino acid changes biochemically would still be an invalid model of evolution because it leaves out population genetics. The biological question is this: if the mutation occurs at least once in a generation, what is the probability that the two mutations will be present in some subsequent generation, after a selection mechanism has operated over time.

    To see the issue, take two extreme examples. (1) the first mutation is non-viable: it kills the descendent. (2) descendants possessing the first mutation replace any lacking it in subsequent generations.

    Can you see why in this case the answer to the question of whether a subsequent generation possesses both involves more than just multiplying the probabilities of each mutation?

    As DNA-Jock says, technically this is related to a conditional probability, Did you ever get a chance to study Bayes rule? That also requires understanding conditional probability.

  45. BruceS: Um… what do you think links are for…?

    I honestly have no idea what your link was for. You prefaced it by saying

    In any event, don’t confuse how we can measure something with what something is.

    Then you gave that link which was a synopsis of how and why we can’t really define fitness. So don’t ask me what you were trying to say, other than the concept of fitness is problematic, and has been problematic for the theory of evolution for quite some time.

    That you think you can measure something, that can’t even be properly defined, seems pretty silly to me.

    Yes, you can measure offspring. But if what you are doing when you try to measure fitness is measure offspring, then call it measuring offspring, don’t call it measuring fitness. And if you have to measure something after the fact, then a model which decides fitness beforehand has nothing whatsoever to do with evolution, other than perhaps the models name.

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