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.
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
Although in asexual single-celled prokaryotes that reproduce by fission, there’s not the distinction to be made when there is only one cell and one copy of the genome prior to fission.
No. There’s variation within individuals as well as between individuals.
Read the Losos book. Individuals adapted. They became more fit because they didn’t die. Individuals. That’s why I asked the question about within-generation evolution in the Improbable Destinies thread.
I said genomes in individuals are fixed. Sure, there’s the possibility of mutations in somatic cells, typically in cancer. Meiosis and gametogenesis is where new variation enters the gene pool.
That’s not adaptation. That’s survival. If that individual passes on more copies of those genes in progeny than other less fit individuals, that will give rise to allele [frequency]* change.
I might well buy Losos’ book. He looks a very competent field biologist from his website.
Yes, and I corrected you.
Losos claims it is adaptation. That was the whole point of the experiments. Will the same adaptations evolve. And yes, it’s survival. Losos used survival as his measure of fitness.
The allele frequencies changed as soon as some other individual died, as keiths will be quick to point out. That’s evolution. By definition.
It’s a good read, in spite of what I say about it. 😉
If the Losos book says that, then it’s a good thing that I didn’t waste my money on it.
Remember mung’s suggestion was that “evolutionists” argue whether individuals evolve. Not the same as somatic mutations accumulating. And where do these somatic mutations accumulate if they are not deleterious as in precancerous cells and developing tumours? In non-coding regions, perhaps? And how do they affect change in allele frequency?
I strongly suspect it says no such thing.
I suppose you are not very fit if you die from cancer before reproducing so I’ll concede that eventuality.
I’m very tempted!
Your statement was false, so I corrected you. Why can’t you simply accept that?
“If @ENCODE_NIH is right, each of us should have 7000000000000000000000000000000000000000000000 children”
Something is sketchy about this whole fitness thingy… Maybe I should look into it… 😉
The most charitable thing I can find to say is your “correction” was, at best, irrelevant.
Why did you put “correction” in quotes? It was a correction, not a “correction.”
As for relevance, what could possibly be more relevant to a statement than a refutation of it?
I have the same suspicion.
But DMD patients, on average, have fewer children than healthy subjects and hence lower fitness. That must be true, since patients can have offspring but usually do not, due to their poor health and a low life expectancy.
Would that be an acceptable statement?
What color hair did they have?
Woman with post graduate computer programming degrees from Ivy league schools and blue eyes and freckles and slender fingers on average have less children than woman nurses from Ohio that have shoe sizes over size 6 who can curl their tongue.
Can DMD patients curl their tongue?
I commented on the very first page of this thread:
Joe claims adaptation is fitness. And that fitness on average increases. What causes fitness to on average increase rather than moving to equilibrium, because I don’t see how you can have it both ways.
Now if fitness on average increases, how is there not some maximization function which brings this about?
ETA: My response to Joe.
Being a beach whale drastically decreases the chances of not only having children but also getting any action at all…I guess that what they mean when they refer to fitness;
If you are fit, you are not makin it 😉
Alleles get into offspring. They become carriers of the allele. The more offspring carriers have, the more new carriers are made. So I don’t really see why you think you have made some brilliant stroke there.
Oh Christ, it’s Big Bad Phoodoo Of The Internet. I am literally crapping myself.
Carriers of the allele would have mean offspring numbers that were infinite. Not rocket science, phoodoo.
I meant to say: If you are NOT fit, you are not makin it… obviously… lol
Right, ALL alleles, including the ability to curl your tongue, alleles for sexual preference, for long toes, for wide noses, for baldness, for hairy backs, for cancers, for pointed ears…thus you can not make any conclusions for why any one INDIVIDUALS have offspring, and since it is individuals that leave offspring, that is the only way to count.
But of course, you don’t want it to be about the individual, because then your whole fitness argument starts to unravel, I know that. Because you will never be able to identify the exact combination that causes anyone to have more offspring.
Things get eaten, they got shot, they live next to another thing, they live far from another thing, they fly south they fly north, they live in one tree they live in another tree, they walk into the river when the alligator is hungry, they walk into the river when the alligator is full, they are in the middle of the pack they are in the end of the pack, they have blue fur they have red fur, they work at Walmart, they work at Costco, woke up at 7 they woke up at 9, they are large but dumb, they are small but smart, they have good skin but bad eyes, they have good eyes, but bad teeth, and on and on it goes.
Fitness is meaningless. Unless you mean healthy, which you don’t. Instead you mean that which exists is fit. Everything that exists is fit. If it exists more, like lice, it is more fit. Its the most silly tautology.
Don’t you think being born with no legs and half a lung might reduce offspring numbers? If this is a genetic trait, it is hard to see how that would increase in the population, for pretty obvious reasons.
This is hitting far too close to home, but think professional sperm bank donor.
Allan, do you agree with Joe that improving adaptation is improving fitness?
Its not a genetic trait, its a combination of 10,000 genetic traits. Maybe they also have blue eyes and a symmetrical face. It exist. Its fit.
Can someone explain what improving adaptation means?
You count the individuals with and without a given allele. The mean fitness of those with is compared to the mean fitness of those without. They may be the same, or different, of course. Very, very simple phoodoo.
