Randomness and evolution

Here’s a simple experiment one can actually try. Take a bag of M&M’s, and without peeking reach in and grab one. Eat it. Then grab another and return it to the bag with another one, from a separate bag, of the same colour. Give it a shake. I guarantee (and if you tell me how big your bag is I’ll have a bet on how long it’ll take) that your bag will end up containing only one colour. Every time. I can’t tell you which colour it will be, but fixation will happen.

This models the simple population process of Neutral Drift. Eating is death, duplication is reproduction, and the result is invariably a change in frequencies, right through to extinction of all but one type. You don’t have to alternate death and birth; choose any scheme you like short of peeking in the bag and being influenced by residual frequencies (ie: frequency-dependent Selection), and you will end up with all one colour.

Is Chance a cause here? Well … yes, in a sense it is, in the form of sample error. Survival and reproduction are basically a matter of sampling the genes of the previous generation. More random samples are a distortion of the larger population than aren’t, so, inexorably, your future populations will move away from any prior makeup, increasing some at the expense of others till only one variant remains.

Selection is a consistent bias upon this basic process. If different colours also differed a little in weight, say, more of some would be at the bottom of the bag than others, so you’d be more likely to pick one type than another. In more trials, the type more likely to be picked would be picked more often, to express it somewhat tautologously. You’d get a sampling bias.

Both of these processes are random – or stochastic, to use the preferred term. In reality, they are variations of the same process, with continuously varying degrees of bias from zero upwards. It makes no sense to call selection nonrandom, unless by ‘random’ you mean unbiased. Where there is no bias, all is Drift. But turning up the selective heat does not eliminate drift – sample error – and so does not eliminate stochasticity.

With a source of new variation, these processes render evolution inevitable. Even with a brand new mutation, with no selective advantage whatsoever, 1/Nth of the time (where N is the population size) it will become the sole survivor. That’s the baseline. If there is a selective advantage, it will be more likely and quicker to fix, on the average. If at a selective disadvantage, it will be less likely and slower.

Conversely, without a source of new variation, all existing variation would be squeezed out of the population, and evolution would stop.

650 thoughts on “Randomness and evolution

  1. Alan Fox: Another case of violent agreement?

    Apparently not. The average turnover for any population size is the total of individual generation times divided by the total population number. To me this seems a very simple idea. Individual variations (age on giving birth, number of live births) are used to compute an individual’s generation time and average of a population (or a representative sample) is independent of population size.

    Am I missing something?

    Yes, you are missing the fact that time has nothing to do with it. The selecting of the M&M’s could represent one week or one year or 10 years. It is simply a reflection of the turnover of the population. Like when you see a playground full of mothers playing with their daughters. There might be ten mothers there and ten daughters. The mothers represent the first generation and the daughters the second generation. Now the kids grow up and are all ready to have babies, some are going to have slightly less and some perhaps slightly more.

    To keep it simple as a concept we say, ok, what if the one baby with freckles has two babies and everyone else has only one baby, and one of the girls has no babies at all. The girl with freckles adds two babies to the next generation, and the 9 girls without freckles add 8 babies. The next generation has a slightly different composition than the last one. Get it?

  2. petrushka: Your revierwer says Shapiro makes a case that mutations ” (arising irrespective of potential need) ” are insufficient. He is wrong about biology and wrong about what Shapiro says.

    I think that’s out of context for what I quoted, which ended with “…and has discussed a wide variety of mechanisms by means of which, in some degree, genetic change is evoked in direct response to environmental challenge.” Wilkins doesn’t say he agrees with all this, but thinks the book is worth reading, and I intend to.

  3. phoodoo: 10 births, 10 deaths, one generation. I told you this from the very beginning.

    I don’t think so. Here, for instance, you clearly indicate otherwise:

    phoodoo: Olegt contends that each round of the M&M game where you eat one, and then double another represents 1/N of a generation. If there are ten in the population, you need to do this ten times to equal one generation on average.

