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. Haha, reading the posts by phoodoo is like the encyclopedia of creationist claims straight off the talkorigins archive. A strange mix of “improbable therefore impossible”-type arguments and blind assertion fallacies. Science can’t prove this or that, proteins can’t do this or that, chihuahua’s can’t survive alone etc. etc.

    Who cloned Duane Gish and let him loose here? To address all the nonsensical assertions would take quite a substantial amount of posts, and all he has to do is simply blindly claim the things he do.

  2. phoodoo: Why do I think this matters?You really need to ask this?

    We are trying to make a model of how a NOVEL mutation, which is not deleterious, can drift through the population and become the norm.So we have to start with it being novel don’t we?Why weight the game so that the novel function has already spread equally throughout the population?Isn’t that obvious.

    Start with one, see where it goes.It will die every time.I can tell you that even without a little computer program.You have to begin the game being smarter than the machine or the machine is useless.

    Credit for making a falsifiable claim, at least. What will you say if someone produces a run in which the novel mutation is fixed?

  3. phoodoo: The more we learn, the less likely Darwinism becomes. The only people who can deny this are the “skeptics”; who quite profoundly possess zero skepticism

    Are you learning from those models you’re making?

  4. phoodoo: We are trying to make a model of how a NOVEL mutation, which is not deleterious, can drift through the population and become the norm. So we have to start with it being novel don’t we? Why weight the game so that the novel function has already spread equally throughout the population? Isn’t that obvious.

    Start with one, see where it goes. It will die every time. I can tell you that even without a little computer program. You have to begin the game being smarter than the machine or the machine is useless.

    I asked phoodoo how he knows that his conclusion is correct. He never responded. I suggested that he run a simulation to check if that is so. Silence.

    So I quickly whipped up a c++ code to see for myself. It starts with 99 MMs whose colors are randomly chosen to be red, green, and blue and adds 1 black MM. It then proceeds according to rules specified in the opening post.

    For instance, the first time it began with 31 red, 36 green, 32 blue, and 1 black MM. {31, 36, 32, 1} for short.

    After t=8783 iterations (each including the death of one MM and the birth of another, identical to a randomly chosen one), the distribution was {0, 0, 100, 0}: all MMs became blue. The code reported this as
    Run 1: {31, 36, 32, 1} at t=0; {0, 0, 100, 0} at t=8783;

    I ran this code 1000 times. Here are the first 10 runs:
    Run 1: {31, 36, 32, 1} at t=0; {0, 0, 100, 0} at t=8783;
    Run 2: {32, 37, 30, 1} at t=0; {100, 0, 0, 0} at t=5158;
    Run 3: {30, 35, 34, 1} at t=0; {100, 0, 0, 0} at t=9856;
    Run 4: {37, 27, 35, 1} at t=0; {0, 0, 100, 0} at t=1922;
    Run 5: {31, 35, 33, 1} at t=0; {0, 0, 100, 0} at t=17289;
    Run 6: {31, 29, 39, 1} at t=0; {0, 100, 0, 0} at t=4395;
    Run 7: {39, 34, 26, 1} at t=0; {0, 0, 100, 0} at t=3395;
    Run 8: {30, 37, 32, 1} at t=0; {100, 0, 0, 0} at t=5106;
    Run 9: {25, 33, 41, 1} at t=0; {100, 0, 0, 0} at t=8707;
    Run 10: {41, 26, 32, 1} at t=0; {0, 100, 0, 0} at t=4931;
    The population became all red, all green, or all blue. Not all black.

    Perhaps phoodoo was right?

    No.

    Here are records for runs 181 through 186:
    Run 181: {36, 31, 32, 1} at t=0; {100, 0, 0, 0} at t=6978;
    Run 182: {37, 27, 35, 1} at t=0; {100, 0, 0, 0} at t=4641;
    Run 183: {31, 34, 34, 1} at t=0; {0, 0, 100, 0} at t=21585;
    Run 184: {29, 39, 31, 1} at t=0; {0, 0, 0, 100} at t=9636;
    Run 185: {38, 30, 31, 1} at t=0; {0, 100, 0, 0} at t=10403;
    Run 186: {37, 32, 30, 1} at t=0; {0, 0, 100, 0} at t=4089;

    In run 184, the lone black MM spread out throughout the population. All MMs became black.

    The fixation of black MM occurred in runs 184, 247, 399, 491, 675, 913, 947, and 985. Eight runs out 1000. That’s close to the probability of fixation of 1/100, as estimated by several posters.

    You were wrong, phoodoo.

