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. Mung: Some people think proteins evolved from other proteins.

    Evolutionary biologists have shown that many proteins are related to each other. But not all. It is not thought that all proteins share common descent.

    Perhaps there is a LUCA for all extant proteins.

    There isn’t. There are quite a number of bona fide ORfan protein genes that have evolved from previously noncoding DNA.

    Like how eyes evolvedfrom other eyes. And the LUCA of all extant eyes is something like a light-sensitive spot.

    It is not thought that all eyes are related.

  2. Rumraket: It is not thought that all proteins share common descent.

    It’s probably just the ones that do not reproduce.that don’t share common descent.

    There are quite a number of bona fide ORfan protein genes that have evolved from previously noncoding DNA.

    Some some proteins evolved from non-coding DNA and other proteins evolved from their protein ancestors?

    It is not thought that all eyes are related.

    It is not thought that all proteins share common descent.

    Proteins don’t leave offspring. They don’t evolve from other proteins. Ever. There are no ancestor proteins and descendant proteins and no sister taxa.

  3. Rumraket: I have no idea what you’re even trying to suggest here.

    There’s no speciation? So no “On the origin of species of cars“? So really, no evolution?

    Rumraket: I don’t know the properties of cars in advance.

    They aren’t programmed in to the program?

    Does the program evolve new car parts that did not exist previously? Square wheels maybe?

    No, the car chromosomes don’t have junk regions.

    And no introns?

    Why did you bring these cars up?

  4. Mung: Rumraket: It is not thought that all proteins share common descent.

    Mung: It’s probably just the ones that do not reproduce.that don’t share common descent.

    That makes no sense. There are dead people with whom I share common descent: They are dead so they no longer reproduce, yet we still share common descent.

    Rumraket:There are quite a number of bona fide ORFan protein genes that have evolved from previously noncoding DNA.

    Mung: Some some proteins evolved from non-coding DNA and other proteins evolved from their protein ancestors?

    The point is that there are protein coding genes that have diverged over time from a common ancestral protein coding gene through duplication and subsequent divergence.

    But it is not the case that all protein coding genes can be traced to a common ancestral protein coding genes.

    Rumraket: It is not thought that all eyes are related.

    Rumraket: It is not thought that all proteins share common descent.

    Mung: Proteins don’t leave offspring. They don’t evolve from other proteins. Ever.

    Techically some amyloids do, but no I was not appealing to amyloids here.

    If you had not insisted on an uncharitable, unusually obtuse interpretation of my words you would have been able to work out for yourself that it is when the organisms that carry protein coding genes in their genomes, reproduce, that the protein coding genes, not the proteins themselves, which have lines of descent.

    Mung: There are no ancestor proteins and descendant proteins and no sister taxa.

    There are ancestor protein coding genes, and descendant protein coding genes.

  5. Mung: And you were not surprised in the least when it produced an airplane?

    Rumraket: I have no idea what you’re even trying to suggest here.

    Mung:There’s no speciation? So no “On the origin of species of cars“? So really, no evolution?

    Evolution is not synonymous with speciation. Evolution can happen without it leading to speciation, but in any case what has this ultra stupid horseshit you’re bringing up have to do with the argument I’m having with Bill Cole regarding “targets”?

    Rumraket: I don’t know the properties of cars in advance.

    Mung: They aren’t programmed in to the program?

    No, they evolve.

    Does the program evolve new car parts that did not exist previously? Square wheels maybe?

    Under my definition of new, yes. You didn’t offer one so I’ll just use mine. Any car component which is different from what they were before in a previous generation, is not how it used to be, so they’re new, so yes. Square wheels are not among them no, but that doesn’t mean nothing new evolves. The fact that it can’t change into anything imaginable doesn’t mean it can’t evolve. Protein coding genes also only code for 20 amino acids, yet they can still evolve.

    No, the car chromosomes don’t have junk regions.

    And no introns?

    What has introns got do do with anything? Many species of prokaryotes have no or very few introns.

    Why did you bring these cars up?

    Why didn’t you first go back and check the exchange I had with Bill before starting an argument?

