Evolution of "Hello World" using random mutation and selection

I was struck by the relationship between this posting and the previous one on Kirschner's work. If I understand Kirschner correctly he is proposing that "random" variation might be biased towards mutations that are at the subroutine or object level rather than the individual instruction. Which I guess would make the evolution of quite complex programs much quicker.

GilDodgen muddies the waters further when he asks "How many simpler precursors are functional?" Translated to biology that can be seen as asking "what was the first self-replicator (or other-replicator plus symbiosis)?"

This changes the problem into a question of abiogenesis rather than of evolution with a given replicator. Genetic algorithms all assume self-replication in their modeling of biology.

Here's another distortion: "what gaps must be crossed to arrive at those islands of function,...?"

The term "islands of function" is also misleading. Drain his pool a little and instead of islands you get mountain ranges and hilly valleys that let a "hill-climbing" algorithm do its work.

Island hopping algorithms might need foresight, hill climbers can be blind.

http://gaul.sourceforge.net/tutorial/hillclimbing.html

What is the probability of arriving at our Hello World program by random mutation and natural selection?

I can't answer these questions, but this example should give you a feel for the unfathomable probabilistic hurdles that must be overcome to produce the simplest of all computer programs by Darwinian mechanisms.

GilDodgen muddies the waters further when he asks "How many simpler precursors are functional?" Translated to biology that can be seen as asking "what was the first self-replicator (or other-replicator plus symbiosis)?"

staring, intrigued, at the description "Dembski personality cult". can anybody think of an example of a personality cult which revolved around a smaller amount of personality?

I fail to see how this 'hello world' program can be taken as an example of evolution by mutations and natural selection. AFAIK, this process is not supposed to reach any objective or solution.

The probability to produce Homo sapiens from Homo habilis with RM + SN is almost zero, of course. This number is also completely irrelevant.

???

one may raise a myriad of objections based on the (unjustified) claim that the method required significant intelligent design

I'm always amused by that claim. It's like saying that, by the mere act of painting a bunch of concentric circles on the wall, you've given someone all they need to be a master archer.

Good to see that GP research is feeding back into the biology field. This kind of experiment is directly testing Darwin's hypothesis in the true scientific spirit and method: predict (there exists a system that, implementing Darwin's evolutionary rules, can produce a behavior meaningful to us but not to the system), design build and run the experiment so that all factors other than those operated on by the process under test are known and fixed, and see it produce the hypothesized result. Very nice.

Somewhat irrelevant are the questions about the logical level chosen for the experiment - could be any level, or all, from atomic through processor architecture thru instructions through algorithmic entities. In life all levels are simultaneously undergoing select and test. But in an experiment, it is only useful when the questioned independent variables are the only ones manipulated, in order to show the relationships. So choosing the highest level while keeping the lower levels fixed and known is the way. Point of interest in scale: this result is obtained on a very small collection of parallel processes and spawnings. Scale up several trillion trillion times in both number of parallel experiments and run time and you begin to approach what actually happened here on Earth.

Now I'll bet the virtual machine itself underwent evolutionary changes along the path to its final design - that is the normal creative process at work, and anyone whose life work involves the development of ideas is familiar with this, though most probably do not (yet) relate their intellectual experience to it's being a direct experience of the evolutionary process in fact, not merely a passing fancy.

Jeannot says:

"I fail to see how this 'hello world' program can be taken as an example of evolution by mutations and natural selection."

"GEMS employs mutation of two types." (Crepeau, p5.)

"As each off-spring is bred, it is evaluated for insertion in the pool using a modification of the process which [Altenberg 1994] calls "upward mobility" selection." (Crepeau, p4.)

"AFAIK, this process is not supposed to reach any objective or solution."

The immediate objective is to increase fitness for survival to reproduce. What that means varies as the species and environment changes so there is no overall objective.

"The probability to produce Homo sapiens from Homo habilis with RM + SN is almost zero, of course. This number is also completely irrelevant."

Exactly. We know it happened, however unlikely it was. We also know evolution happens, so there is no probability associated with that either. What was your point to raising this straw man?

"???"

:| :| :| !!!

Mark,
Re Kirchner, Crepeau says that he thinks his complicated multiple instruction environment succeeds in outputting strings because he intentionally specified a minimum amount of input and output instructions. He also speculates that his phase 2 of shortening the successful programs will be better if he intentionally specifies a minimum amount of halt instructions at this phase.

Corkscrew,
A nice view and metaphor.

The claim is also misunderstanding experiments. All our experiments, instruments or data handling are designed in some manner or they wouldn't give results. That doesn't make them illustrations of creationist theory. It is analogous 'thinking' to their requirement for supernatural explanations. It is also wrong to single out biology.

You are right, it is laughable.

Using this environment, GP is applied to the beginning programmer problem of generating a desired string output, e.g., "Hello World".

staring, intrigued, at the description "Dembski personality cult". can anybody think of an example of a personality cult which revolved around a smaller amount of personality?

staring, intrigued, at the description "Dembski personality cult". can anybody think of an example of a personality cult which revolved around a smaller amount of personality?