  5. phoodoo: Bacteria always return to the original form, dogs do, plants do, …

    Wait, what? What original form?
    What “original form” do you think dogs had? You know it was a wolf or a very close relative of modern wolves, right? But what was the “original form” of the wolf? Where did they come from? Were they created out of thin air? Have they always existed since the dawn of life on our planet? In your view is it possible that wolves arose from a similar-but-not exactly-same animal that previously existed? Then, in that case, what was that animal’s “original form” ? Why don’t wolves return to that previous form?

    If everything always returns to the “original form”, why are there still trees and shrubs in the forest when they were originally much simpler smaller forms? Original form of land plants. [wikipedia image]
    People are not creating/maintaining the breeding of every “kind” or “form” of large plant in the forest. How, in your view, is it possible for those “kinds” or “forms” to begin to exist in the first place, and how is it possible for them to continue to exist for tens of thousands of years without returning to their simple, small original form?
    You claim they always do
    But that’s not what we actually see in the natural world. Please explain why your claim does not match observed reality.

    What was the “original form” of Yersinia pestis? Was it created out of thin air in 5th century AD? If it had always existed in the exact same form, how did it suddenly become dangerous? It certainly wasn’t because of meddlesome human breeders altering its original form! Was it because your Designer meddled with its form? Why haven’t plague bacteria returned to their original form by now, as you claim they always do ?

  6. olegt: I asked phoodoo how he knows that his conclusion is correct. He never responded. I suggested that he run a simulation to check if that is so. Silence.

    So I quickly whipped up a c++ code to see for myself. It starts with 99 MMs whose colors are randomly chosen to be red, green, and blue and adds 1 black MM. It then proceeds according to rules specified in the opening post.

    For instance, the first time it began with 31 red, 36 green, 32 blue, and 1 black MM. {31, 36, 32, 1} for short.

    After t=8783 iterations (each including the death of one MM and the birth of another, identical to a randomly chosen one), the distribution was {0, 0, 100, 0}: all MMs became blue. The code reported this as
    Run 1: {31, 36, 32, 1} at t=0; {0, 0, 100, 0} at t=8783;

    I ran this code 1000 times. Here are the first 10 runs:
    Run 1: {31, 36, 32, 1} at t=0; {0, 0, 100, 0} at t=8783;
    Run 2: {32, 37, 30, 1} at t=0; {100, 0, 0, 0} at t=5158;
    Run 3: {30, 35, 34, 1} at t=0; {100, 0, 0, 0} at t=9856;
    Run 4: {37, 27, 35, 1} at t=0; {0, 0, 100, 0} at t=1922;
    Run 5: {31, 35, 33, 1} at t=0; {0, 0, 100, 0} at t=17289;
    Run 6: {31, 29, 39, 1} at t=0; {0, 100, 0, 0} at t=4395;
    Run 7: {39, 34, 26, 1} at t=0; {0, 0, 100, 0} at t=3395;
    Run 8: {30, 37, 32, 1} at t=0; {100, 0, 0, 0} at t=5106;
    Run 9: {25, 33, 41, 1} at t=0; {100, 0, 0, 0} at t=8707;
    Run 10: {41, 26, 32, 1} at t=0; {0, 100, 0, 0} at t=4931;
    The population became all red, all green, or all blue. Not all black.

    Perhaps phoodoo was right?

    No.

    Here are records for runs 181 through 186:
    Run 181: {36, 31, 32, 1} at t=0; {100, 0, 0, 0} at t=6978;
    Run 182: {37, 27, 35, 1} at t=0; {100, 0, 0, 0} at t=4641;
    Run 183: {31, 34, 34, 1} at t=0; {0, 0, 100, 0} at t=21585;
    Run 184: {29, 39, 31, 1} at t=0; {0, 0, 0, 100} at t=9636;
    Run 185: {38, 30, 31, 1} at t=0; {0, 100, 0, 0} at t=10403;
    Run 186: {37, 32, 30, 1} at t=0; {0, 0, 100, 0} at t=4089;

    In run 184, the lone black MM spread out throughout the population. All MMs became black.

    The fixation of black MM occurred in runs 184, 247, 399, 491, 675, 913, 947, and 985. Eight runs out 1000. That’s close to the probability of fixation of 1/100, as estimated by several posters.

    You were wrong, phoodoo.

    Wonderful, thank you, olegt.

  7. olegt: I asked phoodoo how he knows that his conclusion is correct. He never responded. I suggested that he run a simulation to check if that is so. Silence.