    Do you agree with that concept, or do you agree with my concept that one drawing of the M&M’s has to equal one generation?

    Will the real phoodoo please stand up?

  4. Allan Miller,

    Making a code does absolutely nothing to solve the problem of having the code be logically correct.

    Each generation can only have a slight shifting of the balance of genes-unless you just rig the game to make it totally unrealistic. A game which says the entire populations genes can by totally reversed in one generation is just a meaningless computer trick.

  5. phoodoo: My contention all along has been that the drawing of the M&M’s has to represnt one turnover of the population, where in each of the ten M&M’s is replaced by a duplicate, except for one which looses a replacement, and one which gains two replacements.

    It has seemed obvious to me, all along, that a drawing represented one death (the M&M that was eaten) and one birth (the M&M that was duplicated). One death and one birth is not a generation. You need a turn over of the whole population, not just one member, to have a generation.

    You might have a valid point, that the experiment was not adequately explained at the start.

  6. olegt: I don’t think so. Here, for instance, you clearly indicate otherwise:

    Will the real phoodoo please stand up?

    There is zero contradiction there! One drawing equals ten dying, and ten births. My position hasn’t changed at all! The eating is not the dying, the eating is the ONE who doesn’t reproduce, while the doubling is the one who reproduces a little extra. Geez.

  7. phoodoo: And you are a great mathematician, right Joe?

    Well, he is a Professor of Genome Sciences and of Biology and
    Adjunct Professor of Computer Science and of Statistics who uses Markov Chain Monte Carlo methods in his research. Not that it matters.
    Since you brought it up, what do you do? Not that it affects the validity of your argument, of course, I’m just curious.

    Phoodoo wrote:

    My contention all along has been that the drawing of the M&M’s has to represnt one turnover of the population, where in each of the ten M&M’s is replaced by a duplicate, except for one which looses a replacement, and one which gains two replacements. This is a completed generation!

    Well there’s your problem right there, phoodoo.
    [/auto mechanic]
    Each of your “generation”s has N-1 M&M’s magically replicating themselves 1-to-1, with zero stochastic variation in fecundity. To every one birth/death, you are magically adding N – 1 birth/deaths that you have stipulated cause zero change.
    That makes no sense whatsoever.
    We all agree that the # of births/deaths to fixation scales with N x N, but you seem to be unable to grasp that the amount of time that fixation would take scales with N x N / N, that is, with N.
    Next up, the fact that time-to-fixation scales with N does not mean that the number of neutral alleles that fix per unit time scales with 1 / N. Baby steps.

  8. Neil Rickert: I think the reviewer has either misunderstood Shapiro, or has misunderstood how the expression “random mutation” is used in biology.

    When biologists say that mutations are random, they do not mean that they occur at the same rate at every location in the genome.That is, they do not claim a uniform distribution.There are some locations in the genome where any mutation is likely to be fatal.There are other locations where a mutation is likely to affect fitness, either for the better or the worse.It is in that latter case, where mutations are more likely to occur.And I think that is all that Shapiro is saying.It does not disagree with the standard view.

    I don’t think there is any misunderstanding here. The reviewer knows his material. Shapiro’s argument apparently goes a lot deeper than what your’re letting on or there would not be a controversy over his book.

  9. phoodoo: Yes, you are missing the fact that time has nothing to do with it.

    Obviously not in the simulation as it is a variable we can play with. This is trivial.

  10. Neil Rickert: It has seemed obvious to me, all along, that a drawing represented one death (the M&M that was eaten) and one birth (the M&M that was duplicated).One death and one birth is not a generation.You need a turn over of the whole population, not just one member, to have a generation.

    You might have a valid point, that the experiment was not adequately explained at the start.

    We do have a whole turnover each time. Its just that during that turnover one got a slight reproduction edge. Each drawing starts with a slightly shifted demographic, that is why each drawing is a new generation.

