Subjects: Evolutionary computation. Information technology–Mathematics.
Marks, Dembski, and Ewert open Chapter 3 by stating the central fallacy of evolutionary informatics: “Evolution is often modeled by as [sic] a search process.” The long and the short of it is that they do not understand the models, and consequently mistake what a modeler does for what an engineer might do when searching for a solution to a given problem. What I hope to convey in this post, primarily by means of graphics, is that fine-tuning a model of evolution, and thereby obtaining an evolutionary process in which a maximally fit individual emerges rapidly, is nothing like informing evolution to search for the best solution to a problem. We consider, specifically, a simulation model presented by Christian apologist David Glass in a paper challenging evolutionary gradualism à la Dawkins. The behavior on exhibit below is qualitatively similar to that of various biological models of evolution.
Animation 1. Parental populations in the first 2000 generations of a run of the Glass model, with parameters (mutation rate .005, population size 500) tuned to speed the first occurrence of maximum fitness (1857 generations, on average), are shown in orange. Offspring are generated in pairs by recombination and mutation of heritable traits of randomly mated parents. The fitness of an individual in the parental population is, loosely, the number of pairs of offspring it is expected to leave. In each generation, the parental population is replaced by surviving offspring. Which of the offspring die is arbitrary. When the model is modified to begin with a maximally fit population, the long-term regime of the resulting process (blue) is the same as for the original process. Rather than seek out maximum fitness, the two evolutionary processes settle into statistical equilibrium.
Figure 1. The two bar charts, orange (Glass model) and blue (modified Glass model), are the mean frequencies of fitnesses in the parental populations of the 998,000 generations following the 2,000 shown in Animation 1. The mean frequency distributions approximate the equilibrium distribution to which the evolutionary processes converge. In both cases, the mean and standard deviation of the fitnesses are 39.5 and 2.84, respectively, and the average frequency of fitness 50 is 0.0034. Maximum fitness occurs in only 1 of 295 generations, on average.
I should explain immediately that an individual organism is characterized by 50 heritable traits. For each trait, there are several variants. Some variants contribute 1 to the average number offspring pairs left by individuals possessing them, and other variants contribute 0. The expected number of offspring pairs, or fitness, for an individual in the parental population is roughly the sum of the 0-1 contributions of its 50 traits. That is, fitness ranges from 0 to 50. It is irrelevant to the model what the traits and their variants actually are. In other words, there is no target type of organism specified independently of the evolutionary process. Note the circularity in saying that evolution searches for heritable traits that contribute to the propensity to leave offspring, whatever those traits might be.
The two evolutionary processes displayed above are identical, apart from their initial populations, and are statistically equivalent over the long term. Thus a general account of what occurs in one of them must apply to both of them. Surely you are not going to tell me that a search for the “target” of maximum fitness, when placed smack dab on the target, rushes away from the target, and subsequently finds it once in a blue moon. Hopefully you will allow that the occurrence of maximum fitness in an evolutionary process is an event of interest to us, not an event that evolution seeks to produce. Again, fitness is not the purpose of evolution, but instead the propensity of a type of organism to leave offspring. So why is it that, when the population is initially full of maximally fit individuals, the population does not stay that way indefinitely? In each generation, the parental population is replaced with surviving offspring, some of which are different in type (heritable traits) from their parents. The variety in offspring is due to recombination and mutation of parental traits. Even as the failure of parents to leave perfect copies of themselves contributes to the decrease of fitness in the blue process, it contributes also to the increase of fitness in the orange process.
Both of the evolutionary processes in Animation 1 settle into statistical equilibrium. That is, the effects of factors like differential reproduction and mutation on the frequencies of fitnesses in the population gradually come into balance. As the number of generations goes to infinity, the average frequencies of fitnesses cease to change (see “Wright, Fisher, and the Weasel,” by Joe Felsenstein). More precisely, the evolutionary processes converge to an equilibrium distribution, shown in Figure 1. This does not mean that the processes enter a state in which the frequencies of fitnesses in the population stay the same from one generation to the next. The equilibrium distribution is the underlying changelessness in a ceaselessly changing population. It is what your eyes would make of the flicker if I were to increase the frame rate of the animation, and show you a million generations in a minute.