    So I quickly whipped up a c++ code to see for myself. It starts with 99 MMs whose colors are randomly chosen to be red, green, and blue and adds 1 black MM. It then proceeds according to rules specified in the opening post.

    For instance, the first time it began with 31 red, 36 green, 32 blue, and 1 black MM. {31, 36, 32, 1} for short.

    After t=8783 iterations (each including the death of one MM and the birth of another, identical to a randomly chosen one), the distribution was {0, 0, 100, 0}: all MMs became blue. The code reported this as
    Run 1: {31, 36, 32, 1} at t=0; {0, 0, 100, 0} at t=8783;

    I ran this code 1000 times. Here are the first 10 runs:
    Run 1: {31, 36, 32, 1} at t=0; {0, 0, 100, 0} at t=8783;
    Run 2: {32, 37, 30, 1} at t=0; {100, 0, 0, 0} at t=5158;
    Run 3: {30, 35, 34, 1} at t=0; {100, 0, 0, 0} at t=9856;
    Run 4: {37, 27, 35, 1} at t=0; {0, 0, 100, 0} at t=1922;
    Run 5: {31, 35, 33, 1} at t=0; {0, 0, 100, 0} at t=17289;
    Run 6: {31, 29, 39, 1} at t=0; {0, 100, 0, 0} at t=4395;
    Run 7: {39, 34, 26, 1} at t=0; {0, 0, 100, 0} at t=3395;
    Run 8: {30, 37, 32, 1} at t=0; {100, 0, 0, 0} at t=5106;
    Run 9: {25, 33, 41, 1} at t=0; {100, 0, 0, 0} at t=8707;
    Run 10: {41, 26, 32, 1} at t=0; {0, 100, 0, 0} at t=4931;
    The population became all red, all green, or all blue. Not all black.

    Perhaps phoodoo was right?

    No.

    Here are records for runs 181 through 186:
    Run 181: {36, 31, 32, 1} at t=0; {100, 0, 0, 0} at t=6978;
    Run 182: {37, 27, 35, 1} at t=0; {100, 0, 0, 0} at t=4641;
    Run 183: {31, 34, 34, 1} at t=0; {0, 0, 100, 0} at t=21585;
    Run 184: {29, 39, 31, 1} at t=0; {0, 0, 0, 100} at t=9636;
    Run 185: {38, 30, 31, 1} at t=0; {0, 100, 0, 0} at t=10403;
    Run 186: {37, 32, 30, 1} at t=0; {0, 0, 100, 0} at t=4089;

    In run 184, the lone black MM spread out throughout the population. All MMs became black.

    The fixation of black MM occurred in runs 184, 247, 399, 491, 675, 913, 947, and 985. Eight runs out 1000. That’s close to the probability of fixation of 1/100, as estimated by several posters.

    You were wrong, phoodoo.

    No, I said a starting population of 1000. And then try adding in a virus which kills off thirty percent of the population randomly. The closer you get it to reality the farther away your goal will get.

    Furthermore, it is estimated you need a population of closer to 2000 to have a good likelihood of that population not going extinct.

  8. phoodoo: You were wrong, phoodoo.

    No, I said a starting population of 1000. And then try adding in a virus which kills off thirty percent of the population randomly. The closer you get it to reality the farther away your goal will get.

    Maybe if you ask instead of whine, olegt will share xis exact code and you can then run it yourself with your desired 1000 instead of 100.

    Will you, or do you prefer to be seen as a pointless whiner, carping instead of doing the work?

  9. Viruses that kill 30 percent of populations are really the norm, you know. Happens all the time.

  10. phoodoo: No, I said a starting population of 1000.

    Sure, phoodoo. I have just run the same code with populations of 1000 MMs. Here is an excerpt from the output:

    Run 1168: {316, 332, 351, 1} at t=0; {1000, 0, 0, 0} at t=1336055;
    Run 1169: {330, 355, 314, 1} at t=0; {0, 1000, 0, 0} at t=1750295;
    Run 1170: {344, 321, 334, 1} at t=0; {0, 0, 1000, 0} at t=145398;
    Run 1171: {318, 342, 339, 1} at t=0; {0, 0, 1000, 0} at t=2663251;
    Run 1172: {332, 331, 336, 1} at t=0; {0, 0, 0, 1000} at t=1556280;
    Run 1173: {326, 332, 341, 1} at t=0; {1000, 0, 0, 0} at t=299787;
    Run 1174: {360, 324, 315, 1} at t=0; {1000, 0, 0, 0} at t=301662;
    Run 1175: {317, 342, 340, 1} at t=0; {0, 1000, 0, 0} at t=525590;

    In run 1172, the sole black MM took over the population. The probability of that happening was 1/1000, so it is not surprising to see the run number.