Fitness is a number of offspring, which is not meaningless. If you counted the individuals’ fitnesses of all carriers and all non-carriers of a given allele, again you’d end up with a statistic which is not meaningless. By summing, you will tend to smooth the effects of different alleles and random effects on individual lives.
At least, you will find this usage throughout evolutionary biology. They could all be stupid, or you could be missing something. I know you think you’re smarter than the average bear, but could an entire scientific field really be all stupid?
No, that’s not what I mean at all. When have I mentioned existence? A sterile individual exists, but its fitness is zero. So obviously, I am not talking about existence.
You object to something because it is trivially, self-evidently true? That would be pretty dumb. Yes, of course the type with the greater offspring numbers would be expected to increase in the population. Duh. Does that make it untrue?
You think possessing such a genetic disease might not disqualify one from such a route? Is ‘professional sperm bank donor’ itself heritable, for that matter?
Right, the same fitness as a professional football player bachelor like Cristiano Ronaldo. His fitness is zero.
That’s why it is such a meaningless concept.
An assertion is not a scientific claim.
Could you direct me to what he actually said? Unfortunately (given the pointlessness of trying to make headway on even the basic concept of fitness) we have to consider whether we are talking of relative or absolute fitnesses.
Which allele is it that makes Cristiano Ronaldo unfit Allan?
All of them?
Except when it isn’t.
ETA: Survived = Adapted = Fit
Can it be made any clearer than that?
He must not have adapted yet. If he had adapted, he would be fit.
Oh. Is it? So this is your master stroke to defeat fitness?
Yeah, maybe all sorts. Fuck knows what your point is though.
So, when I say ‘it exists’ is not fitness, you come back and say it is. Perhaps if I say ‘it isn’t’ again, you’ll completely ignore it again? What fun!
You see Allan, this line of yours is the epitome of the silliness of the tautology.
You are claiming that if you take larger samples you can rule out the affects of luck on reproduction. But what if luck is the biggest cause of reproduction? You are saying that if we take more samples, luck is ruled out, simply because you are already concluding that luck can’t be the cause over the long term.
We rule out luck, because over the long term we rule out luck.
If luck were the main cause, how would you know it?
We have been here before. If an allele causes carriers to die more often, even if it doesn’t directly affect fecundity, fewer offspring accrue to carriers of that allele. Strictly, fitness is the number of ‘full organismal cycles’, for example zygote-zygote interval, which obviously includes survival as well as fecundity.
So take your gotcha and …
Even if ‘luck’ were the main cause, you would still get evolution. That’s genetic drift.
So, are you proposing that all alleles are selectively neutral?
I’ll answer that: you are. You are saying that there is no difference in any life resulting from the particular alleles possessed. A possessor of a gene that enables it to run faster will pass it on to just as many offspring as one that makes its possessors lame.
How well adapted an organism is can be simply its fitness, or one can take part of the life cycle and get a component of fitness, such as examining viability without yet looking at fertility. Or one can take some particular function, such as ability to find prey. In Losos’s case he uses a component of fitness, viability.
And yes, Allan, good point: we need to distinguish between relative and asolute fitness. I avoided that complication. Mostly I have been talking about relative fitness. So a fitness of 1.03 means that the genotype’s fitness is 1.03 times as great as that of some genotype that we pick as a standard (which by definition has fitness 1.00). This is particularly useful when the population density changes through time, and in times when it is high, density regulation depresses everyone’s fitness by multiplying it by the same factor. In cases like that the absolute fitnesses of genotypes can vary through time, but the relative fitnesses might not. And it is they that affect the gene frequencies.
In the computer models the density regulation is usally very tight (such as always having 1000 adults survive) so both relative and absolute fitnesses stay constant and we don’t have to distinguish between them.
No,no Mung, you see its very simple. Its all about offspring.
You see, simple, just count the offspring. Or count that which exists. Take your choice.
They may be the same. Or different. Of course.
This. This shows clearly that phoodoo will never get within a million miles of understanding evolution. What’s the heritability of ‘being from Ohio’, ‘being a nurse’ – even being a woman?
I’m tempted to say something Guano-worthy. I won’t, but y’all know what I’m thinking.
So you’re right and Losos is wrong. They weren’t counting number of offspring and there were no zygotes involved. It was a within-generation “evolutionary” experiment.
Why not just admit there’s more than one “metric” for evolutionary fitness and that yours isn’t the only one?
No, you don’t count existence. I’ve said that several times now, and you persist in saying that’s what you do. I’m sure in your head you’re being really clever. But out here, it just looks ignorant.
My goodness Allan, its as if you believe each individual carriers one and only one quality.
What is someone is fast but has a small brain, does he have an advantage over someone with a bigger brain, but smaller hands and worse teeth but good at art? And do both of them have an advantage over a guy who is medium fast, but has less hair on his back to trap heat, and but doesn’t have a cancer gene?
And who wins when you have one guy who is really really fast, but he has lactose intolerance and bald? But I mean he is REALLY fast!
Each time evolution selects for one trait it deselects for another one. And we are supposed to believe THIS is how you can make new and better traits. So when the artist who is slow gets picked over the dumb guy who is fast and then his son is still going to have to figure out a new path to fast again, even though we just selected against it. And THIS will make better knees over the long term!
You don’t count existence.