Animation 2. As the mutation rate increases, the equilibrium distribution shifts from right to left, which is to say that the long-term mean fitness of the parental population decreases. The variance of the fitnesses (spread of the equilibrium distribution) increases until the mean reaches an intermediate value, and then decreases. Note that the fine-tuned mutation rate .005 ≈ 10–2.3 in Figure 1.
Let’s forget about the blue process now, and consider how the orange (randomly initialized) process settles into statistical equilibrium, moving from left to right in Animation 1. The mutation rate determines
- the location and the spread of the equilibrium distribution, and also
- the speed of convergence to the equilibrium distribution.
Animation 2 makes the first point clear. In visual terms, an effect of increasing the mutation rate is to move equilibrium distribution from right to left, placing it closer to the distribution of the initial population. The second point is intuitive: the closer the equilibrium distribution is to the frequency distribution of the initial population, the faster the evolutionary process “gets there.” Not only does the evolutionary process have “less far to go” to reach equilibrium, when the mutation rate is higher, but the frequency distribution of fitnesses changes faster. Animation 3 allows you to see the differences in rate of convergence to the equilibrium distribution for evolutionary processes with different mutation rates.
Animation 3. Shown are runs of the Glass model with mutation rate we have focused upon, .005, doubled and halved. That is, uʹ = 2 ⨉ .005 = .01 for the blue process, and uʹ = 1/2 ⨉ .005 = .0025 for the orange process.
I have selected a mutation rate that strikes an optimal balance between the time it takes for the evolutionary process to settle into equilibrium, and the time it takes for maximum fitness to occur when the process is at (or near) equilibrium. With the mutation rate set to .005, the average wait for the first occurrence of maximum fitness, in 1001 runs of the Glass model, is 1857 generations. Over the long term, maximum fitness occurs in about 1 of 295 generations. Although it’s not entirely accurate, it’s not too terribly wrong to think in terms of waiting an average of 1562 generations for the evolutionary process to reach equilibrium, and then waiting an average of 295 generations for a maximally fit individual to emerge. Increasing the mutation rate will decrease the first wait, but the decrease will be more than offset by an increase in the second wait.
Figure 2. Regarding Glass’s algorithm (“Parameter Dependence in Cumulative Selection,” Section 3) as a problem solver, the optimal mutation rate is inversely related to the squared string length (compare to his Figure 3). We focus on the case of string length (number of heritable traits) L = 50, population size N = 500, and mutation rate uʹ = .005, with scaled mutation rate uʹ L2 = 12.5 ≈ 23.64. The actual rate of mutation, commonly denoted u, is 26/27 times the rate uʹ reported by Glass. Note that each point on a curve corresponds to an evolutionary process. Setting the parameters does not inform the evolutionary search, as Marks et al. would have you believe, but instead defines an evolutionary process.
Figure 2 provides another perspective on the point at which changes in the two waiting times balance. In each curve, going from left to right, the mutation rate is increasing, the mean fitness at equilibrium is decreasing, and the speed of convergence to the equilibrium distribution is increasing. The middle curve (L = 50) in the middle pane (N = 500) corresponds to Animation 2. As we slide down the curve from the left, the equilibrium distribution in the animation moves to the left. The knee of the curve is the point where the increase in speed of convergence no longer offsets the increase in expected wait for maximum fitness to occur when the process is near equilibrium. The equilibrium distribution at that point is the one shown in Figure 1. Continuing along the curve, we now climb steeply. And it’s easy to see why, looking again at Figure 1. A small shift of the equilibrium distribution to the left, corresponding to a slight increase in mutation rate, greatly reduces the (already low) incidence of maximum fitness. This brings us to an important question, which I’m going to punt into the comments section: why would a biologist care about the expected wait for the first appearance of a type of organism that appears rarely?
