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
Rumraket,
’tis true. Dichotomous thinking abounds. Qualifiers or terms of degree are barely noticed; cautious statements are interpreted as universals (… often!).
Rumraket,
Hence OMagain’s earlier question about Mung’s “work”:
What has Mung actually accomplished in his 15-odd years of sniping?
I have no problem believing that organisms are adapted to their environment. This idea seems to have been commonly accepted at the time of Darwin, even by Creationists.
I’d really like to see the discussion about adaptation have it’s own thread or move to the Purpose and Desire thread.
I have lots of books. I have a book just on adaptation.
Adaptation and Natural Selection
Say it isn’t so boys.
Which color bear. 😉
White bears move slower because they count on camouflage over speed. Please let it be a white bear.
Good one! LoL! And not too far from the truth. 🙂
Mung,
Polar bear speed: 25 mph
Mung speed: slooow
(double entendre fully intended)
Result: Mung is bear lunch.
Mung,
Ah, it’s a George Williams glove-puppet you have on now. Very nice.
I disagree with Williams (writing in 1966, incidentally). There – easy.
What’s your view then? If group selection and genic selection are separate ‘theories of evolution’, which one do you think has the edge?
No Joe. I never said generally either. Substituting “always” with “generally” isn’t going to change things for you.
I was merely pointing out that you had in fact argued that evolution maximizes fitness. Let’s not read into that any more than is necessary. All I needed was one single case of you doing so.
The purpose was to call into question the model presented in the OP and your obvious disagreement with Tom, which neither of you seem willing to admit to. I brought this up way early in the thread and it was never resolved.
Given that you were in fact aware of models of evolution in which fitness was maximized, why didn’t you say so right off the bat?
Say what aint so?
What is your point? How is this in any case relevant? It seems to be just another case of a pointless book-blurp.
Can you say a single unambigous thing, instead of just flail around aimlessly and incoherently for no other purpose than, seemingly to try to inflate a sense of controversy?
Are we supposed to refute anything and everything ever said by someone regarding evolution which you find somehow indicates there isn’t an irrefutable and absolute certainty about everything related to biology?
What were we supposed to be disagreeing about? I made (by email with Tom) some predictions about the equilibrium distribution of the OP simulations. They were very close to the results. So we can’t be too far apart.
No it seems you didn’t actually say anything about anything. Instead what you’re doing is just trying to manufacture conflict and controversy. It’s ridiculous.
Evolution, in some circumstances, do not result in increasing fitness. Mung, so what? What are the implications of that fact with regards to Tom’s OP that spawned this thread?
From the OP:
That would be false. I made a claim about something Joe may or may not have written. Joe indicated that he didn’t think he had ever written any such thing. I demonstrated conclusively that he had in fact written such a thing.
I don’t see it that way. Surprise! I brought to light something that was being denied.
Tom gave us a specific model of evolution and from that model he made certain generalizations. Those generalizations were not warranted. That’s the danger with models.
Does that help you?
I don’t care. Are they in conflict? How is having two conflicting theories of evolution not an indication of a lack of coherence? [That’s a rhetorical question.]
Oh good. I’m sure your disagreement follows from evolutionary theory just as his ideas follow from evolutionary theory. He’s right you’re wrong. You’re right he’s wrong. You’re both right. You’re both wrong. Any or all of the above.
You want to know what really impresses me about evolutionary theory? It’s coherence.
Moved another post to guano.
So…you wouldn’t have a problem if one day…not long from now… it would be demonstrated that say every other mutation, or 50% of them, tuned out to be non-random, would you?
As is Tom :
Tom English: “By the way, I am not conflating all probabilities in scientific models with physical chances, as Dembski et al. generally do. Much of what is modeled as random in biological evolution is merely uncertain, not attributed to quantum chance. The vitally important topic of interpretations of probability, which Dembski deflects with a false analogy to interpretations of quantum mechanics (Being as Communion, p. 157), will have to wait for another post.>
Did Tom keep your word and expanded this idea? I would like to read it and comment on it… especially on the clear implication of quantum coherence and quantum entanglement in cell-differentiation and morphogensis… I think Joe Felsenstein would like that … 😉
Considering that I have tried to convey in pictures a bit of what you address in your book (though I used a model developed by a Christian apologist in a paper critical of Richard Dawkins, and thus headed off the claim that I had rigged things to make ID look bad), the error would be mine if we were in disagreement.
You and I have disagreed openly on this blog at times. Neither of us sees anything wrong with that. So when we say that we agree, folks should accept that we agree. However, I’m not sure that I’ve gotten at what is going on with Mung. He may be saying that, even though we say that we agree, he’s got evidence that we actually don’t agree. We’re Darwinists, you and I, benighted by sin. And Mung, with his incisive textual analysis and superior powers of ratiocination, can establish beyond a reasonable doubt, for any fair-minded judge of the facts, that we are wrong to say that we agree. You and I, confronted with such overwhelming evidence, ought to stand tall in the dock, confess our crimes, and throw ourselves on the mercy of the court.
Tom, are you surprised that your model demonstrated what you designed it to demonstrate?
Confession is good for the soul. 🙂
Are you really a Darwinist though. Is Joe?
Possibly my favorite verse in the Bible is James 2:13. As translated by Heinz Cassirer: “Mercy has nothing to fear from judgment.”
https://en.wikipedia.org/wiki/Heinz_Cassirer
So be merciful.