  11. Piltdown2: I don’t think there is any misunderstanding here. The reviewer knows his material. Shapiro’s argument apparently goes a lot deeper than what your’re letting on or there would not be a controversy over his book.

    Perhaps you can point to a particular location in his book (which I have read and I still have the Kindle version available).

  12. Alan Fox: Obviously not in the simulation as it is a variable we can play with. This is trivial.

    You can play with the variables and call it any amount of time you wish. You can’t play with the variables and say that ONE ancestor has ten successive descendants, and we do nothing to the rest of the population to compensate for the fact that ONE is having generation after generation. That is pure silliness.

  13. First we had this:

    phoodoo: Olegt contends that each round of the M&M game where you eat one, and then double another represents 1/N of a generation. If there are ten in the population, you need to do this ten times to equal one generation on average.

    Do you agree with that concept, or do you agree with my concept that one drawing of the M&M’s has to equal one generation?

    In this comment phoodoo clearly defines one drawing , a.k.a. one round, as a replacement of one M&M.

    phoodoo: There is zero contradiction there! One drawing equals ten dying, and ten births. My position hasn’t changed at all! The eating is not the dying, the eating is the ONE who doesn’t reproduce, while the doubling is the one who reproduces a little extra. Geez.

    Now he defines one drawing as a replacement of N M&Ms.

    No contradiction whatsoever. No Sir.

    Which one is it, phoodoo?

  14. phoodoo: You can play with the variables and call it any amount of time you wish. You can’t play with the variables and say that ONE ancestor has ten successive descendants, and we do nothing to the rest of the population to compensate for the fact that ONE is having generation after generation. That is pure silliness.

    The silliness is all yours, phoodoo. No one says that this is the only way for fixation to occur in a population of 10. It is one possible scenario but not the only one and not even the typical scenario.

  15. phoodoo: You can play with the variables and call it any amount of time you wish.You can’t play with the variables and say that ONE ancestor has ten successive descendants, and we do nothing to the rest of the population to compensate for the fact that ONE is having generation after generation.That is pure silliness.

    That’s what averaging is about. There is a statistical mean (in any theoretical or real population) that can be approached by taking larger and larger samples. Individuals may lie a long way outside the mean.

  16. olegt:
    First we had this:

    In this comment phoodoo clearly defines one drawing , a.k.a. one round, as a replacement of one M&M.

    Now he defines one drawing as a replacement of N M&Ms.

    No contradiction whatsoever. No Sir.

    Which one is it, phoodoo?

    Could it be the light bulb in the Creationist’s cranium has finally started to glow a little? We’ll see.

  17. DNA_Jock,

    No that’s BS DNA. Joe’s paper on his wall, or his frat handshake, do nothing to improve the logic being employed.

    Of course you can add some more stochastic variation into the process. You could pull out two M&M’s, and allow one to have 3 babies if you want. You can allow 6 to have no babies, and four to have ten babies. It just depends how far you want to stretch the law of averages. It doesn’t change it from being a generation each time.

    The original premise just uses a slight shift of one each time to make it simpler to understand. Make it 3 if you want. Make it four. Who decides how much imbalance in breeding you want to assume each round? It still has to be one generation.

  18. thorton: Could it be the light bulb in the Creationist’s cranium has finally started to glow a little?

    *looks sternly at Thorton*

  19. As an aside, phoodoo, both my ‘variant’ and my ‘standard’ models run through every M&M in the bag, either keeping it, or culling it and replacing it with another M&M from the bag. Based on my understanding of how M&Ms reproduce in the wild 🙂 , one cycle through the bag represents one generation. The ‘standard’ model selects the new color at random from the bag. In the ‘variant’ model, I select the new color from amongst the offspring (i.e. a parent has more than one surviving child). The reason it fixes so fast is that I don’t shuffle the order of the M&M’s between generations.
    Humm, I think I’ll randomly ‘cut’ the deck after each generation. That should do the trick…

  20. phoodoo: It doesn’t change it from being a generation each time.