Evolution doesn't have any specific objective nor problem to resolve. A fitness increase is not a specific objective, contrary to the program described here.

Caledonian, I think you missed something in what I said.
But we have the same ideas. What if I told you I am a graduate student in evolutionary biology? ;-)

I said that a fitness increase was not a specific objective (goal if you prefer) similar to the 'hello world' program, I didn't said it wasn't an objective concept (that's another matter).

I totally agree that nylonase never was an objective. Thus, it would be useless to calculate the probability to produce the nylonase gene in a initial bacterial population.

Genetic algorithms are not perfect evolutionary simulations in that they have a predefined goal which is used to compute fitness. They demonstrate the power of random variation, recombination, and selection to produce novel solutions to problems, but they are not a full simulation of evolution (and are not intended to be). In simulations of biological evolution, fitness is evaluated only locally; survival and reproduction is based only on information about local conditions, not on ultimate goals. However, the simulations demonstrate that distant fitness peaks will be reached if there are conditions of intermediate fitness (Lenski et al. 2003). Evolutionary processes do not "search." They respond to local fitness topography only. The fact that evolution (occasionally) reaches fitness peaks is a by-product of evolving on correlated fitness landscapes using purely local fitness evaluation, not an intended outcome.

— talkorigins

Jeannot, I think you raise an important distinction, but I also think it's a little harsh to call GAs/GP "totally irrelevant" to evolutionary biology. When we plate bacteria on nylon-rich media, we effectively define a fitness function which favors the ability to produce nylonase. When, lo and behold, nylonase-producing bacteria arise and flourish, should we not attribute this to RM/NS because we (effectively) set an artificial objective? After all, this objective is not one that would arise in nature (without manmade nylon).

I think it can be argued that in the GP example, the objective is similarly contained within the fitness function, which is this time explicitly defined; the "organisms" are not "aware" of it and cannot "consciously" work towards it. Of course, there are a lot of other issues in drawing any direct comparisons, but I think GAs can be helpful to evolutionary biologists insofar as they illustrate the general computational principles underlying RM/NS.

On the other point, I also can't believe that at this point anyone is still parading around "Sequence length n, alphabet length k, probability 1/k^n, HA!". It's a total emabarassment.

Yes, I may have been a little harsh with my 'totally irrelevant' if these simulations can be assimilated to a climb toward an adaptive peak.
But at most, regarding evolutionary biology (not informatics), these simulations are rather useless since the fundamental theorem of natural selection has been demonstrated by Fisher 76 years ago.

Evolution doesn't have any specific objective nor problem to resolve. A fitness increase is not a specific objective, contrary to the program described here.

— jeannot

Another point, quite apart from genetic algorithms, may be worth mentioning. The beginning programmer quite likely did not get his "Hello world" program correct the first time. Then he had to make modifications to it and select the version which worked best. In other words, his program evolved. This is certainly the case in more complicated computer programs. The programmers of these take much of their code from previous programs, and even then most of their work goes into fixing bugs which were inadvertently introduced. The process is different in important ways from biological evolution, to be sure, but the process still embodies the basics of evolution: modification and selection of existing forms. In short, design is a kind of evolution. To accept design is to accept evolution, and to reject evolution is to reject design.

The response is empty. Pim Van Meurs cites a program (written by intelligent agents I presume) that can create a "Hello World" program from some unspecified genetic algorithm.

— DaveScot

The way this is accomplished is not disclosed and if it were disclosed I'm sure we'd find the program is cheating by sneaking information in via the filter which ranks the "fitness" of the intermediate outputs.

— DaveScot

Trial and error and the choosing of partially successful intermediate solutions requires purpose and direction. These are supplied by the programmers of the so-called genetic algorithms.

— DaveScot

The frequency of structures that reproduce more efficiently increases, independently of the notions of problem and solution. These notions only exist in intelligent minds that can identify them.

Similarly, adaptive peaks don't exist before they are reached.

But this is just a problem of semantics.

Several things pop out immediately from this data.

The first is the incredible power of a little bit of natural selection pressure.

The odds of generating the final 58 line program by random chance is truly huge (660^58). That kind of number has the flavor of the improbability numbers that the ID proponents like to throw out everyday. I doubt that there's enough storage space on the planet to hold all those permutations.

Yet throw in a little survival-of-the-fittest pressure and you can get answers like that in a few thousand generations.

Secondly, look at the graph of fitness over time. Damned if there wasn't a little mini "Cambrian Explosion" right at generation 400, where the program suddenly became much, much more fit in a very short span.

Oh, and the third thing is how quickly a primitive precursor of "Hello World" established itself.

I would be curious to see the intimate details of the Panda's Thumb program. I'll bet dollars to donuts that the programmer cheated by defining intermediate fitness goals with the Hello World program in mind.