You will not make sense of what you’ve seen if you cling to the misconception that evolution searches for the “target” of maximally fit organisms, and that I must have informed the search where to look. What I actually did, by fine-tuning the parameters of the Glass model, was to determine the location and the shape of the equilibrium distribution. For the mutation rate that I selected, the long-term average fitness of the population is only 79 percent of the maximum. So I did not inform the evolutionary process to seek out individuals of maximum fitness. I selected a process that settles far away from the maximum, but not too far away to suit my purpose, which is to observe maximum fitness rapidly. If my objective were to observe maximum fitness often, then I would reduce the mutation rate, and expect to wait longer for the evolutionary process to settle into equilibrium. In any case, my purpose for selecting a process is not the purpose of the process itself. All that the evolutionary process “does” is to settle into statistical equilibrium.
Sanity check of some claims in the book
Unfortunately, the most important thing to know about the Glass model is something that cannot be expressed in pictures: fitness has nothing to do with an objective specified independently of the evolutionary process. Which variants of traits contribute 1 to fitness, and which contribute 0, is irrelevant. The fact of the matter is that I ignore traits entirely in my implementation of the model, and keep track of 1s and 0s instead. Yet I have replicated Glass’s results. You cannot argue that I’ve informed the computer to search for a solution to a given problem when the solution simply does not exist within my program.
Let’s quickly test some assertions by Marks et al. (emphasis added by me) against the reality of the Glass model.
There have been numerous models proposed for Darwinian evolution. […] We show repeatedly that the proposed models all require inclusion of significant knowledge about the problem being solved. If a goal of a model is specified in advance, that’s not Darwinian evolution: it’s intelligent design. So ironically, these models of evolution purported to demonstrate Darwinian evolution necessitate an intelligent designer.
Chapter 1, “Introduction”
[T]he fundamentals of evolutionary models offered by Darwinists and those used by engineers and computer scientists are the same. There is always a teleological goal imposed by an omnipotent programmer, a fitness associated with the goal, a source of active information …, and stochastic updates.
Chapter 6, “Analysis of Some Biologically Motivated Evolutionary Models”
Evolution is often modeled by as [sic] a search process. Mutation, survival of the fittest and repopulation are the components of evolutionary search. Evolutionary search computer programs used by computer scientists for design are typically teleological — they have a goal in mind. This is a significant departure from the off-heard [sic] claim that Darwinian evolution has no goal in mind.
Chapter 3, “Design Search in Evolution and the Requirement of Intelligence”
My implementation of the Glass model tracks only fitnesses, not associated traits, so there cannot be a goal or problem specified independently of the evolutionary process.
Evolutionary models to date point strongly to the necessity of design. Indeed, all current models of evolution require information from an external designer in order to work. All current evolutionary models simply do not work without tapping into an external information source.
Preface to Introduction to Evolutionary Informatics
The sources of information in the fundamental Darwinian evolutionary model include (1) a large population of agents, (2) beneficial mutation, (3) survival of the fittest and (4) initialization.
Chapter 5, “Conservation of Information in Computer Search”
The enumerated items are attributes of an evolutionary process. Change the attributes, and you do not inform the process to search, but instead define a different process. Fitness is the probabilistic propensity of a type of organism to leave offspring, not search guidance coming from an “external information source.” The components of evolution in the Glass model are differential reproduction of individuals as a consequence of their differences in heritable traits, variety in the heritable traits of offspring resulting from recombination and mutation of parental traits, and a greater number of offspring than available resources permit to survive and reproduce. That, and nothing you will find in Introduction to Evolutionary Informatics, is a fundamental Darwinian account.
The Series
Evo-Info review: Do not buy the book until…
Evo-Info 1: Engineering analysis construed as metaphysics
Evo-Info 2: Teaser for algorithmic specified complexity
Evo-Info sidebar: Conservation of performance in search
Evo-Info 3: Evolution is not search
Evo-Info 4: Non-conservation of algorithmic specified complexity
Evo-Info 4 addendum
I see keiths has decided to join the merry band of men who think that you can just count eyes and make an inference from that. Why am I not surprised.
He quotes DNA_Jock:
keiths:
It’s not correct, because it LEAVES OUT the proportion of eyes to not eyes.
It doesn’t matter how many red balls you draw from the bag if for every red ball you draw you also draw a green ball. The proportion doesn’t change. The relative frequency doesn’t change.
…if you keep drawing eyes from the bag…
Relative to what?