    Which time? The time taken on average for the population to turn over once or something else?

  21. phoodoo:

    The original premise just uses a slight shift of one each time to make it simpler to understand.

    It worked too, all except for one particularly rice farmer.

    It still has to be one generation.

    Where one generation still means one turn over of the whole population.

  22. Alan Fox: That’s what averaging is about. There is a statistical mean (in any theoretical or real population) that can be approached by taking larger and larger samples. Individuals may lie a long way outside the mean.

    Of course. We could do the same thing with a million. Each time take out ten, and double another twenty. You can make the numbers as confusing and random as possible. You still start with a new population demographic with each generation. You can’t be selecting between someone from someone seven generations ago, at the same time as 8 generations are all alive at the same time to be selected from. Or twenty or 100 generations.

    You must be selecting from people of the same assumed time period.

  23. Neil Rickert: Perhaps you can point to a particular location in his book (which I have read and I still have the Kindle version available).

    I have the Kindle book also, and I have cited the exact location where Shapiro states categorically that mutation does not anticipate need.

    What Shapiro does — which some interpret as IDish — is assert that evolution is smarter than random higgledy piggledy. That’s pretty mainstream. No one denies that evolvability has evolved. He compares it to the immune system, and we have lots of partial or lesser immune systems demonstrating possible scenarios for evolving.

    If intelligent or non-random behavior were the hallmark of a designed system, we would not have to look at mutation. We could look at brains. Or Venus flytraps.

    I think it would be a great ID research project to demonstrate that it is even possible — in principle — to foresee the outcome of a mutation. Outcome at the level of chemistry, outcome at the level of phenotype, and outcome at the level of reproductive success.

    That would be a cool ID research project.

    I wonder why, in the 200 years since Paley, that no one in the ID movement has proposed or even mentioned such a project.

  24. DNA_Jock:
    As an aside, phoodoo, both my ‘variant’ and my ‘standard’ models run through every M&M in the bag, either keeping it, or culling it and replacing it with another M&M from the bag. Based on my understanding of how M&Ms reproduce in the wild , one cycle through the bag represents one generation. The ‘standard’ model selects the new color at random from the bag. In the ‘variant’ model, I select the new color from amongst the offspring (i.e. a parent has more than one surviving child). The reason it fixes so fast is that I don’t shuffle the order of the M&M’s between generations.
    Humm, I think I’ll randomly ‘cut’ the deck after each generation. That should do the trick…

    And so what? That is a completely different idea then selecting one each time isn’t it. Because each time you select, you are not allowing the same one to be selected again. It only can be selected once per round. That is NOT what happens with Olegts notion., and not how the original game was played.

    That is a completely different concept, if you can get your head around it.

    Go ahead and play another computer simulation game if you want. It has zero to do with this one.

  25. phoodoo: Go ahead and play another computer simulation game if you want. It has zero to do with this one.

    But the concept of population turnover as deriving from an average of individual “births” and “deaths” is the same in all such sims, I suspect.

  26. olegt:
    First we had this:

    In this comment phoodoo clearly defines one drawing , a.k.a. one round, as a replacement of one M&M.

    Now he defines one drawing as a replacement of N M&Ms.

    No contradiction whatsoever. No Sir.

    Which one is it, phoodoo?

    Replacing one with two, represents the slight increase one random member gets in reproducing during each generation! Each M&M could represent a set of 1000 M&M’s and the concept is still the same. So 1000 (one M&M) got a slight increase in frequency for that generation, and 9000 (9 M&M’s) experienced a slight decrease.

    There is no contradiction, Four does not equal one.

  27. keiths:
    Piltdown2,

    You misread my question.Option B is that the designer mimics macroevolution, not that macroevolution mimics a designer:

    Remember, a designer can take many, many paths that aren’t open to unguided evolution.Hence my other questions:

    No, I didn’t misread the question, just making a play on words at the end. I took it at face value that you were asking me to choose between 2 scenarios knowing that I did not necessarily agree with the premise (Macroevolution appears to be unguided). Maybe I’m thinking of the word “unguided” differently that you, but macroevolution results in organisms being better adapted to their environment, so the environment may provide some degree of guidance.

