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
It really sucks when you don’t have a [metaphorical] leg to stand on, doesn’t it? The argument isn’t over whether the model can actually produce a living organism.
Sheesh.
Though I have to say, some people do claim their model really is a live case of evolution in action, or really is a live case of natural selection in action.
Not that dazz ever spoke up when they did so.
You claimed that evolution never halts. I gave you an example from real life. You need to keep track of your argument instead of trying to fob off your silliness on me.
When you claimed that evolution never halts were you talking about computer programs? Because even in that scenario a power outage coupled with the absence of an alternative power source will surely bring that to a halt.
Now you can claim that evolution never halts unless it halts. Go ahead. You can do it!
You were the one who brought it up. I just pointed it out when you did.
You pick a sequence and label it ” the max fitness sequence.” Now explain how that particular sequence came to be ” the max fitness sequence.” Please.
Then explain why that particular sequence, which you have dubbed ” the max fitness sequence,” isn’t a target. Is it because you didn’t know in advance what the max fitness sequence would be?
There’s a “max fitness sequence” in Tom’s model too. How do you suppose it got there?
Priceless. I’m really trying to resist the conclusion that you’re just as hopelessly retarded as phoodoo or Billy. You’re making it really hard though
Like keiths, if you don’t have an argument, resort to insult. Back on ignore.
Congratulations dazz.
I sure as hell hope this site doesn’t exemplify the best that atheism has to offer.
Actually, on reflection, it’s probably par for the course.
Note the obsession that the commenter has with skepticism about its ingrained delusion.
One might think, on reflection, that mutations continue to occur, selection continues to select, environments continue to change. So evolution cannot halt, unless life itself halts. And this is quite possible, given the appropriate catastrophe (sun expanding to a red giant, for example).
For the true believer, even then evolution would not halt. But nice of you to take up the thread that dazz himself didn’t follow. When he was talking about evolution he obviously didn’t mean ALL EVOLUTION EVERYWHERE.
Nice try.
Is there some doubt somewhere that the original Glass model instantiates a search algorithm?
Mung:
There is no gorilla. Just a couple of confused Mungphoodians trying and failing to find fatal flaws in various evolution-related models.
I’m still waiting for you to defend your dumbass notion that there’s something wrong with assigning fitnesses in an evolutionary simulation.
The simulator is not the simuland. When you stop observing the simulated evolutionary process, it doesn’t mean that the process being simulated has stopped.
You recall all of those people telling you to read their evolutionary programs? I was not one of them. For much of what a simulator does, there is nothing in nature doing the same. In particular, there is no fitness function in nature. The call to a fitness function in a simulator seems to MDE to provide the “search” with information. In one of the passages I quoted at the end of the OP, they refer to an “external information source.” It’s a pathetic error for them to have made. But it’s an entirely predictable error for techies who think that the evolutionary process must be what the program does, and that an analysis of the program is an analysis of the evolutionary process.
There’s a great deal else I’d like to respond to. But I need to go back to work on something else. I’ll try to say more tomorrow.
Yes. Try reading my OP closely. Look at his algorithm. The target is a parameter of the model. It’s part of the definition of the evolutionary process — in particular, fitness.
Can you specify the target independently of the evolutionary process? If so, then do it. This scan-and-quote “gotcha” formula of yours has grown tiresome.
I guess I don’t understand your complaint here. Evolution doesn’t stop so long as its conditions obtain:
1) Traits are heritable
2) Replication is inexact
3) There is an excess of offspring over what can survive.
If you have found a condition where these do apply but evolution does not happen, then I missed it.
The simulator is not the simuland. You’re thinking about the code, and ignoring the simulated process. If you reread my OP, you’ll see that I consistently described the simulated process, and not the simulation of it.
The link in your OP takes me to a paper on the Dawkins WEASEL program.
Parameter Dependence in Cumulative Selection
This dependence is investigated as parameters are varied in a simple problem where the goal is to find a target string starting with a randomly generated guess.
Did you link to the wrong paper?
ETA:
That’s exactly what I did, and that’s where I found a search algorithm. I think you made a mistake.
Evolution doesn’t stop so long as evolution doesn’t stop. That’s obvious.
I wonder why the fans of Andreas Wagner here at TSZ haven’t banded together to at least attempt to refute Tom.
Tom is vastly outnumbered here at TSZ by people who think evolution is a search, yet they remain strangely silent now.
Mung thinks evolutionary models are searches because some algorithms have targets at which they halt, and evolution halts when extinction happens, so evolution is a search and that’s intelligent design. His logic is water-tight, y u no see it?
To be clear, you don’t think it is a search
From the OP:
Let’s add the fans of Daniel Dennett to our list.
Chapter Eight of his book Darwin’s Dangerous Idea carries the title Biology Is Engineering.