…if you keep drawing not-eyes from the bag…
Relative to what?
… then your estimate of the proportion in the bag rises …
It should only rise if the proportion changes. If you keep drawing MORE eyes from the bag relative to NOT-EYES.
…your estimate declines…
It should only decline if the proportion changes. If you keep drawing MORE not-eyes from the bag relative to EYES.
In the case of balls that are only distinguishable by colour in a
gigbig bag, shake the bag! (I think I already said that.) In the general case, it depends what you are sampling. If you are testing pool water, dip your sampling cell well below the surface, after allowing any added chemicals to mix in. If you are sampling opinions, make sure your interviewees are a cross-section of age, sex, income etc of the group whose opinions you are sampling. If you are taking DNA samples, extract from a source that is as free from contamination as possible, such as the inside of a tooth. It’ doesn’t seem a difficult concept in principle or in practice.My conclusion would be you need a bigger sample. And it might be difficult to get answers from dead people.
ETA Gig bag?
No, Mung, and neither are Rumraket and DNA_Jock. You are deliberately misunderstanding us in an attempt to save face.
Your desperation is showing.
Now keiths is doing the Gish Gallop.
At one moment Rumraket is making one argument and then he’s not making that argument. At one moment sampling is important, and at the next moment sampling is not important.
What, we have a big bag full of eyes that evolved and eyes that did not evolve and we’re drawing our samples from that bag? And every time we draw an eye from that bag we find it’s an eye that evolved? That’s Rumraket’s argument?
What a waste of time you are, keiths.
If you think that DNA_Jock should have written something other than what he did, take that up with him. And next time use your own words rather than quoting something that doesn’t actually say what you actually meant.
The failure to communicate is yours.
Mung,
No. Rumraket is making the following argument:
He’s correct, and you’re wrong. It’s not surprising — he’s smarter and better educated than you.
Mung,
I don’t. I understood exactly what he meant. This is not difficult, Mung.
Another example:
The only life-forms we know exist for sure are on Earth. We don’t know how big the universe is and we have no indication of life elsewhere. We can’t say we are unique but there’s no evidence to suggest otherwise with our single sample. If life, unrelated to terrestrial life turned up on Mars, a sample of two, would force us to consider that life is widespread.
Fuck’s sake, Keiths, can you not post without the snark?
Increasingly likely relative to what? We can’t simply look at the number of times that eyes have evolved and calculate a relative frequency from that, can we, keiths?
If you keep sampling posts, and they keep coming up snark, it becomes increasingly likely that the next post will come up snark.
keiths found a post where Rumraket used the word frequency. LoL.
keiths quoting Rumraket:
The frequency is high relative to what? What were the other samples that were taken upon which the proportionality was based? He doesn’t say. keiths doesn’t say either.
I agree.
Mung,
Time to look up the meaning of ‘frequency’ in a probabilistic context.
Too funny.
Close not quite there yet
Alan,
Rumraket is indeed smarter and better educated than Mung, and it’s highly relevant. When Mung finds himself disagreeing with Rumraket, his first thought should be “how am I screwing up?”, not “Rumraket is wrong!”
Here’s how I put it earlier:
Similar advice applies to you, Alan.
Mung,
Will it tell us how many snarks vs non snarks are in the bag? 🙂 Or better yet what actually caused the snark to be in the bag in the first place?
keiths,
I take it that’s a no then. You (and others) must expect comments that break the rule on questioning fellow member’s intelligence may move to guano.
Not sure but didn’t you start out claiming you could count the number of times eyes evolved and make an inference? Wasn’t that what the coin flip analogy meant to show?
No, the bag-argument was not really about my argument about eyes. The bag-argument was about how you can draw inferences about probabilities by observing frequencies.
The bag-argument was a tool of communication, meant to answer the question “what is a frequentist probability”? That is it. It was not meant to be a replacement for my actual argument, it was just meant to be an easy to understand example of the application of the frequentist interpretation of probability.
