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
Please pay attention newton.
More like a case of Equivocation.
a priori is not a posteriori. Joe knows this, you know this, phoodoo and I know it, hell, even keiths knows it.
Yes, I think Joe can assign “fitnesses” to organisms at random and then figure out a way to get the “fitter” ones to leave more offspring.
#JoeDesigner #JoeModeler
phoodoo:
newton:
Mung:
He asked for an example, Mung, not an exhortation.
Joe:
Mung:
How so? Be specific.
Mung,
Suppose we are modeling, via computer simulations, the orbital dynamics of various hypothetical planetary systems. Before each run, we specify the masses, positions, and velocities of the virtual planets and of the associated virtual star.
An onlooker — let’s call him ‘Bung’ — complains that by specifying these values rather than measuring them, we’re invalidating the modeling effort. The whole setup is designed, according to Bung, and it therefore cannot be an accurate model of what would happen in an unguided planetary system operating strictly according to the laws of physics.
Bung’s objection is stupid, of course, as intelligent readers will immediately recognize.
What relevantly distinguishes Bung’s idiotic logic (applied to planetary models) from that of his real-life rhyming counterpart (applied to evolutionary models)?
keiths,
I tried an almost identical thought experiment a while back.
I anticipate the same result, and we all know what that is.
At this point Mung is nothing but derp material
You might want to click, read, think, and tweet again, Tweety.
Tom invites is to descend again into the murky depths of probability theory.
Fitness is a propensity, says Tom.
So I reach into my hat of propensities, and declare that an organism shall have the propensity drawn from my hat. And somehow, it comes to pass that the organism does in fact have that propensity.
Note that in the example I gave, the person who assigned the fitnesses was asking what would happen if they had a particular property. (The person was actually R.A. Fisher, back in 1922).
As Fisher designed the fitnesses, does that mean he wasn’t studying the consequences of natural selection?
Mung,
Since you’re in desperate-deflection mode, I’d better stick it in your face:
The question is not “What is fitness — really?” The question is: “What do we mean by fitness in this context?”
I’ve used the term propensity in explanation of the model. If you don’t like that term, then stick to what Maynard Smith said. In any case, the model is what the model is, irrespective of what you or I say about it.
Folks like me have to work with models, because God does not grant us direct access to Reality. And as G.E.P. Box said, “All models are wrong; some models are useful.”
Tom, when Joe mentioned different fitnesses for for the three possible “genotypes” he was referring to an allele, not an organism. He was using sloppy language. It takes more than one allele to make a genotype.
Your own “type” of organism reminds me greatly of the creationist “kinds” except that you would apparently argue that every organism is its own “type.”
But that all hardly matters given that you still have an a priori fitness.
Sal would love it!
I should remind everyone that I’m using a model that David Glass, a Christian apologist, found useful in challenging Richard Dawkins.
We have noted how the term often changes meaning.
If fitness has one meaning in the context of a model it’s hardly fair to say that the model is a model of something else in which fitness has a different meaning when the context there is different.
In your model the context of fitness is a string of ‘0’ and ‘1’ which when all added together become the “fitness” of that string.
Your own OP makes it pretty clear that average fitness will NOT on average increase. Perhaps Joe failed to take note of that. What’s to be gained from defending his claim when it contradicts your own model?
And sometimes it isn’t. I really don’t know of anyone who counts up the actual number of offspring and declares that to be the fitness.
So “fitness” has nothing at all to do with the number of offspring it will leave. More like whether it will even survive to reproduce. I guess phoodoo was right all along.
Now y’all need to work on grasping the meanings. There’s quite a bit more to that than scanning for loops of thread. And I can tell you from personal experience, evolutionary computation sets up all the wrong intuitions.
I really don’t know how someone who had read a survey paper on fitness could not know. Here’s one I read last week:
H. Allen Orr, 2009. Fitness and its role in evolutionary genetics.
[ETA: See the section “Empirical issues: measuring fitness in contemporary populations.”]
Now let’s see you (1) turn a brief, low-level survey into scripture, (2) highlight the verses that suit you, and (3) evince nothing in the way of gestalt comprehension. You know already that it’s got to be wrong. And it’s not as though you need great knowledge of the field to see it. No, anyone who has not been stripped of common sense and rationality by so-called education can figure out what’s wrong — right? (ID proponents always have “super powers” that grant them insights into evolutionary biology that evolutionary biologists do not possess.)
Mung,
There’s no need to try so hard to misunderstand. Your limitations make that fairly inevitable, even with no effort on your part.
Mung, to Tom:
As I’ve explained, assigning fitnesses isn’t problematic. Your objection is idiotic.
You’ve let down Team Jebus once again.
Mung,
You quote the Wikipedia article on fitness — the paragraph immediately following the paragraph I quoted:
If you were the critical reader you crack yourself up to be, you’d have seen immediately that it’s not equivalent at all. The first word should be “alternatively.” As the opening paragraph of the article notes, fitnesses can be associated with genotypes, or they can be associated with phenotypes. (To avoid going into detail in the OP, I wrote generically of heritable traits.)