    As to your other questions:

    How do you explain the fact that out of zillions of alternative design patterns, the designer chose one of the very few that we would expect to see if macroevolution were in fact unguided?

    I’m fine with common descent explaining most of the nested hierarchy we see.

    Is the designer shy and attempting to hide? Is the designer a big fan of evolution who wants to emulate it?

    Could be the designer is hiding in plain sight if some form of design mechanism is built into our cells (and we may be thinking of “designer” in different terms).

  28. phoodoo: Replacing one with two, represents the slight increase one random member gets in reproducing during each generation! Each M&M could represent a set of 1000 M&M’s and the concept is still the same.

    Oh, what a tangled web we weave! 🙂

    Fine, you seem to have changed your mind and now accept that one generation = N deaths. Which is what all of us here (except you) have been using as a definition of a generation all along.

    Can we now hold hands and sing Kumbaya?

  29. phoodoo,

    Yea, your game would do that. that is the whole problem with your game. You are starting to make assumptions that we don’t know are true or not. Your game starts to assume that the black mutation happens often. maybe the black mutation happens in 10% of the population. But we have no way of concluding that. Maybe the black mutation is so rare it only happens in .01% of the population, so in a small population we never expect it to happen twice.

    So that’s your game, and that;’s why you don’t have the right to make assumption about evolution, that you don’t know if they are true.

    My program says every black mutant gets wiped out every third drawing of an M&M. Does that disprove your game? You can make up any game you want, it doesn’t mean your conclusions are valid.

  30. olegt: Oh, what a tangled web we weave!

    Fine, you seem to have changed your mind and now accept that one generation = N deaths. Which is what all of us here (except you) have been using as a definition of a generation all along.

    Can we now hold hands and sing Kumbaya?

    No No, nothing has changed. You can’t get out of it that easy. I stated over and over EXACTLY my premise that each drawing represented a turnover of the entire population. You claimed it doesn’t. And yet it must, to make any sense at all.

    Each drawing represents ONE generation. Your logic simply can’t work, if you put all the M&M.s back in the bag for each drawing.

  31. Piltdown2:

    I’m fine with common descent explaining most of the nested hierarchy we see.

    Could be the designer is hiding in plain sight if some form of design mechanism is built into our cells (and we may be thinking of “designer” in different terms).

    Of course the designer is hiding in plain sight. The designer is evolution.

    Do we know everything about it? Of course not. Do we know that chemistry itself was not designed to make it possible for evolution to work? How could we know that?

    But ID advocates make the design metaphor by citing humans as exemplars of designers, and humans cannot design novel biology. May never be able to design biology without copying what already exists, of by evolving new biology under controlled conditions.

    We do not have any evidence that it is even possible to know — in principle — how to anticipate emergent properties. Human invention proceeds by taking what is known and making variations and combinations. Trial and error at the edge of what is known.

    The ID/evolution “debate” centers on two assertions that are not necessarily related.

    One is the “fact” of evolution. That would be the history of life and common descent. Common descent could be true, but could also be the result of continuous intervention.

    The other prong of the debate is over “random” mutation. This has been studied for a hundred an fifty years. There is no reason whatever to believe there is a way to anticipate what mutations will be beneficial. As far as the eye can see, populations test every possible change and keep those that are not fatal.

  32. Piltdown2: the environment may provide some degree of guidance.

    If I were a theist, I could reconcile the apparently unguided process of evolution as environmental design. God only has to guide the environment and the rest follows.

  33. Neil Rickert: Perhaps you can point to a particular location in his book (which I have read and I still have the Kindle version available).

