My emphasis:
Why should what you think influence anyone else?
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Not necessarily, no. It is true that some times ancestral functions can be enhanced, for example by increasing the activity and specificity of a particular reaction catalyzed by an enzyme.
And in others a protein can completely change it’s function and gain one it didn’t have before.
eLife digest
For billions of years, life on Earth was made up of single cells. In the lineage that led to animals – and independently in those that led to plants and to fungi – multicellular organisms evolved as cells began to specialize and arrange themselves into tissues and organs. Although the evolution of multicellularity is one of the most important events in the history of animal life, very little is known about the molecular mechanisms by which it took place.
To form and maintain organized tissues, cells must coordinate how they divide relative to the position of their neighbours. One important aspect of this process is orientation of the mitotic spindle, a structure inside the dividing cell that distributes the chromosomes —and the genetic material they carry — between the daughter cells. When the spindle is not oriented properly, malformed tissues and cancer can result. In a diverse range of animals, the orientation of the spindle is controlled by an ancient scaffolding protein that links the spindle to “marker” proteins on the edge of the cell.
Anderson et al. have now used a technique called ancestral protein reconstruction to investigate how this molecular complex evolved its ability to position the spindle. First, the amino acid sequences of the scaffolding protein’s ancient progenitors, which existed before the origin of the most primitive animals on Earth, were determined. Anderson et al. did this by computationally retracing the evolution of large numbers of present-day scaffolding protein sequences down the tree of life, into the deep past. Living cells were then made to produce the ancient proteins, allowing their properties to be experimentally examined.
By experimentally dissecting successive ancestral versions of the scaffolding protein, Anderson et al. deduced how the molecular complex that it anchors came to control spindle orientation. This new ability evolved by a number of “molecular exploitation” events, which repurposed parts of the protein for new roles. The progenitor of the scaffolding protein was actually an enzyme, but the evolution of its spindle-orienting ability can be recapitulated by introducing a single amino acid change that happened many hundreds of millions of years ago.
How could a single mutation have conferred such a dramatically new function? Anderson et al. found that the ancient scaffolding protein uses the same part of its surface to bind to the spindle-orienting molecular marker as the ancient enzyme used to bind to its target substrate molecule, and the two partner molecules happen to share certain key chemical properties. This fortuitous resemblance between two unrelated molecules thus set the stage for the simple evolution of a function that is now essential to the complexity of multicellular animals.
So what used to be an enzyme suffered a mutation that gave it a radically new function: the ability to orient the mitotic spindle and therefore contribute to the evolution of organized multicellular tissues.
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That still doesn’t make any sense. I suspect the math you are describing is not the math you are doing, or the other way around. It would help if you could write it down to show us. Use paper+pencil and take a photo, or you can use LaTeX if you know it.
Back to the math above, the number of steps is irrelevant. What matters is the number of trials needed to accomplish each step.
You seem to be focused on complex features, and applying questionable math to support your position that these cannot evolve. Instead, try demonstrating your math on with a simple example, explain all your assumptions, and demonstrate you are doing it right.
Here is a very simple example: What is the probability of reaching 1 step in N trials, 2 steps in N trials, etc…
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The functionality being binding specificity. And Behe says two new protein-protein interactions are too improbable to be biologically reasonable.
But again, Behe observes what evolution did, and with intermittent selection in place.
I don’t know if other genes interact with PfCRT, but I don’t know that it matters, once PfCRT is in operation due to mutation, that’s all Behe needs for his argument.
If it evolves, yes. When something happens the probability of it happening are 100%, BECAUSE IT HAPPENED.
Are you denying that neutral mutations reach fixation without needing to be selected for?
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See my response to Roy, I think I’ve got it correct now, though probability is tricky!
But I’m gearing off the paper, which proposes a change of 1% at each step–which steps involve many trials, certainly.
But in the scenario I am envisioning, there are two trials, each with 2000 steps. And I am trying to compute the probability, not the expected value.
