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
Allan Miller,
Just off to bed but made me chuckle!
One more time. It really is tomorrow now. And the prize is a full 24 hours without possibly being wrong! About anything!
#keithsAward
Might I suggest that you get rid of the kids and get a cat instead?
Every time I see a comment by J-Mac, I hear the wheezing snigger of a cur.
ETA: This is a comment that I sent to the trash, not knowing that I was using special privileges as author of the OP. Now back by popular demand. See comments below.
It’s true!
ETA: Crap. I should have said I concur. Much better.
Dammit Tom, lol.
Now my comments will make no sense! Again.
Mung,
Oh, great. Now Tom is deleting his comments, just like KN.
For the record, the deleted comment was a link to a youtube video of Muttley laughing, with a comment that said “Whenever I read a comment by J-Mac, I hear the wheezing laughter of a cur”, or something like that.
Either that, or I am on some really good drugs. When I want to delete a comment, it requires moderator approval.
Self-policing, not ass-covering. The comment couldn’t have been up for a minute before I decided that it belonged in Noyau (and then thought, why bother?).
I didn’t use the “Edit” button. I used “More Options,” expecting to request deletion, and instead saw an option to delete. I thought it was a change in the way the site works.
Here’s something close to what I originally posted:
Every time I see a comment by J-Mac, I hear the wheezing snigger of a cur.
Tom, I loved your comment. I just felt that I was robbed in being able to say that I concur, lol. It bothers me when my wit fails to come through. 😉
>>>>🍜
Rescued from the trash heap.
dude. Something nefarious was underfoot. Because keiths sez so.
Damn! I should have never let them comment starting from the last comments first…lol
The last shall be first!
Mung,
I said he deleted his comment. He confirmed that and reposted it.
Is your need to lie about your opponents really so irresistible?
People already know you’re a bottom feeder. You don’t have to belabor it.
I think it is because you are the author of the topic.
wtf are you ranting about. deep breath. inhale. fart.
Is that why you often seem bothered?
i
An obvious conspiracy!
I see now that I got confused in the rush. I’ll probably not get confused enough anytime soon to do the same thing again.
Well shit. That’s not even a full shelf.
Poor Mung.
So many books. So little understanding.
Mung, did ever see comments by evolutionists about mutations being governed by quantum mechanics?
An obvious defect on my part! 🙂
Unlike you, at least he knows a thing or two about quantum mechanics…
J-Mac,
Do tell how you assessed my knowledge of quantum mechanics.
keiths:
Mung:
To you, maybe.
You are always commenting excessively on every subject once the primer has been established… You have been mute reg. QM…That’s how I know…
J-Mac,
Your methodology needs a little tuning, to put it mildly.
keiths,
I’ll catch you later! 😉
Mung,
Just did. Packed Final Child off to university yesterday, leaving behind the sodding cat she manipulated me into agreeing to when she was 10. Bastard killed a finch, just to underline how much I hate it. The cat, not the kid.
Yes, it absolutely was a dastardly conspiracy. We said to each other “If we don’t mention quantum mechanics to J-Mac, he will believe that we are ignorant of QM and that he can slay evolution by just mentioning quantum mechanics.” So we kept quiet about that.
I recommend any old elementary college chemistry book. In the beginning they usually make clear that the properties of atoms result from the solution of thje Schrödinger Wave Equation. i.e., quantum mechanics. So all chemistry is based on quantum mechanics.
Before you post on “Mysteries of Evolution. 17: Quantum Mechanics Tells Us That Evolution Couldn’t Happen” you might want to read up on that. And what quantum mechanics does and doesn’t say.
Then, after that, you can go back to giving us lectures about how we do not understand science.
I feel that we’ve hit maximum Dunning-Kruger effect.
Glen Davidson
Yes, it absolutely was a dastardly conspiracy.We said to each other “If we don’t mention quantum mechanics to J-Mac, he will believe that we are ignorant of QM and that he can slay evolution by just mentioning quantum mechanics.”So we kept quiet about that.
I recommend any old elementary college chemistry book.In the beginning they usually make clear that the properties of atoms result from the solution of thje Schrödinger Wave Equation.i.e., quantum mechanics.So all chemistry is based on quantum mechanics.
Before you post on “Mysteries of Evolution. 17: Quantum Mechanics Tells Us That Evolution Couldn’t Happen” you might want to read up on that.And what quantum mechanics does and doesn’t say.
Then, after that, you can go back to giving us lectures about how we do not understand science.
Sometimes a man has gotta do what a man has gotta do… 🙁
I guess I have to begin with the fundamentals… where you and others here have learned how quantum mechanics governs all chemical reactions, including those involved in mutation, the same way quantum mechanics governs processes, such as rocks rolling down a hill…
I guess I’ll see you later…I guess much later…
Like you, he’s a mind reader.
Too funny.
Someone calling himself ‘ET’ over at UD commented:
My book on QM says evolution can’t happen. Or maybe that was the book on statistical mechanics.
Interesting. Do tell.
PS In J-Mac’s “humble pie” comment above, most of it was from my comment to which J-Mac was replying. The last three paragraphs were J-Mac’s. This is the result of a WordPress bug which does not properly indent quotes-within-quotes. In the present comment I had to insert <blockquote> … </blockquote> to repair that.
Mung,
ET is Joe Gallien. Spotted him after one sentence in the ‘galls’ thread you drew attention to. Need I say more?
Oh! I totally forgot to ask you the other day; in which book on quantum mechanics did you learn that quantum mechanics could govern processes, such rock rolling down the hill, which you claim quantum mechanics does…
I alluded to this issue more than once in my previous comments, but I forgot to ask you that particular question directly…
Would you be so kind?
Thanks in advance!
J-Mac,
Equating “governs” with “determines” is pathetic. The preparation of a quantum experiment generally does not determine the outcome. But one can say, reasonably, that the preparation determines the probabilities of the possible outcomes of the experiment.
Ironically, Marks, Dembski, and Ewert gave Chapter 4 the title “Determinism in Randomness.”
No one has a satisfactory account of how (the appearance of) a classical macrocosm emerges from the quantum microcosm. It’s your right to wheeze and snigger at that. And it’s our right to dismiss you as a cartoon of a discussant.
O”RLY? lol
Why don’t you talk to Joe Felsenstein then, as he says that quantum mechanics governs biochemical reactions, mutations, and even rock rolling down the hill…lol
One of you must be obviously wrong… I say both lol
BTW: You, and Joe as a matter fact may start reading the basics of quantum mechanics starting with quantum entanglement… 😉