    I’m at a little bit of a disadvantage here since, as I’ve already indicated, I don’t have the book. That’s why I referenced a review of the book and not the book itself. Here’s another link if the first one was bad: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3342868/
    And here’s another quote: “Yet, the book’s contention that natural selection’s importance for evolution has been hugely overstated represents a point of view that has a growing set of adherents.” Again, Wilkins makes it clear that he doesn’t agree with many of Shapiro’s conclusions.
    Once I get the book I’ll let you know and we can discuss.

  34. phoodoo: I stated over and over EXACTLY my premise that each drawing represented a turnover of the entire population. You claimed it doesn’t.

    That’s not the scenario described in the original post, which is one baby being born per turn.

  35. Alan Fox: If I were a theist, I could reconcile the apparently unguided process of evolution as environmental design. God only has to guide the environment and the rest follows.

    I think most ID’st believe some version of this. Or that there is an inherent mechanism within all organisms that assists them is progressing their own evolution, that we simply have not completely uncovered yet.

    Since there is so much we really don’t understand about how the genome works, and how epigenetics work, it is entirely plausible.

  36. Zachriel: That’s not the scenario described in the original post, which is one baby being born per turn.

    I agree it wasn’t, and that is the fault of whoever had that idea. It simply must represent a percentage of an extra birth to one random segment. And that is why I corrected it. Because it is totally illogical otherwise.

  37. petrushka: As far as the eye can see, populations test every possible change and keep those that are not fatal.

    It may be worth rethinking this statement. Natural selection does not have the opportunity to act on every possible change, only those changes that actually occur.

  38. phoodoo: I think most ID’st believe some version of this.Or that there is an inherent mechanism within all organisms that assists them is progressing their own evolution, that we simply have not completely uncovered yet.

    Since there is so much we really don’t understand about how the genome works, and how epigenetics work, it is entirely plausible.

    Well said.

  39. Piltdown2: It may be worth rethinking this statement.Natural selection does not have the opportunity to act on every possible change, only those changes that actually occur.

    The Lenski experiment, confined to a small laboratory for only a couple of decades, pretty nearly exhausted the possibilities for point mutations. (This is based on sampled data, so it’s possible the Designer’s finger was stirring the soup.)

    The important question — which Shapiro explicitly addresses — is whether variation is produced by a mechanism that can anticipate the consequences of a variation. Shapiro says this is impossible.

    The question is not whether design is being done, but whether the process is using Braille rather than foresight.

  40. phoodoo: No No, nothing has changed. You can’t get out of it that easy. I stated over and over EXACTLY my premise that each drawing represented a turnover of the entire population. You claimed it doesn’t.

    LOL. Just to make sure, phoodoo, do you agree with me that 1 generation = N deaths?

    I have been saying that since page 2 of this thread. Here, for example, and here and here.

    And here are you, on page 3:

    Every death and birth substitution is one generation, ok, go with that.

    Heh

  41. If you wish to assert that some process within the cell “knows” what mutation to produce when needed, then propose some research to demonstrate this. Shapiro doesn’t.

    Simply demonstrate that it is possible to anticipate emergent properties in chemistry.

    ETA:

    You could start with something simple like demonstrating you can predict the properties of water from the properties of hydrogen and oxygen. Then you could work up to predicting the effects of a base change in a protein coding sequence.

    Having done that, you could then demonstrate how you can predict the effect of a regulatory sequence change affects the tail feathers of a peacock and his mating success.

    Then demonstrate how you balance the effect of the feathers on the birds’s ability to live and prosper.

  42. phoodoo,

    Making a code does absolutely nothing to solve the problem of having the code be logically correct.

    Each generation can only have a slight shifting of the balance of genes-unless you just rig the game to make it totally unrealistic. A game which says the entire populations genes can by totally reversed in one generation is just a meaningless computer trick.

    I didn’t say one generation, I said N generations (converging on 2N).

    eta: (N, of course, being population size)

  43. petrushka:
    If you wish to assert that some process within the cell “knows” what mutation to produce when needed, then propose some research to demonstrate this. Shapiro doesn’t.