    Bill Cole seemed to claim that a highly unlikely sequence, such as a protein-coding gene, could not evolve without a pre-specified target towards which evolution is somehow “made to select towards”, and he referenced Dawkin’s Weasel program as an substantiation of that claim.

    My claim is that the BoxCar2D simulation proves this claim wrong, in that the cars and the chromosomes that encode them, are analogous to proteins and the genes that encode them. And highly unlikely car chromosomes, which are sequences, still evolve, and I have argued how someone like Bill Cole could mistakenly go look at any particular char chromosome and argue it could not have evolved because it’s too unlikely out of the total space of all possible car chromosomes, so it “must have been a target.” So in the same way we can SEE that Bill’s claim is wrong for the BoxCar2D simulation, the claim is also wrong for protein evolution.

  6. Rumraket,

    So in the same way we can SEE that Bill’s claim is wrong for the BoxCar2D simulation, the claim is also wrong for protein evolution.

    Mung has showed you that the analogies don’t work. Now at this point I am not sure who is right but you are miles from a convincing argument. This is the same mistake you have made arguing that proteins can evolve as you tend to use poor analogies because they are much simpler then reality. What I give you lots of credit for is you at least try and support your claims.

    When I say we cannot simulate RMNS I mean real biology or at least real translatable functional sequences.

  7. DNA_Jock:
    Mung,
    IMO, you appear to be trolling.
    Just so you know.

    I agree. Saying that it isn’t “evolution” unless there is speciation is an exercise in restricting definitions so as to dismiss a simulation as irrelevant (in this case BoxCar2D).

    As someone who has worked for years on theoretical population genetics, which is mostly about changes within species, I am very unimpressed by this restriction on what is “evolution”.

  8. DNA_Jock,

    Chou-Fasman rule is we need 4 or more helix formers, and no helix breakers.
    Bill’s rule is 1 in 2^6, i.e. only 1.5% of six-mers will be able to fold a stable fold. Any stable fold.
    Since 11/20 (EHWKAMVILQF) are helix formers, and only 4 (NGY and, of course, P) are helix breakers, we calculate that 31% of six-mers will be alpha helix nucleation sites. Gee, only a 20-fold difference, but raise it to the 13th power…

    Thank you for this.

    So now you need 80 AA’s to from into a secondary structure. I will agree with you calculations for argument sake. How do you form this structure with alpha helixes and beta sheets. If you think substitutability is less greater then 50% lets see your plan. I will think about it also.

  9. colewd: This is the same mistake you have made arguing that proteins can evolve as you tend to use poor analogies because they are much simpler then reality. What I give you lots of credit for is you at least try and support your claims.

    When I say we cannot simulate RMNS I mean real biology or at least real translatable functional sequences.

    Nice goalpost shift, Bill.
    Here’s what Rumraket was responding to :

    Dawkins tried to build one with Weasel but for selection to be effective the target sequence had to be incorporated in the model.

    BoxCar2D is a truly awesome refutation of your point.
    The irony being that Rumraket’s understanding of the evolvability of ‘translatable functional sequences’ in ‘real biology’ is orders of magnitude ahead of yours.

  10. colewd: Mung has showed you that the analogies don’t work.

    He has completely misunderstood what you and I have been arguing about.

    I suspect he was conflating the argument I was making to Mung earlier in this thread, using the BoxCar2D simulation, with the one I was making to you, and he came back in the middle of our exchange and thought I was continuing the argument I had with him earlier for which I also employed the BoxCar2D simulation in an analogy. A different analogy, with a different point to make.

    This is the same mistake you have made arguing that proteins can evolve as you tend to use poor analogies because they are much simpler then reality. When I say we cannot simulate RMNS I mean real biology or at least real translatable functional sequences.

    What is it you think the analogy is missing?

    Put it back in the context in which I first brought up the simulation. You said back there:

    Colewd: There is no model that shows the generation of the FI that builds the motor. Dawkins tried to build one with Weasel but for selection to be effective the target sequence had to be incorporated in the model.

    Notice the claim here that for selection to be effective, a target sequence has to be incorporated in the model. I then proceed to argue why that isn’t true, and reference the BoxCar2D simulation as substantiation of that. And I further argue that the BoxCar2D simulation is also apposite to our discussion regarding protein sequence evolution, because in the same way that protein sequence space is extremely large, and most sequences are bad or nonfunctional, that the same is true for the BoxCar2D simulation’s car-chromosomes.