I thought the article was generally OK, for what was there (why no sexual reproduction?). I recall now that I noticed that sentence, some months back. I’m sorry if you were genuinely confused by that part. If you were confused, then you need to ask yourself why it is you think it’s for you to set me straight. Mind you, I do make mistakes. I’m not in my depth here, and I’m not pretending otherwise. I’m counting on the biologists in the crowd to set me straight if I get something wrong. What I will do, in response to correction, is to read. And if I don’t understand, after I’ve done some reading, I’ll ask questions. This isn’t a pretty story I’ve made up about myself. It’s how I actually operate. Among the many things I’ve gotten wrong in my life, it’s one thing I know I’ve gotten right.
I was referring to a pair of alleles — for this one locus, that is a genotype. I was not being sloppy. Mung just was, when Mung said I was “referring to an allele”.
Sheesh.
Geez, we are back to the numbskull notion that fitness is a probability of reproducing, not ACTUALLY reproducing, so now fitness is whatever someone says it is. I declare it is more probable!
If I am wrong, and my probabilities don’t come to fruition, then it wasn’t the fittest after all. Now I just go back and change the probabilities!
phoodoo, Mung
I am late to the party so I was hoping you could help me catch up. I understand Dawkins Weasel program and have played with it to see what optimized mutation rates are. In this program a set of strings in question is compared to the “target” and the best fit is selected.
Joe claims in his prior post is that this is a demonstration how selection is better then a random search. I disagree because selection mechanism requires you know the target sequence. Selection in nature does not have a target so he is comparing and apple (selection with a target) to an orange (selection without a target).
As far as I can tell Joe’s more complex model which integrates population genetics also uses a gene sequence target to improve gene sequence fidelity and ultimately is part of which organism is selected. Is this how you see it?
It appears doubtful that speaking of fitness as a propensity adds anything meaningful to the conversation.
colewd,
Can you give a specific example of selection in nature?
Mung,
Well, how do they do it, these people who don’t do it like that?
phoodoo,
Can you give us an example of this happening? Or is it a just so story you tell about evolutionists?
colewd,
Out of interest, then, when Weasel finds a correct letter, can that letter change in subsequent rounds or it is “latched” in place permanently?
Are you talking about the OP? That’s a model Tom is playing with which is from David Glass. In my opinion it has nothing to do with gene sequence fidelity or gene sequence target, but I’m not all that familiar with it.
WEASEL will halt when it reaches the target phrase. In the model in the OP there is no such halting condition. But there clearly is a “fittest” genotype, one with all 1’s.
As such, it could obviously have been programmed to halt on “finding” the first occurrence of the “fittest” genotype and a somewhat less circumspect Darwinist could declare that ID [or Hoyle] is dead.
Perhaps Tom will weigh in on whether the program could be halted on the first detection of a genotype with a fitness score of 50 and whether that would then turn it into a “search” algorithm.
Mung,
ID will never die because ID has never been alive. A designer that did something, sometime, somehow, somewhere can never be killed. The gap it can live in is the size of a bacterial flagellum. Or smaller yet, in the gaps in protein space.
So all that we can really do is say that ID is dead in a very specific narrow area and that process basically is what you are doing right now.
An ID proponent makes a series of claims and is educated. There are some very patient, generous people out there. Round and round we go.
Once the ID sufferer understands sufficiently why what they originally thought is incorrect ID is indeed dead for that person in that area. Or they continue to believe, and just go silent when facts or questions are raised they cannot suffer. J-Mac, you out there buddy?
As there are as many versions of ID as there are people (see previous fruitless attempts to get you all to find some common ground) then it’ll take some time. But that’s what the internet is for. It’s all here now, ready to be reread by someone struggling with the same misconceptions. Over and over.
colewd,
colewd,
I think yours is a perfectly accurate explanation of the program with seeing Weasel as anything more than simply telling it to find certain letters, and then the program magically finds those letters.
I think its not even remotely interesting or relevant to anything, other than perhaps as a supplement to the Dewey Decimal System.
phoodoo,
Indeed. So why do you ID creationists keep going on about it?
site:uncommondescent.com weasel
OMagain,
No, it does not latch. It accumulates and improves sequence fidelity by selection that best fits the target. Then the best fit is mutated as per the mutation rate over the population and the best fit is selected. Since it does not latch a high mutation rate is problematic (along with a long string) since to finish it must correct several errant letters at once. My experience is with over 80 letters and a mutation rate of 5% it would run for days. Once you reduce the mutation rate, sat to 1% it would then finish.
colewd,
No, it does not. As ultimately determined by a video of Dawkins’ demonstrating the program at the time.
You may find this interesting: http://austringer.net/wp/index.php/2008/10/19/dembski-and-marks-are-still-mischaracterizing-dawkins-weasel/
Note the date.
Since it seems to have been overlooked.
In the OP Tom writes:
If fitness ceases to change, then fitness doesn’t on average increase. Why am I wrong?