    Simply demonstrate that it is possible to anticipate emergent properties in chemistry.

    I’m not at all saying the cell knows which mutation to produce. What I saw was that beneficial mutations may be more likely than simple random variation would predict in response to environmental pressures.

  44. petrushka: The important question — which Shapiro explicitly addresses — is whether variation is produced by a mechanism that can anticipate the consequences of a variation. Shapiro says this is impossible.

    You really think this is the important question?

  45. Alan Fox,

    phoodoo: Yes, you are missing the fact that time has nothing to do with it.

    Alan F: Obviously not in the simulation as it is a variable we can play with. This is trivial.

    Actually, it is a significant parameter, but it isn’t one we twiddle directly. Any version of the population consists of all the members ‘alive’ at that moment in time.

    From pop0, any future population popf,will have a distribution of generation counts at tf – each will have a different number of generations tracing back to their ancestor in pop0. Each would give a different account of how long a generation takes – it’s tf – t0 divided by their individual generation count. But the mean generation time for that succession of populations is clearly tf – t0 divided by the weighted mean of the generation counts of the entire population.

    Phoodoo is clearly attempting to weight matters in such a way that evolution is forbidden because of the case at one extreme. If a generation is 10 years, and in the extreme every birth could be a succession in the same lineage, it would ‘take too long’. But the extreme does not dictate the mean (any more than the other extreme, when every individual reproduces). For any run from t=0 to t=f, the mean generation time is whatever it is, not whatever the worst case is!

  46. Piltdown2: You really think this is the important question?

    It is the question that directly addresses what biologists mean when they say that mutation is random. Shapiro is clearly agreeing with what they mean, but he does not like their use of the word “random” with that meaning.

  47. phoodoo:
    phoodoo,

    Yea, your game would do that.that is the whole problem with your game.You are starting to make assumptions that we don’t know are true or not.Your game starts to assume that the black mutation happens often.maybe the black mutation happens in 10% of the population.But we have no way of concluding that.Maybe the black mutation is so rare it only happens in .01% of the population, so in a small population we never expect it to happen twice.

    Completely and utterly wrong. There is NO MUTATION in any of these models. I start with 1 black, and 999 white.

    So that’s your game, and that;’s why you don’t have the right to make assumption about evolution, that you don’t know if they are true.

    My program says every black mutant gets wiped out every third drawing of an M&M.Does that disprove your game?You can make up any game you want, it doesn’t mean your conclusions are valid.

    Well, in my program the black M&M gets wiped out in the first generation about one third of the time. If your model can wipe out every black M&M every third drawing of an M&M, then you appear to have made a mistake in your code. Would you like to exchange programs?

  48. Allan Miller,

    Actually, it is a significant parameter..

    I was thinking purely of simulations. Speed of runs, parallel computing using banks of computers or, in OMs sim, playing with the speed button..We are merely fast-forwarding, as we might if we had photos of all transitional species in identical poses and made a movie. We could play the movie fast or slow without affecting the ending.

    Sure real life is different and a prime argument employed against evolutionary theory is “there is not enough time”

    Phoodoo is clearly attempting to weight matters in such a way that evolution is forbidden because of the case at one extreme. If a generation is 10 years, and in the extreme every birth could be a succession in the same lineage, it would ‘take too long’. But the extreme does not dictate the mean (any more than the other extreme, when every individual reproduces). For any run from t=0 to t=f, the mean generation time is whatever it is, not whatever the worst case is!

    Is that right, phoodoo? I’m shocked!

  49. phoodoo: It simply must represent a percentage of an extra birth to one random segment.

    No. In the original scenario, there are exactly 64 individuals. First one reproduces, then another, then another. Which one is next is random. After 64 births, we count a generation. We could have all 64 reproduce simultaneously, then cull them afterwards, still counting one generation. The result would be similar.

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