My actual argument is what Keiths quoted. I get that it is confusing to try to keep track of all the different things different posters are saying, and you’re not the only one to lose track here. Earlier on, Allan Miller apparently worked himself into the idea that the pull-something-from-a-bag-and-count example was meant to be an example of how evolution works. It was of course not meant to do that, so even though Allan Miller was the first guy to even bring up the argument about pulling balls from bags to begin with, he managed to get confused about what everyone was arguing about.
It is really helpful to try to keep track of the many different threads any particular discussion here spawns, I some times forget what exactly I meant to be arguing in a previous post and have to go back over the last couple of posts to get the context right. I think this goes for all of us.
Rumraket was kind enough to do that already and post it. Have you not been following along? You thought you’d just inject yourself without knowing what was being argued?
How does that help you?
Keiths, I appreciate that you’re trying to defend me against some pretty dumb shit. But I have to agree, this talk about me being smarter and better educated is snarky and counterproductive. The fact is it just doesn’t sit well with me and I have to admit I regret it every time a discussion devolves into this kind of viscious circle of mud-throwing. I’m not really better than anyone else, I can troll along with the worst of them, but I’d rather not. Can we all just desist from this shit?
Rumraket,
No, no, I just pointed out the fact that Mung/phoodoo had sought to critique it as if a model of evolution … I added it to the discussion for no better reason than that the conceit of using eye-spots as a mark on the balls allowed me to make the hil-a-rious pun of drawing ‘eye-balls’ from the bag.
I’ll get my coat.
Rumraket,
I disagree. It’s highly relevant, because the following is true:
When you and Mung disagree on a technical issue, you are most likely correct, and Mung is most likely wrong.
Note that I am not arguing that a smarter or better informed person can never be wrong. Far from it. I’m simply pointing out that it’s a mistake to assume at the outset that the smarter and better informed person — or worse yet, an entire field of smarter and better informed people — is wrong.
Mung, phoodoo and colewd do this constantly.
Ok, well that ironically just proves my point even better. I also failed to understand what the hell you were trying to argue. 😀
Seems like if you thought the were dim you wouldn’t want to act the same way.
Disregarding myself here, it’s not that I disagree with you that this is what usually transpires, I just don’t believe that you pointing it out is conducive to discussion.
In a more ideal world it should be possible to point something like that out to a person and compel them to seriously reassess their position, but ironically we are all too much just another species of ground-apes for that.
newton,
I don’t.
This!
Reminder:
We have sandbox for off-topic, noyau for gloves-off and moderation issues for “not fair”. Is it too much to ask for a little self-discipline?
Increasingly likely relative to our previous, less well-informed, estimate.
Yet another analogy:
Bert: “A perfect game is incredibly unlikely — it has only ever happened once, ”
Ernie: “I don’t think so, Bert. There have been 23 Perfect Games in MLB. I guess Perfect Games are more likely than you originally thought.”
Big Bird: “Guess so, kids.”
Bert: “Rubbish! You don’t know how unlikely a Perfect Game is! How many times has a game not been a perfect game, huh? Did you take into account the players’ strike and the introduction of the Divisional Series? Huh? Huh?”
Big Bird: “No Bert, what Ernie said is true.”
So when Mung writes:
He is conceding the argument in its entirety.
He may or may not know this.
There’s no way of telling.
Alan,
Oh, the irony.
Rumraket,
I’m not sure that anything is conducive to a productive discussion with guys like Mung and phoodoo.
But when Mung attributes this sort of argument:
…to you, or DNA_Jock, or me, it is worth asking an obvious question: If even Mung can spot the fallacy, what are the odds that you, Jock and I have all missed it?
Practically zero. Mung wastes everyone’s time by assuming (or pretending to assume) that his opponents are less intelligent than he is, when the opposite is generally true.
keiths:
Mung,
Pay attention, Mung. What Rumraket posted was not a definition of frequency, but a description of the frequentist interpretation of probability.
DNA_Jock,
Without any knowledge of the history of baseball, what is the likelihood that these games were pitched by a player under the age of 12?
Well gee, without any knowledge of the history of baseball, I don’t know.
If you told be that ONE of them was pitched by a player under 12, then my estimate for how unlikely THAT event is would be similar to Bert’s original estimate for the likelihood of any Perfect Game. Less than one –> less likely. More than one –> more likely.