As I said in an earlier post, it increases until it doesn’t. Then what.
It just seems odd to me to say that fitness increases more often than not when it’s not increasing at all. And infinity is a long time, as we all know. There will be far more generation where fitness does not increase than there will be generations where fitness did increase. So, on average, well … you work it out and tell me if you come to a different conclusion.
Remember Richard’s algorithm? The one with an infinite search space, where fitness was determined by evaluating an algebraic expression and comparing it to PI?
Is there a maximum fitness sequence there? Is there a target specified in advanced? The answer is no. Those things are not required
OMagain,
Not at the biochemical level where DNA is changing. The closest is Lenski’s experiment but the complex sequence that was involved to break down citrate already existed in the bacteria.
In the OP algo fitness doesn’t cease to change. It’s just that the average fitness converges to a certain value, one that is higher than the average fitness of random sampling.
meh
To paraphrase Minsky, what class of problems is your technique good at solving?
I fail to see how this is a “central fallacy” of evolutionary informatics. It’s so obviously true that it’s not even in dispute.
Even if we grant that evolution is at times not modeled as a search process it doesn’t at all follow that what they wrote is false.
Now perhaps any program which models evolution as a search isn’t really modeling evolution. Or perhaps any program which models evolution as a search isn’t really a search.
But the 800lb gorilla is still in the room. How does the model presented in the OP demonstrate the power of cumulative selection? And if it doesn’t, why doesn’t it? I thought that cumulative selection is what you got for free with evolutionary models.
Is anyone going to take up the challenge to use the model from the OP to evolve an eye, or any complex function? Is there a reason that they did not use that model in Avida?
Models of evolution which pose no challenge to intelligent design by failing to offer any sort of designer substitute, well, it poses no challenge to intelligent design, obviously.
But if people stop using computer algorithms to demonstrate what evolution can allegedly do, what are they left with?
Have folks forgotten that the map is not the territory? Can a particular model of evolution actually settle the question of whether evolution is search?
I don’t think we should be allowed to construct a “model of evolution” in which evolution is not search and then triumphantly declare that the model we constructed conclusively demonstrates that evolution is not search. It seems more like begging the question.
ETA: If I created a model of evolution in which evolution is search would that mean that evolution is search?
If I got Tom & Joe right so far…
Evolution doesn’t halt. Using models that have fitness defined in terms of the Hamming distance to some arbitrary sequence doesn’t make that sequence a “target”. Even the weasel algo will produce countless sequences that are similar but different to the max fitness sequence after such max sequence has been sampled: you need an arbitrary halting condition independent from the algo to call it a search.
So evolutionary models are sampling processes, which produce samples that are, on average, fittest than the average fitness of random sampling. All those evolutionary models demonstrate the power of cumulative selection because of that, and prove that DEM are wrong when they claim that evolutionary models can’t do better than random sampling
Of course. I just created a model in which the universe is a huge cheese burger. And just like that hunger in the world is a thing of the past
Sure it does.
How do you know? Are you just making this up? What does make a sequence a target?
I’d say that assigning “maximum fitness” to a sequence qualifies as making that sequence a target. Else why bother.
According to Hoyle?
I’ll take your word for it that you learned that from Joe and Tom.
https://en.wikipedia.org/wiki/Heuristic_(computer_science)
What do you think dazz. Algorithms which employ a heuristic cannot be search algorithms?
By the way, for petrushka, Section 3.2. in that article is about the traveling salesman problem.
Really? What organism did evolution halt at?
You tell me. The algo simply samples the fitness landscape. It produces sequences at each iteration. You can have it halt at any arbitrary condition, but that doesn’t change the way the algo works. Your only way out here is your classic “there doesn’t need to be a single target”, but then you’re essentially saying that every sampled sequence is a target: in short, you either add an arbitrary criteria to define a target, one that the algo doesn’t depend on (meaning that the algo doesn’t require a target), or you redefine “target ” to mean the entire sample set of sequences the algo produced. See the problem there?
ugh…
They can be used to obtain a solution, just like GA’s, but I’m pretty sure I can use DEM’s logic to “prove” that heuristics can’t work any better than pure random sampling: if, for every heuristic that on average, improves performance by a factor of X above random sampling, I can produce one that decreases performance by the same factor X, then heuristics don’t work any better than random sampling. Does that sound right to you?
Not organism, absence of organism. Extinction. A population that ceases to exist no longer evolves. Evolution halts.
10 Hail Darwin’s and 10 Our Ape Father’s for you!
LMFAO. You mean to tell me biological extinction is analogous to a GA halting when fitness of a sequence is at, or above an arbitrary threshold? Are you fucking kidding me? It’s one thing to mix up simulator and simuland, but that’s just plain ridiculous. That’s a complete misunderstanding of what the model is simulating
I have another challenge for you.
Use any gravitational model to produce Saturn. Rings and all. Or any large celestial body. If you can’t we must have an honest discussion about your pathetic argumentation gimmicks