    So your claim’s two central aspects;
    A) That targets are necessary for selection to even work,
    and
    B) The vastness of the total space of possible sequences prevents specific, well functioning sequences from evolving as that would be too unlikely.
    – I maintain the BoxCar2D simulation show to be false.

  11. DNA_Jock,

    Bill: Dawkins tried to build one with Weasel but for selection to be effective the target sequence had to be incorporated in the model.
    Jock:
    BoxCar2D is a truly awesome refutation of your point.
    The irony being that Rumraket’s understanding of the evolvability of ‘translatable functional sequences’ in ‘real biology’ is orders of magnitude ahead of yours.

    Dawkins model was against a sequence in the ENGLISH LANGUAGE. Nice goal post shift by both of you slick guys 🙂

    To refute the claim you need to find a comprehensible english sentence from a random sequence of letters without a target.

    I am sure Rumraket understands this better then I do so I expect a better response from him.

  12. colewd: Dawkins model was against a sequence in the ENGLISH LANGUAGE

    How incredibly stupid. The weasel algo does in no way depend on the target making any kind of linguistic sense. You can pick any string as a target. Poor Billy, as confused as always.

  13. DNA_Jock,

    Do you know the original point? If not, you are the pot calling the kettle black on you trolling comment.

    The point originally was about a biological model of natural selection in evolution.

  14. dazz,

    How incredibly stupid. The weasel algo does in no way depend on the target making any kind of linguistic sense. You can pick any string as a target. Poor Billy, as confused as always.

    And what language did the characters in the string come from in this case?

  15. colewd: What I give you lots of credit for is you at least try and support your claims.

    You don’t see any irony in that remark, Bill?

  16. colewd:
    dazz,

    And what language did the characters in the string come from in this case?

    LOL, you can build any number of languages from a character set, how is that relevant to anything? You could even tweak the weasel algo to work with made up symbols, or even pictures. IT HAS ZERO TO DO WITH LANGUAGE. Keep digging, Bill, keep digging.

  17. colewd: And what language did the characters in the string come from in this case?

    Regarding “Weasel”, the program Dawkins came up with nearly 40 years ago is not considered by anyone, including Dawkins, as anything other than a simple demonstration of the difference between cumulative selection against random selection. Dawkins came up with a better model; his biomorphs. Remember models are maps, reality is the territory.

    ETA missing “anything other than”

  18. dazz,

    IT HAS ZERO TO DO WITH LANGUAGE.

    Really? I can think of a few things it has to do with language. Lets see if you can get a clue 🙂 Your incompetent arrogance is somewhat charming.

  19. colewd:
    dazz,

    Really?I can think of a few things it has to do with language.Lets see if you can get a clue

    I’m sure you can make up some shit about the weasel and language, but that doesn’t change the fact that it was NOT about coming up with a meaningful sentence, let alone one in english in particular.

    colewd:
    dazz,
    Your incompetent arrogance is somewhat charming.

    Hahaha, your lack of self awareness is pathetic

  20. Alan Fox,

    Regarding “Weasel”, the program Dawkins came up with nearly 40 years ago is not considered by anyone, including Dawkins, as anything other than a simple demonstration of the difference between cumulative selection against random selection. Dawkins came up with a better model; his biomorphs. Remember models are maps, reality is the territory.

    ETA missing “anything other than”

    Point taken. The issue with Weasel is that it simulated similar sequence space to proteins with a rare solution representing a highly specified gene. I would like to understand box car better but I think it probably simulates population genetics well but has holes from an evolutionary perspective. Finding function through the sequence is tricky. My comment to Rum is sincere as he really tries and is competent. I just think you guys have a terrible hand in this argument. I also think Jock does a remarkable job with a pair of 2’s. 🙂

  21. colewd: I just think you guys have a terrible hand in this argument. I also think Jock does a remarkable job with a pair of 2’s.