    You’re wrong, my friend.

  11. olegt,

    You didn’t hear me very well, Do the experiment like it was first suggested. It starts with five colors.

  12. Like I said Olegt, the closer you get to reality, the further you get to you goal. Its doesn’t surprise me one bit you would try to manipulate it as much as you could to try to get the result you want, because your are not really a scientist, you are a preacher.

  13. phoodoo: You didn’t hear me very well, Do the experiment like it was first suggested. It starts with five colors.

    LOL. You can run, phoodoo, but you can’t hide.

    Let’s start with 999 MMs randomly assigned five colors (red, green, blue, yellow, and brown). Add 1 black MM. The probability of fixation remains the same, 1/1000.

    Sure enough, here are excerpts from the output:

    Run 1054: {213, 184, 192, 207, 203, 1} at t=0; {0, 0, 0, 1000, 0, 0} at t=255390;
    Run 1055: {201, 215, 193, 197, 193, 1} at t=0; {0, 0, 1000, 0, 0, 0} at t=2553259;
    Run 1056: {194, 208, 203, 197, 197, 1} at t=0; {0, 0, 0, 0, 0, 1000} at t=1556280;
    Run 1057: {195, 197, 198, 202, 207, 1} at t=0; {1000, 0, 0, 0, 0, 0} at t=318359;
    Run 1058: {209, 206, 204, 194, 186, 1} at t=0; {0, 0, 1000, 0, 0, 0} at t=747326;

    Run 1842: {201, 203, 206, 199, 190, 1} at t=0; {0, 0, 1000, 0, 0, 0} at t=1389824;
    Run 1843: {181, 189, 230, 192, 207, 1} at t=0; {0, 0, 1000, 0, 0, 0} at t=319021;
    Run 1844: {203, 196, 185, 220, 195, 1} at t=0; {0, 0, 0, 0, 0, 1000} at t=798428;
    Run 1845: {200, 201, 213, 197, 188, 1} at t=0; {0, 0, 0, 0, 1000, 0} at t=689841;
    Run 1846: {202, 202, 204, 200, 191, 1} at t=0; {1000, 0, 0, 0, 0, 0} at t=285106;

    Run 2196: {192, 203, 216, 192, 196, 1} at t=0; {0, 1000, 0, 0, 0, 0} at t=344892;
    Run 2197: {193, 203, 203, 208, 192, 1} at t=0; {0, 0, 0, 1000, 0, 0} at t=444397;
    Run 2198: {189, 201, 210, 195, 204, 1} at t=0; {0, 0, 0, 0, 0, 1000} at t=583474;
    Run 2199: {192, 225, 207, 169, 206, 1} at t=0; {0, 0, 0, 1000, 0, 0} at t=1604035;
    Run 2200: {208, 181, 219, 188, 203, 1} at t=0; {0, 0, 0, 0, 1000, 0} at t=129059;

    Fixation occurs as expected!

  14. olegt,

    So we can conclude that in a population less than is needed for preventing extinction, we can expect a novel mutation to drift through that population in approximately on average 600,000 generations, without any other causes of competing mutations, and periods of rapid decline. If the population was 2000 I guess we could expect it to occur in about a million and a half generations, even without any other factors.

    So what we see is, in mammalian populations for example, drift is for all intents and purposes statistically impossible. Wow, impressive.

  15. phoodoo: Start with one, see where it goes.It will die every time.I can tell you that even without a little computer program.

    Brilliant! Creationism, starting with the conclusion and then just knowing it’s true without testing. And you better not bother testing… would be so inconvenient to discover you didn’t actually “know” what you wanted to.

    I guess mindless doctrinal statements of faith like these aren’t just for fun: http://i.imgur.com/kKsHA5x.gif

  16. phoodoo: So we can conclude that in a population less than is needed for preventing extinction, we can expect a novel mutation to drift through that population in approximately on average 600,000 generations, without any other causes of competing mutations, and periods of rapid decline. If the population was 2000 I guess we could expect it to occur in about a million and a half generations, even without any other factors.

    No, phoodoo, you cannot conclude that. Your inferred times are wrong. They should be divided by a factor of N, i.e., 1000 in my example.

    The t variable ticks up by 1 when a death occurs. In a population of N MMs, a death occurs every 1 unit of time. Therefore, a generation (the lifetime of a single MM) is N units of time. It took about 1000 generations for the fixation to occur.