But the joint probability of independent events is the same, whether the events occur in sequence, or in parallel. So whether you roll two dice 6 times, or one die 12 times, you’re going to get the same distribution.
You are talking like I’m sampling organisms, but I’m sampling lineages of organisms instead. Once a lineage gets through the last step, that is marked a success. So 2000 steps, each involving myriads of organisms, in one population. So for an expected value of 10 evolutions of the eye, we would seem to need 65e27 populations!
Well, an expected value of chloroquine resistance evolving 5 times at a probability of 1 in 10^20 would require a population of 5 x 10^20, so this seems reasonable. My calculation for the evolution of the eye twice is 2 successes in 2 populations / trials, which is the square of the probability. With more populations (say 10 or 100) it doesn’t make much difference, the probability is still about the same order, as far as I can tell.
If you refer to Nilsson & Pelger, the steps aren’t what you think they are, and there aren’t really anything you would call “trials”. Eyes happen when 1) there is selectable variation involving increased and decreased visual acuity and 2) there is a selective regime that favors increased visual acuity. If you actually read the paper, you will see that the 1% figure is arbitrarily chosen so as to allow the description of steps. The key point is the calculation of the number of generations necessary to produce the magnitude of change given various simple assumptions, none of which involve the probabilities of mutations. The unstated assumption is in fact that selection does not over the long term decrease population variance, meaning that random mutations must continue to recharge that variance as alleles are lost. But that’s quite a reasonable assumption for quantitative traits and is borne out by observation. Anway, you should read section 4, The Number of Generations Required, if you want to understand the model.
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Yeah … but no. You really need to be writing this down.
You are treating trials and success as the same thing.
Try this: trials are the number of times the die is rolled (N), steps are the number of successes desired (x). (Note: x is a particular value, and X represents a random variable.) If the probability of success is 1% (p=0.01) then, the probability of at least one success in N trials is:
P[X>0] = 1-(1-p)^N
This probability goes to 1.0 as N goes to infinity (and p>0).
The number of successes X in Ntrials follows a binomial distribution, OR the number of trials N to reach x successes follows a negative binomial distribution (written as the number of failures before the x^{th} success).
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I think the whole 2000 independent steps is a non-starter anyway.
The chance of vertebrates evolving is not independent of the chance of eukaryotes evolving which is not independent of the chance of RNA world happening.
The one hundred prisoner problem is an example of how much a difference independent vs independent steps is.
If you haven’t heard the one hundred prisoner problem, then it goes like this.
There are 100 prisoners, numbered 1 to 100. There are 100 envelopes numbered 1 to 100. There are 100 slips of paper, numbered 1 to 100, and randomly distributed with 1 slip of paper in each envelope. All the envelopes are placed in a sealed room.
The guards of the prison make a deal with the prisoners. Each prisoner will be permitted, one at a time, to enter the room with the envelopes, and open 50 envelopes of their choosing. Once a prisoner has been to the envelope room, they are sequestered in a separate part of the prison and have no further communication with the remaining prisoners. If all of the 100 prisoners find the envelope with their own number, then all the prisoners will be set free. Otherwise, they will rot in jail forever.
The prisoners are permitted to confer with one another before the challenge begins. What is the optimal strategy for the prisoners to agree on and implement, in order to maximize their chance of being freed?
On first glance, each prisoner has only 50% chance for successfully opening their own envelope. Given 100 prisoners, then the probability of all 100 prisoners opening their own envelope if each prisoner opened 50 envelopes at random is, yes indeed, (1/2)100, which when evaluated is 7.9E-31.
But, on optimum strategy, the probability of success is actually an incredible 31%.
@Dan_Eastwood, if we had a similar problem but with 2000 prisoners where each could open 1980 boxes ie an individual 99% chance of each of opening their own number, what would be the probability of success for the 2000 prisoners to go free?
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Non sequitur.
Either you’re envisaging a starting population of two, or you don’t know what trials are.
False. Rolling one die produces a linear distribution from 1 to 6. Rolling two dice produces either a linear distribution from (1,1) to (6,6) or a non-linear distribution from 2 to 12.