Naked contentiousness. You need to take some time off. Pull out the couch cushions, look under the bed, check the glove compartment, etc., etc., etc., until you find your mojo. You’re not going to get it back, doing what you’ve done for the past couple days.
I accept that you agree on those things that you agree on. My interest is where you disagree, and why, and more specifically, why Joe did not register his disagreement with your broad generalization. Or did he, and did you just miss it?
I raised this very early on in this thread. Joe even wanted to make a wager.
How could Joe know this?
Humor is the sincerest form of mercy.
— I Made That Up
No, I just finally decided to comment on what should have been obvious to anyone reading the OP. Designer intervention to obtain the desired results is conspicuous.
Your model did what you designed it to do.
Joe Felsenstein:
Can Tom model this and then derive a generalization from the results?
Tom’s (and David Glass’s) model is close to the one used in that proof. The genotypes are asexual and haploid. However, the population size is finite, so there is genetic drift, and there is mutation.
If we abolished mutation, and had a truly infinite population, then the state of the population would be simply the frequencies of the 51 phenotype classes (how many matches to the target phrase among the 50 letters). No simulation would be needed, one could just use the formulas that I gave in Chapter II. We have the fitnesses of the 51 classes; the most-fit class that had a nonzero initial frequency would take over.
Tom’s description and mine could be reconciled by noting that the equilibria are having 100% of any of the 51 classes. Whichever was the highest class that existed in the initial population would determine to which of these equilibria the system went.
Once you put mutation in, then one does not go to 100% of the best class, but has an equilibrium distribution such as Tom found. It would look like the simulation results, but with no genetic drift. Because there is mutation away from the best class (and all of them, in fact) one does not end up with it taking over.
In such a case (with mutation) it is not possible to say that the process is a “search” for the most fit genotype. Because starting with only that genotype, the distribution of genotypes evolves away from that and ends up with few or none of that genotype. In that case Tom’s description of the process would remain the same as with the OP, and my statements about the most fit genotype taking over would be inoperative because of the mutation.
And what of mean population fitness? Whether it went up or down would depend on the starting distribution in that case. Though if we started from the equilibrium distribution of a population that had no selection, that would be way to the left, with an average of a bit less than 2 matches per genotype. Upon turning selection on by cosmic decree, the distribution would shift to the right along the scale until it ended up at the place where Tom finds it in the OP. Mean fitnesses would be increasing the whole time, but would slow down and stop moving right at a point well short of the right-hand end of the scale.
Mung,
No. Not in 2017, 51 years on, they aren’t. Selection at multiple levels can operate, but there can be conflicts of ‘interests’. Among units of selection I mean, not among authors.
So if any two authors in any science disagree on anything, their subject is incoherent? [That too is rhetorical, BTW].
Mung,
No, my disagreement is a semantic one. Group selection and genic selection are not different ‘theories of evolution’ in the sense I would use the term. The same thing – selection – can operate at different levels.
I can hardly agree with everyone about everything, can I?
Darwinism is Dogma, yet No Two Darwinists Ever Agree About Anything. Now, there’s a coherent critique of a scientific field.
(Strawman? I am sure I could ‘do a Mung’ and Google up some quotes where each of those positions is advanced).
Mung,
A politician’s answer. The question is whether such adaptation can result from differential reproduction, and whether the multiple occurrences of seasonal colouration change can reasonably be attributed to that cause.
More generally, is there a way a trait can get to an adaptive peak, from which all mutations are ‘downhill’ and hence detrimental and selected against, other than to be placed there deliberately?
Because they’re two different theories. Not the same one. Any one theory by itself is entirely coherent, but it might be practically very difficult to determine which one correctly maps on to reality. Perhaps they have different, non-overlapping domains of validity. Could that be it?
Your rhetorical question is a failure.
The Newtonian theory of gravity is in conflict with Einstein’s general relativity theory of gravity. Does that make “gravitational theory” incoherent?
That was also a rhetorical question.
Oh, two people disagree, that must mean it’s all up for grabs, nobody could ever make sense of it, and the subject of their disagreement must be entirely incoherent.
What really impresses me is the lack of coherence of the arguments you try to advance.
Does a result have to be surprising to be convincing or valid?
That’s a rhetorical question.
If I set up an experiment to demonstrate that things fall down, and I design and perform the experiment, and the result is that things fall down, does that mean the experiment is invalid?
That’s another rhetorical question.
If I was really good I’d put it in Trumpian terms, but I am not that good. 🙂
I’ve no objection to new innovations spreading through the population due to their utility and possible effects on reproductive success. Just look at cell phones.
Mung,
Conceded through gritted teeth! I can see why people go for mad positions like ‘species-immutablism’. Concede the tiniest amount of ground to ‘undirected evolution’, all Hell will break loose.
The revived discussion turned out to be what I’d hoped for initially. I thank Alan Fox for featuring the post, and Elizabeth Liddle for providing the forum.
“Natural selection is a process analogous to hill-climbing, in which the best phenotype is reached by a series of steps, each step leading to a type that is fitter than the previous one.”
– John Maynard Smith
Fitness is a property, not of an individual, but of a class of individuals — for example homozygous for allele A at a particular locus. Thus the phrase ’expected number of offspring’ means the average number, not the number produced by some one individual. If the first human infant with a gene for levitation were struck by lightning in its pram, this would not prove the new genotype to have low fitness, but only that the particular child was unlucky.
— John Maynard Smith [who was awarded the Darwin-Wallace Medal in 2008 (posthumously), along with Joe Felsenstein, who is very much with us, and hopefully will continue to be very much with us for a long time to come]