  17. phoodoo:
    olegt,

    So we can conclude that in a population less than is needed for preventing extinction, we can expect a novel mutation to drift through that population in approximately on average 600,000 generations, without any other causes of competing mutations, and periods of rapid decline.If the population was 2000 I guess we could expect it to occur in about a million and a half generations, even without any other factors.

    So what we see is, in mammalian populations for example, drift is for all intents and purposes statistically impossible.Wow, impressive.

    So you were wrong in your initial claim and have now changed your tune to a different argument, one that still falls victim to the same basic fallacy.
    Improbable =/= impossible. A classic creationist fallacy.

    Of course, since all members of the population carry multiple neutral mutations (the average human carries over 100, every single one of us), chances are one will fix quite often due simply to drift. But please, don’t bother testing (like actual scientists do) .. it’s so easy to just start with your conclusion right?

  18. petrushka:
    Viruses that kill 30 percent of populations are really the norm, you know. Happens all the time.

    Good point. The 1918-1920 influenza pandemic was among the worst health disasters of all time.The mortality among infected people was somewhere between 10-20 percent; since about one-third of the human population was infected, the overall mortality was about 5 percent. And that horribly large figure of 5 percent mortality was with the absolutely maximum conditions for the spread of a pandemic: cities extra-crowded with war refugees, plus population with global travel (including flight) to spread the infection everywhere.

    30% mortality is not to be expected from any disease in any natural population nor any reasonable test model.

    The 1918 influenza epidemic does bring up another interesting point against phoodoo as well. Where did it come from?!?
    It was a spontaneous mutation in the previously-existing but previously not-infectious-to-humans H1N1 virus. Just like phoodoo’s single black M&M – which xe says cannot become dominant in the population, but which we have proved actually can and will in some trials – the sole mutant was then replicated among the existing population of virus. Until, bad luck to us, it became prevalent enough to spark a pandemic.

  19. phoodoo:
    Like I said Olegt, the closer you get to reality, the further you get to you goal.Its doesn’t surprise me one bit you would try to manipulate it as much as you could to try to get the result you want, because your are not really a scientist, you are a preacher.

    GUANO

  20. Allan Miller:
    SophistiCat,

    Interesting – how many runs did you do to establish the time to fixation? It’s pretty variable, as you can see from staring at Lizzie’s grid, so would need quite a few runs at each parameter to get a realistic distribution.

    I used 500 runs for each setup. The time remains variable – it doesn’t converge with the increase of runs. A smaller number of runs would probably do just as well, but I am too lazy/incompetent to do the math.

  21. phoodoo: Start with one, see where it goes.It will die every time.I can tell you that even without a little computer program.

    Brilliant! Creationism, starting with the conclusion and then just knowing it’s true without testing. And you better not bother testing… would be so inconvenient to discover you didn’t actually “know” what you wanted to.

    I guess mindless doctrinal statements of faith like these aren’t just for fun: http://i.imgur.com/kKsHA5x.gif

    Interesting. My prediction would have been that someone discussing this topic in good faith, per Lizzie’s rules, would have responded with “Hmm. Apparently my intuition about this is incorrect. Perhaps I should acquire more knowledge and reconsider my position. Thank you for taking the time to test my claim.” Clearly I need to reevaluate my mental model.

    By the way, the link doesn’t work for me (404).

  22. phoodoo:

    Start with one, see where it goes. It will die every time. I can tell you that even without a little computer program.

    Oops. That’s gotta hurt.

    Phoodoo, when you collide with reality, reality wins. Keep that in mind.

  23. keiths,

    It’s OK to make a mistake. You won’t learn if you don’t make mistakes.

    That said, I am far from certain that phoodoo has learned anything from this example. (I could be wrong, of course.)

  24. olegt,

    That said, I am far from certain that phoodoo has learned anything from this example.

    That’s the problem.

    And his/her childish accusation:

    Its doesn’t surprise me one bit you would try to manipulate it as much as you could to try to get the result you want, because your are not really a scientist, you are a preacher.

    Phoodoo, do you know how to program? If so, how about writing your own version, running it, and sharing your results (and your code) with us?

  25. Rumraket:

    …If what piltdown2 imagines was really true, the outcome of Lenski’s experiment should be impossible. Yet after 50.000 generations, we have a population with significantly superior fitness compared to the ancestral one and over 600 mutations have fixed in the population. Many of those directly contributed to an increase in fitness, i.e. they are beneficial mutations.