    Yet I understood Jock’s math while you didn’t. You’re clearly innumerate and almost illiterate (will you ever get the difference between “than” and “then” or “your” and “you’re”?)

  22. dazz,

    I’m sure you can make up some shit about the weasel and language, but that doesn’t change the fact that it was NOT about coming up with a meaningful sentence, let alone one in english in particular.

    Not with a specific target but if you want to simulate a general solution as with box car then the language becomes important. It would be nice if your vision was a little further then your big toe 🙂

  23. colewd:

    To refute the claim you need to find a comprehensible english sentence from a random sequence of letters without a target.

    I have trouble conceiving of a simulated environment that emergently selects for genes encoded by sequences that form valid english sentences.

    But in a way that is exactly my point. That is both what makes Weasel a bad analogy to evolution, and what is wrong with your own thinking. You think there has to be targets, and that functional sequences are targets.

    Real evolution doesn’t have targets, so what evolves there was not somehow pre-specified before hand. The problem is you are considering the sequences we see in biology, such as protein sequences, to be “targets” towards which evolution had to be guided. As if they were sentences in English, being judged by some Great Reader by how well they convey some meaning.

    And you could be claiming the same thing for the car-chromosomes which result from 100 generations of the BoxCar2D simulation. And apply all the same arguments that you do for protein sequences, to the idea that the car chromosomes also had to be targets. In this way the car in the BoxCar2D simulation is analogous to a single protein.

    Which seem to be, essentially, that the total sequence space of car chromosomes is incredibly big, and most of them are useless assemblages of wheels and triangles that fall apart as soon as they hit the ground. We could be making the same arguments you do for protein sequences, for the car chromosomes.

    And yet we know there are no targets in the BoxCar2D simulation. And yet better and better cars incrementally evolve, where after something like 100 generations we end up with cars that work very well. And we can then go and look at the car chromosome of some car that results from 100 generations of evolution in the simulation, and see that it is some extremely unlikely combination. So how did it evolve without being a target?

  24. if you want to see something curious in the BoxCar2D algorithm, try turning wheels off entirely by putting the “wheel freq.” to 0.

    Then go and pick the Terrain called “The Peak” in the input seed / choose terrain option.

    Now let it evolve. The selection criterion of the algorithm is of course the ability of the car to move to the right, so what happens when there are no wheels?

    Well, now the cars spawn as random assemblages of triangles, and they have this funny property of being able to fall apart, or tip over because they’re unbalanced, when they hit the ground. But they don’t have wheels to propel them, so surely movement to the right can’t evolve?

    Well, the simulation starts with the “car” being dropped from a bit above the ground, so now if there is some chance ability to turn that downward force into movement to the right, if the triangle assembly is structured int he right way, for that ability will be selected for.

    At generation 23, I had it sliding down the hill.

  25. Rumraket: And we can then go and look at the car chromosome of some car that results from 100 generations of evolution in the simulation, and see that it is some extremely unlikely combination

    And let’s see if Billy-Genius can enlighten us on how that sequence relates to language.

  26. Rumraket: At generation 23, I had it sliding down the hill.

    It’s at generation 42 now, and it’s an octagon, essentially the best approximation of a slightly off-balance wheel the simulation allows.

  27. Congratulations, Rumraket!
    You have demonstrated the power of Intelligent Selection, since you chose to set “wheel freq.” to 0.
    </IDist>

  28. We have achieved new heights today. I have never seen anyone claim that it matters that Weasel had a target that was a sentence in ENGLISH LANGUAGE before.
    Bill does realize that Weasel works for any 20 – 30 character string, including slowly changing ones, right?
    Perhaps not. He clearly fails to see that BoxCar2D generates gobs of FI without any target at all.
    On the topic of my disagreement with Bill, if he needs further experimental demonstration that he is wrong about his 50% rule, he should check out McLaughlin et al 2012

    This analysis indicates a heterogeneous, distributed and physically contiguous network of functional residues in PSD95pdz3 (Fig. 2b–d). Most positions show little effect on mutation, tolerating nearly every substitution even if radically different in chemical character

    Bill would expect 50% of all nearest neighbours to be completely nonfunctional. Not even close.