Dawkins, Dennett, Wagner. Is it any wonder fans of evolution think evolution is a search [or an engineer]? And I guarantee you it doesn’t end with those three.
Mung,
Let’s see if I have this right.
Mung seems to be claiming that Shakespeare did not write all of those great plays; he just ran a search.
I’m perfectly content with Tom’s model. It poses no challenge to intelligent design because it doesn’t even attempt to explain how evolution can solve engineering problems or bring about “adaptations” that give the appearance of having been designed. I’m also not worried about population genetics.
I’ve no idea what this has to do with anything.
Evolutionists need evolution to be an engineer, and more specifically, a bad engineer.
LoL. It’s poor engineering. It’s delicate engineering. It’s anything you need it to be!
Little-known fact about the I in ID: it’s not an abbreviation.
Mung,
Surprise! surprise!
In the same book??
#IntelligentDesign
Absolutely.
Delicate and poor are not necessarily contradictory statements. For example, delicate can simply mean it is fragile and can be easily destroyed or changed.
Wow Mung, you really got him there.
No, I got you, with your lame defense. Any port in a storm.
I bet you they’re metaphors, and that you can’t go to where you want by being obsessed with labels. But I explained all this already.
Assume they are metaphors, even though they don’t say that Biology is LIKE Engineering. Why does “evolutionary theory” need to use metaphors like these?
I don’t believe they actually need to. But I do think they’re convenient. For example, we also describe ant-colonies essentially like little monarchical societies, with a queen, workers and soldiers. It helps communication. And with that, the structure of ant society is comprehensible even to very young children. It helps communication and comprehension to portray the unknown and unfamiliar in known terms and concepts. We know these things about social roles and hiarchies very well with these terms.
We can describe evolution, and various cellular entities and biological relationships without using metaphors, but it often takes a longer time and will be more difficult to understand for people trying to undestand it for the first time.
That’s why we find the majority of these metaphors used in books and articles intended for lay audiences, or in teaching materials.
When I was a kid my grandfather would describe the outer gas giant planets of the solar system as big vacuum cleaners that help suck up comets and asteroids so they don’t bombard the inner solar system as much. Did he need to use a vacuum cleaner metaphor for that? Not really, but he did and I instantly understood what he meant.
Rumraket,
Writers write for cooperative readers. Mung is not a cooperative reader. He’s an adversarial lawyer seeking to impugn the testimony of expert witnesses in court. Whether or not he is literally an lawyer, his behavior suits a sociopolitical movement engineered by a law professor — the author of Darwin on Trial.
It’s not like that I have to search far and wide just to find quotes like this one:
Evolution is a creative process in every sense of the word creative.
They literally fall into my lap all the time.
Throw this person an equivocation dictionary.
I can find many quotes like that myself. What do you think this should cause us to think? You seem to think this is some sort of issue in the field of biology? but I really don’t see why.
For someone whom purports to have a modicum of erudition, this is an astoundingly dense statement.
ALL organisms are fit. ALL organisms have a propensity to leave offspring. Otherwise, life would not exist.
Fecundity preceeds evolution. It does not proceed from it. Two different animals.
English and Felsenstein would have you believe the latter, irrational position.
Enough said.
Dead organisms tend to leave fewer,
Metaphors do not require the use of “like”, maybe you are thing about similes.
I’m inclined to agree with that, though it is perhaps overstated.
and so do sterile ones. At the beginning of Animation 1, there are quite a few individuals of fitness 0. They are of types that leave no offspring at all.
Do not ask for whom the bell purportedly tolls.
For him the bell purportedly tolls.
He who tolls the bell is purportedly erudite.
For someone who tolls a bell, he is uncommonly erudite.
I do? I would have you believe what?
Different genotypes often have different phenotypes (is Steve OK with that?). Those different phenotypes can lead to different probabilities of survival and different expected amounts of reproduction. (Is Steve OK with that, or is that controversial?)
I don’t know his position for sure, but I suspect that Steve would have you believe some extraordinarily silly things. Such as that the White Crowned Sparrow and the Golden-Crowned Sparrow were separately created.
Joe Felsenstein,
Looks like Steve asks, Which came first, the organism or evolution? Was there at first the organism and then it began to evolve, or was there evolution at first and evolution produced evolving organisms?
Steve assumes your answer would be the latter. Your latest comment misses the point. I assume your actual position is something like It’s a silly chicken-egg type of question.
Obviously. If one is looking at jungle fowl in the wild, and asking about their genotypes, phenotypes, and fitnesses, solving the chicken-egg problem is hardly the highest priority.
Probabilities and expectations don’t effect populations one bit.
Something that isn’t expected to reproduce that reproduces, has the exact same effect on populations as something that is expected to reproduce and reproduces.
Once again the concept of fitness is meaningless.