False. If you were sampling lineages, you’d use the total number of lineages, not the total number of organisms.
[yes, 13.0e37 was a typo]
Only if one evolution of an eye needed 6.5e27 populations. You’re shifting back and forth between the number of organisms vs the number of populations.
And now we’re back to counting organisms, not populations.
Since you didn’t (can’t?) do the maths, have little or no grasp of either probability or scaling, and can’t even keep your imagined scenario consistent, you can’t tell.
Oh, and your suggestion that there were only 10 or 100 populations of organisms that might have evolved eyes is hilariously inept.
Have you worked out the odds of drawing a full house yet?
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Well. Apparently the chance of 2000 prisoners all opening their own box if they each open 1980 boxes is a cool 1-(H2000-H1980) = 1-(8.17837-8.16832) = 99.00 chance of success.
Which is new.
He’s wrong. Your immune system produces thousands of those interactions in only 2 weeks. And HIV evolved 5 new ones.
Again, that’s false on many levels. Behe quote-mined a sentence from a review, while ignoring all of the other reasons why chloroquine resistance is rare, from the same review:
It’s OK to cite someone with whom you disagree, but it’s not OK to pretend that you are in agreement.
So what Behe needs for his argument is more important than knowing the actual mechanisms of a disease that is killing millions of children?
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You haven’t. You never will, because you’re trying to support a falsehood, not trying to find the answer.
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Agreed. My purpose is to show that the naïve scheme of “multiplying probabilities together and calling it quits” is not valid. It’s also a gross oversimplification of evolution, but we can’t have a better model without first getting a simple model right.
I hadn’t seen that, or maybe I had forgotten, but thanks in any case. 
I will leave that question for the interested reader, but you are right that evolution is contingent. No doubt life might have evolved differently, but we never get to see what that might have looked like.
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So I’m trying to be generous, and assign a probability of 99% for each step.
But I didn’t mention either, here. And it seems you confirm my point, that the distributions are the same:
But the distribution of 1-6 numbers on the dice rolled is the same, is my point. Rolling one die twice is the same as rolling two dice once.
I do use the total number of lineages, that’s the number of populations.
No, one evolution of an eye needed 1 population.
Yes, because generating chloroquine resistance is possible in one organism, and generating an eye is possible in one population, not in one organism.
Why so?
That has nothing to do with the current discussion…
Or do we . . . ?
@Rumraket linked two interesting papers earlier in the thread.
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Well, not technically, since there is already some binding.
But Behe is talking about evolution, not the immune system, which he is well aware of.
“We can adapt the lessons of the immune system and shape space to help understand the problems random mutation would face in making new protein-protein binding sites in the cell.” (The Edge of Evolution, pp. 130-131)
And I’m only aware of one new protein-protein binding site in HIV, the (disputed) Vpu.
But all these factors were applicable when chloroquine was being applied. And Summers et al. confirm Behe’s conclusion of two mutations being required: “A minimum of two mutations sufficed for (low) CQ transport activity, and as few as four conferred full activity.”
You are missing a basic concept in probability. What is the distribution that you are calculating? What does it represent?
The only distribution you have mentioned is that of a six-sided die, or a Bernoulli trial with p=0.99. That is a starting assumption, not what you are trying to calculate.
But you aren’t trying to calculate the distribution of two dice, you want to calculate the probability of a given number of “successes” (x) in some number of trials (N: x<=N). Your calculation is only valid for x=N. ex: If a success is rolling a “6” what is the probability of rolling two 6’s in N=2 trials.
Again, this would be much clearer if you would simplify your example and write it down. Get the easy case right first, then make it more extreme. It should be clear from my comments and @Witchdoc’s that the calculation you keep trying to do isn’t meaningful, but the best way to understand why is to work thru a simple case for yourself.
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Your attempt whizzes by the actual point. Do you ever actually read what I post? Have you read anything I have said about quantitative characters, genetic variance, or anything else?
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