    Mutations that are considered beneficial in one set of environmental factors may be harmful in another environment. For example, from a 2009 paper on the Lenski experiment at http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2632098/ “In contrast to their fitness-enhancing effect in the environment where they evolved, both mutations decreased cellular resistance to osmotic stress. Moreover, one mutation reduced fitness during prolonged stationary phase. Therefore, alteration of the PBP2 concentration contributed to physiological trade-offs and ecological specialization during experimental evolution.” Also, an organism that thrives in laboratory conditions may not do so well in the wild, and I am not aware of any study that tested the Lenski-mutated bacteria in the wild.

  26. petrushka:
    Dop you have any evidence that deleterious mutations accumulate to the point where a population is endangered? Why are bacteria not extinct?

    Deleterious mutations will impact a population’s ability to adapt to changing environments which will lead to an endangered species. In this vein, bacteria in general are not extinct because they have an incredible ability to adapt to extremely diverse environments, but individual colonies or populations have gone extinct.

    In particular, how do you account for the hundreds of mutations fixed in the Lenski experiment?

    I’m fine with the standard evolutionary explanation for how mutations get fixed within an asexual population.

    Lenski’s population started from a single cell and underwent 58,000 generations. Why didn’t it go extinct.

    Lenski’s population did not go extinct because it had sustenance to survive. Even those samples that were unable to consume citrate still had glucose.

    Dou you have a quantitative model that accounts for this?

    Don’t see that this is necessary. To my knowledge, the experiment tested relative fitness, not extinction.

  27. Piltdown2: Mutations that are considered beneficial in one set of environmental factors may be harmful in another environment. For example, from a 2009 paper on the Lenski experiment at http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2632098/“In contrast to their fitness-enhancing effect in the environment where they evolved, both mutations decreased cellular resistance to osmotic stress. Moreover, one mutation reduced fitness during prolonged stationary phase. Therefore, alteration of the PBP2 concentration contributed to physiological trade-offs and ecological specialization during experimental evolution.”Also, an organism that thrives in laboratory conditions may not do so well in the wild, and I am not aware of any study that tested the Lenski-mutated bacteria in the wild.

    Absolutely correct, the effect of mutations depend on environment. But that’s how evolution works, there are no super-organisms that are perfectly adapted to all environments. Moving from one niche to another, organisms for the most part trade fitness in their previous environment for fitness to their new environment. You will notice that despite being a mammal, a dolphin have a terrible set of legs. It won’t ever outrun a terrestrial predator. Nevertheless, it still evolved. It doesn’t matter that it would die on land, that’s not where it lives.

    So really, this retort of yours is wholly irrelevant, both to the point you orignally made and to the plausibility of evolution in general. Lenski experiment proves that beneficial mutations happen and get fixed in populations. In so doing, it also demonstrates a key feature of the theory of evolution: adaptation through natural selection to the extant environment.

  28. Lizzie, my point is that The Lenski experiment involved hundreds of mutations that did not affect the viability of the colonies. Where’s the meltdown?

    More to the point, Lenski only involved 58,000 generations and a few vials of bacteria. Why haven’t bacteria in general melted down?

  29. petrushka:
    Lizzie, my point is that The Lenski experiment involved hundreds of mutations that did not affect the viability of the colonies. Where’s the meltdown?

    More to the point, Lenski only involved 58,000 generations and a few vials of bacteria. Why haven’t bacteria in general melted down?

    Good point. Even if YEC is true and the Earth is only 6000 years old, that’s still over 26 million bacterial generations (assuming an average generation time of 2 hours). Shouldn’t all bacterial populations on the planet have succumbed to genetic meltdown long ago? I mean, since they all carry mutations and since, as ID/creationists insist, almost all mutations are deleterious, why are there still bacteria?

  30. phoodoo,

    Why do I think this matters? You really need to ask this?

    We are trying to make a model of how a NOVEL mutation, which is not deleterious, can drift through the population and become the norm.

    And I have answered this, explicitly. A novel mutation has a frequency 1/N and will become fixed on average once every N replicates. ANY member of the starting population, regardless how many other members share its allele, will become the ancestor of all future population members with a probability of 1/N.

    Do the math, as they say.

  31. phoodoo,

    Start with one, see where it goes. It will die every time. I can tell you that even without a little computer program.

    Oh, that is hilarious!

  32. Ah, just seen oleg’s results. Thanks, oleg! My original post was a thought experiment; I didn’t realise I might have to whip up some code to back it up! I have the very thing somewhere, but I have been dipping in and out amongst other chores, as I’m sure does everyone else.