I have a sneaking suspicion that you think you are heading for a gotcha that isn’t there…
Pretend you’re me, then read what I wrote again. LoL.
Is no one paying attention to what I actually say?
Given the context of the current debate, how seriously ought one take this as an argument? I am, in fact, engaging in precisely the same sort of argument that I’ve been arguing against. You got that much right.
If the posts keep coming up snark relative to what? Should anyone ask that question? Or does that just not matter?
keiths,
Ack! Given the context that Mung is quoting from, his misinterpretation of Rumraket’s comment is even more egregious than I had originally supposed. Leading me to mentally adjust certain probabilities…
DNA_Jock,
We know that eyeballs exist and have appeared on earth in different forms. What is the chance the “blind watchmaker” is the cause?
And yet you just can’t bring yourself to put us on Ignore.
You also came to the conversation late. So it doesn’t surprise me to find you missing the point.
Yup, just as I thought. You may have missed this:
Rumraket: If something evolves over and over again, then yes obviously it is evident that the event is increasingly likely for every time it occurs.
Mung: If you keep sampling posts, and they keep coming up snark, it becomes increasingly likely that the next post will come up snark.
If keiths posts snark, every time he does post snark, it makes it increasingly likely that he does post snark.
Erm, no.
Mung, you read the post where I clarified what I wrote there, yes? So why do you keep giving that statement the most uncharitable possible interpretation you can when I have explicitly elaborated on what I meant?
You keep making up this caricature that I somehow claimed that independent events aren’t actually independent.
I guess one can be forgiven for misreading my original statement that way, but now that clarification has been offered multiple times, and I have explicitly denied advancing a line of reasoning like the one you try to connect me with, shouldn’t you stop trying to connect me with it?
My recent post has nothing to do with independent events. It has to do with sampling. It has to do with not specifying either the number of eyes sampled nor the number of “not eyes” sampled. It has to do with not knowing what the relative frequencies are because we lack the relevant data.
I actually offered you an opportunity to admit this at one point, and you declined.
The post of yours I am responding to, does. You quote me making a particular statement, and then you caricature it with an uncharitable interpretation. I want you to stop quoting that statement and giving that stupid interpretation of it when I have explicitly denied having engaged in such a line of reasoning. I think this is a fair request.
There’d be no reason to “admit” to a factoid not relevant to any argument I’ve made.
If you disagree that it isn’t irrelevant, I have to ask what specific argument of mine you think the relative frequencies of eyes vs “not eyes” applies to?
I’m just going to quote that and leave it for keiths and DNA_Jock and Allan Miller.
For example, DNA_Jock started out like this:
Now I guess we have to trace back and see where “this analogy” came from. You say it doesn’t come from anything you wrote. Is that right?
Let’s see if we can’t get back to something we both agree on.
I quoted a couple authors who claimed that it’s easy to evolve an eye and that eyes are not so improbable after all. I took exception to those claims pointing out they were based on lousy reasoning. Ring any bells?
Then you came to the defense of those arguments.
Are we on the same page yet?
Yep, same page so far.
Oh dear, Mung. You seem very confused. You probably should have paid more attention to the phoodoo quotation that preceded my opening statement, viz:
I was addressing phoodoo’s misconception, phoodoo’s hopeless analogy, re the effect of the size of the bag, which I “got out of the way first”. You even admitted that you disagree with phoodoo, here.
In the second half of my opening post, I went on to separately deal with your misconstrual of Rumraket’s argument. That’s a more subtle situation, from a modeling standpoint, since the probability that the next ball carries an eye depends on both the proportion in the bag and the degree of bias in the sampling procedure. Luckily that all comes out in the wash, and it is still true that the higher the frequency (technical term) with which an event is observed implies that the event has a higher probability.
I understand that you are being deliberately obtuse; I really would expect you to be better at it.
You’re galloping, badly.
Rumraket, to Mung:
It’s a request that shouldn’t need to be made. Your intended meaning was obvious from the outset, and you clearly were not making the dumb mistake that Mung was attributing to you. He was dishonestly attempting to score gotcha points.
What do you accomplish with this bottom-feeder behavior, Mung?