  29. Mung: Some people think proteins evolved from other proteins. Perhaps there is a LUCA for all extant proteins.

    Like how eyes evolvedfrom other eyes. And the LUCA of all extant eyes is something like a light-sensitive spot.

    Ha.

    The first protein was probably like a protein in soup. The most evolved protein must be a protein shake.

  30. DNA_Jock:
    Congratulations, Rumraket!
    You have demonstrated the power of Intelligent Selection, since you chose to set “wheel freq.” to 0.
    </IDist>

    I have a better one. Disabling wheels is a “loss of function” mutation, so it’s devolution, not evolution!

    Checkmate, atheists!

  31. I’m glad people are bringing up BoxCar2D in response to the absurd assertion that all the information in the target state has to already be present in the evolutionary algorithm in order for it to find that state. BoxCar2D is finds well-adapted solutions using only selection on whether the form moves rightwards. No details of design of the resulting form are included in the BoxCar2D program.

    A similar issue arises for artificial selection. Creationists and ID advocates commonly argue that it (a) isn’t a realistic model of natural selection and (b) the selection puts the information in, so it is Intelligent Design. But it isn’t ID, because all the selection does is judge whether there is improvement in the goal (say higher body weight, whatever we are selecting on). It does not provide any design details at all as to how the organism gets there. None.

    Finally, any computer simulation is called Intelligent Design, because we have to intelligently design the computer program. We intelligently design it, yes, but intelligently design it to mimic natural processes. A computer program can simulate erosion, or landslides, or Brownian Motion, or segregation of chromosomes in Mendelian inheritance. And no one then calls those natural phenomena the results of ID. But if we simulate any model of evolution, then suddenly we hear the argument that this only shows that the reaults can be achieved by intelligent design! No one argues that a computer model of erosion shows that erosion can only be achieved by intelligent design.

  32. It’s probable, so it has to have happened…If it is probable than it must have happened, as per evolutionary ideology… Evidence?

  33. Interesting how quickly the ID community tries to shift the burden of proof. If they are going to claim that something like the bacterial flagellum is improbable then they need to show their calculations. If the probabilities are unknowable then they are unknowable. You don’t get to insert a designer into the gaps in our knowledge.

  34. Joe Felsenstein,

    Finally, any computer simulation is called Intelligent Design, because we have to intelligently design the computer program. We intelligently design it, yes, but intelligently design it to mimic natural processes.

    What natural process do you think it mimics? Please describe how you think it mimics it?

  35. Joe Felsenstein,

    Finally, any computer simulation is called Intelligent Design, because we have to intelligently design the computer program.

    We also inserted functional information used to build the cars in the form of shapes and dimensions.

  36. T_aquaticus,

    Interesting how quickly the ID community tries to shift the burden of proof. If they are going to claim that something like the bacterial flagellum is improbable then they need to show their calculations.

    30000 amino acids that all need a secondary fold. Every 6 AA’s has a 31% chance of a secondary fold based on Jock’s hypothesis. 3^-5000 chance of a secondary fold. Smashing the 500 bit rule 🙂

  37. You’d think any designer worth his salt could make a protein space rich in function, so he could go off and play golf or something while organisms busy themselves navigating it.

  38. Allan Miller: You’d think any designer worth his salt could make a protein space rich in function, so he could go off and play golf or something while organisms busy themselves navigating it.

    A concept keiths never seemed capable of grasping. A designed space with designed pathways to traverse the space. Good for you.

  39. Mung: A concept keiths never seemed capable of grasping. A designed space with designed pathways to traverse the space. Good for you.

    So what are the others on about then? It needs tinkering, they say.

  40. T_aquaticus: You don’t get to insert a designer into the gaps in our knowledge.

    It’s ok as long as the Designer is Natural Selection.

    T_aquaticus: If the probabilities are unknowable then they are unknowable.

    Does that only apply to ID, or does it also apply to evolution? Are the probabilities of evolution unknowable?

  41. Joe Felsenstein: I’m glad people are bringing up BoxCar2D in response to the absurd assertion that all the information in the target state has to already be present in the evolutionary algorithm in order for it to find that state.

    Who has made that claim? I’m reading the posts in reverse order so maybe i just haven’t come across it yet.

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