    Interesting that phoodoo thought 5 ‘rival’ colours would make a difference, or that the neutral result that happens in a population of N would stop happening in a population >>N, or that a 30% bottleneck (eg, my son dipping his mitts in my bag of M&M’s) would prevent fixation.

    Population size does have an effect, of course – it reduces the influence of drift, making it harder for deleterious alleles to fix among other things.

  33. phoodoo,

    And a Chihuahua in the wild will live to about a week, assuming someone helps it find water.

    Which just goes to show that artificial selection is no substitute for the real thing!

  34. phoodoo: No, I said a starting population of 1000. And then try adding in a virus which kills off thirty percent of the population randomly.

    Actually, that makes the problem much more tractable because fixation by drift occurs quicker in small populations (though more code). Each variant has the same chance of being fixed in the population by neutral drift. If there are a thousand in the population, then each has a one in a thousand chance of being the winner (excluding the occasional extinction). To test this, we rewrote the simulation to include your obnoxious neighbor chowing down on the bag of M&Ms.

    Trials: 10000
    Population: 1000
    Chance of obnoxious neighbor grabbing the bag of M&Ms: 5% per turn
    Obnoxious neighbor’s mouthful: 30% chance of each M&M being eaten without replacement

    The population drops drastically from 1000 down to just a few. At that point, fixation occurs very quickly.

    Extinctions: 11, obnoxious neighbor eats the last few multicolored M&Ms
    Fixation of black M&M: 12
    Average turns: 286.8
    Average final population: 5.86
    Average obnoxious neighbor mouthfuls: ≈15

  35. Ran a 1000 trials to determine average generations. As the population was in rapid flux, generations are counted as 1/population per turn.

    Average generations to fixation: 8.8

  36. olegt: No, phoodoo, you cannot conclude that. Your inferred times are wrong. They should be divided by a factor of N, i.e., 1000 in my example.

    The t variable ticks up by 1 when a death occurs. In a population of N MMs, a death occurs every 1 unit of time. Therefore, a generation (the lifetime of a single MM) is N units of time. It took about 1000 generations for the fixation to occur.

    olegt: No, phoodoo, you cannot conclude that. Your inferred times are wrong. They should be divided by a factor of N, i.e., 1000 in my example.

    The t variable ticks up by 1 when a death occurs. In a population of N MMs, a death occurs every 1 unit of time. Therefore, a generation (the lifetime of a single MM) is N units of time. It took about 1000 generations for the fixation to occur.

    So if I have four M&M’s and it takes two turns to go from a 50-50 population to 100% blue, that happened in 1/2 a generation?

  37. Piltdown2,

    While many proteins will allow some variation if the rest of protein is unaltered, multiple substitutions will generally lead to a loss of function. So the question is whether the extremely rare beneficial mutation can become fixed in the population before the more common deleterious mutations are allowed to accumulate.

    Maybe, but note the effects of population size, linkage, and the relative nature of the classifications ‘beneficial’ and ‘deleterious’.
    – Only smaller populations are strictly at the mercy of drift when the alleles are non-neutral. This means that deleterious alleles have a much harder task in becoming fixed by it (and they ain’t gonna be fixed by anything else!).
    – Since you are talking of a single protein, the idea of a rare beneficial version being swamped by the greater production of deleterious versions does not fly. If mutated version B is beneficial, all the existing alleles A are immediately (relative to it) deleterious. They were doing fine till it arrived! Now, the tendency is for them be eliminated, the flipside of B being fixed. If mutations continue to occur, even if the bulk of them are deleterious, they too will tend to be eliminated in the same way. If mutation C, D etc is even more deleterious than A, it has both A and B to compete with.
    – In the event that a deleterious mutation did become fixed by drift, that is not the end of the story. The population has moved a little down the adaptive hill, which opens up the way for a beneficial mutation to take it back up again. If, at the same time, it becomes large, the tenure of this fixed deleterious mutation is even more likely to be brief.

    The single color M&M’s would simulate asexual reproduction. I think I see what you’ve done to expand it to 2-color M&M’s to get the same result for a sexual population, just taking longer. Thanks.

    Well, it doesn’t take longer if you count the same things – allele copies, rather than individuals. In diploids, alleles are paired. (As an aside, in my view, the diploid organism is an illusion anyway; I think we are just a phase in the lifecycle of a haploid organism, spermandeggs!)

    I’m not convinced that only novel mutations can restore diversity. Don’t want to get too far out of my depth, but since the genome contains large amounts of non-coding region, diversity could be maintained by the existing genome.

    As I said to Neil, I’d regard that as a mutation, though this may simply be a semantic quibble. But it is a sequence at a locus that is different from the sequence that was there before. In order to counter the loss of population diversity, it would have to increase in frequency in exactly the same way as any (other) mutation.

    And I do not deny the possibility of new mutations being fixed, I just realize how long it takes, especially in a large sexually-reproducing population.

    By drift alone, glacially slow per allele, but they produce more, so the net result is the same – fixation at the mutation rate, irrespective of population size.

    But still, the illustration was to get across the baseline – the thing you can’t turn off: loss of variation with or without selection, unless new mutations arise (and then, the same process fixes them). Diversity arises from the lag, with simultaneous progressions at various stages of their unfolding.

  38. phoodoo: So if I have four M&M’s and it takes two turns to go from a 50-50 population to 100% blue, that happened in 1/2 a generation?

    Yes. That would be the shortest time possible. There can also be longer paths to fixation: {2,2} goes to {3,1}, then back to {2,2}, {1,3}, and finally {0,4}. That would take four turns, or one generation. You can see that in my runs the time to fixation fluctuates.

  39. petrushka: The question is why do bacteria not succumb to genetic meltdown?

    Thought you’d get a kick out of this. Over on his blog Joe Gallien (banned here for linking to porn) came up with this wonderful answer to your above question:

    If you are referring to Sanford, well, that only applies in a world built by darwinian evolution and eons of time. That bacteria haven’t succumb to genetic meltdown would be evidence against darwinism and eons of time.

    As I told you morons before design can get around natural deterioration. You’re just too set in your dogma to listen. Evolution by design does not lead to genetic meltdown

    There you have it from the expert himself. GAWD gave human a crappy design so our genome would fall apart in just a few thousand years but The Big Guy designed the bacteria genome to last forever!

    So much for us being the special ones. 🙂

  40. olegt: Yes. That would be the shortest time possible. There can also be longer paths to fixation: {2,2} goes to {3,1}, then back to {2,2}, {1,3}, and finally {0,4}. That would take four turns, or one generation. You can see that in my runs the time to fixation fluctuates.

    You need at least two births with the mutation, so how is that half a generation?

  41. phoodoo: You need at least two births with the mutation, so how is that half a generation?

    I define the time of a generation as N deaths. Each death is accompanied by a birth (the number of MMs is kept constant). In the above example with 4 MMs, 4 deaths = 1 generation.

  42. olegt: I define the time of a generation as N deaths. Each death is accompanied by a birth (the number of MMs is kept constant). In the above example with 4 MMs, 4 deaths = 1 generation.

    I thought you just said it was half a generation?

    Now let’s say you start off with all four one color, then you have one death and one novel mutation. That’s one generation. After 3 more tries you could end up with all four the new color. According to your formula, the whole population changed in one generation.

  43. phoodoo: Now let’s say you start off with all four one color, then you have one death and one novel mutation. That’s one generation.

    With 4 MMs,
    4 deaths = 1 generation.
    1 death = 1/4 of a generation.

    After 3 more tries you could end up with all four the new color. According to your formula, the whole population changed in one generation.

    Yes. 4 deaths = 1 generation.

    Or it could take longer. You start with all 4 of one color, {4,0}, and undergo the following sequence:
    {4,0}, {3,1}, {2,2}, {3,1}, {2,2}, {1,3}, {0,4}.
    That is 6 transitions, or 1.5 generations.

  44. olegt: With 4 MMs,
    4 deaths = 1 generation.
    1 death = 1/4 of a generation.

    Yes. 4 deaths = 1 generation.

    Or it could take longer. You start with all 4 of one color, {4,0}, and undergo the following sequence:
    {4,0}, {3,1}, {2,2}, {3,1}, {2,2}, {1,3}, {0,4}.
    That is 6 transitions, or 1.5 generations.

    You don’t see a logical problem with claiming that you can go from zero in a population of 4 to a novel mutation becoming fixed in the population in ONE generation? That makes sense to you? That’s how your math works?

  45. phoodoo: You don’t see a logical problem with claiming that you can go from zero in a population of 4 to a novel mutation becoming fixed in the population in ONE generation? That makes sense to you?That’s how your math works?

    ROFL! I’m greatly enjoying phoodoo wriggle and squirm looking for boundary condition “gotchas” in the simplest example possible so he can continue his evolution denial.

    Sadly for him, looks like reality is going to win again.

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