— GilDodgen

DaveScot wrote: Trial and error and the choosing of partially successful intermediate solutions requires purpose and direction. These are supplied by the programmers of the so-called genetic algorithms.

The frequency of structures that reproduce more efficiently increases, independently of the notions of problem and solution. These notions only exist in intelligent minds that can identify them.

—

Circuits can be and are designed both by versions of the genetic algorithm and by conscious human design. While both kinds of solutions work, those produced by artificial natural selection tend to be more robust in actual use than those made rationally. Like living systems such as metabolic pathways, artificially evolved systems go on functioning even when some of their parts are damaged while designed systems tend to be much more brittle. Andreas Wagner discusses this constrast in his book Robustness and Evolvability in Natural Systems. It is the zillionth reason to believe that living things were produced by chance and selection rather than conscious design.

Circuits can be and are designed both by versions of the genetic algorithm and by conscious human design. While both kinds of solutions work, those produced by artificial natural selection tend to be more robust in actual use than those made rationally. Like living systems such as metabolic pathways, artificially evolved systems go on functioning even when some of their parts are damaged while designed systems tend to be much more brittle. Andreas Wagner discusses this contrast in his book Robustness and Evolvability in Natural Systems. It is the zillionth reason to believe that living things were produced by chance and selection rather than conscious design.

On the other point, I also can't believe that at this point anyone is still parading around "Sequence length n, alphabet length k, probability 1/k^n, HA!". It's a total emabarassment.

DaveScot wrote: The way this is accomplished is not disclosed and if it were disclosed I'm sure we'd find the program is cheating by sneaking information in via the filter which ranks the "fitness" of the intermediate outputs.

DaveScot wrote: The way this is accomplished is not disclosed and if it were disclosed I'm sure we'd find the program is cheating by sneaking information in via the filter which ranks the "fitness" of the intermediate outputs.

Caledonian, I think you missed something in what I said. But we have the same ideas. What if I told you I am a graduate student in evolutionary biology? ;-)

Funny, the most natural thing in the world is for organized systems to become less organized over time. It's called the second law of thermodynamics. Dr. Behe's theory follows this law. And by the way, for you anti-sticker apologists, a law is more of a fact than a theory. http://www.pandasthumb.org/archives/2005/01/a_complex_regul.html#comment-13950

Davescot If you can give me a clear and precisely worded example of an `intelligent' agency causing a violation of the second law, please do. Me writing this sentence. -ds Comment by physicist --- March 7, 2006 @ 11:30 am http://www.uncommondescent.com/index.php/archives/886#comment-26392

Trial and error and the choosing of partially successful intermediate solutions requires purpose and direction. These are supplied by the programmers of the so-called genetic algorithms.

Funny, the most natural thing in the world is for organized systems to become less organized over time. It's called the second law of thermodynamics.

Next thing ya know, the IDiots will be blabbering (again) about "no fossil transitions", "bombardier beetles can't have evolved", and "radio-dating is unreliable".

Lenny would love AFDave

Second Law of Thermodynamics and Biology: Read "Into the Cool", a cool book about NET(Non-Equilibrium Thermodynamics) and a relationship to biological processed.

The bottom line is that the theory of random mutation and natural selection is dead as an explanation for the origin of life's complexity, diversity, information content and functionally integrated machinery. Actually, it isn't even a theory; it's wildly wishful speculation that flies in the face of common sense and hopelessly huge improbabilities. There isn't a shred of evidence that RM+NS has the creative power attributed to it. This is not science.

But it's all the Darwinists have, so it will be defended to the death by any means available, no matter what.

I understand that natural selection requires each step to be functional but not a step toward a predetermined goal. That is my point about why these programs are invalid. Teleology is invariably smuggled into the algorithms. Goals and fitness criteria suitable to reach them are predefined (although sometimes subtly), and intermediate islands of "function" are rigged to be easily reachable by trial and error.

I know very little about these programs but my guess is that you are asking them to be a complete simulation of evolution when all they are doing is illustrating some aspect of how complexity can be achieved through trial and success. After all the example that kicked off this thread was hardly an accurate representation of life and yet you felt that there lessons to be learned from it.

Discussions of computer models of evolutionary processes typically dissolve into confusion due to the failure to carefully distinguish between two kinds of models that differ in the information used to calculate fitness.

1. Models with global fitness calculations. These are Dawkinsian METHINKSITISLIKEAWEASEL sorts of models, where the fitness of a replicator is calculated as the distance of its phenotype from some target phenotype. The fitness equation "knows" the target state, and replicators are more or less fit (and therefore survive to replicate and/or recombine) based on relative similarity (e.g. the Hamming distance) to that target state. These kinds of models are not models of biological evolution, and claims that they are such models flatly misconstrue biological evolution. However, they are useful in demonstrating the power of cumulative selection, which is all Dawkins sought to do with his METHINKS illustration. He explicitly said that the METHINKS program was not a model of evolution, but only of cumulative selection and its power to transform tiny probability into high probability. Creationist have consistently and persistently misconstrued that program since it was published, and Dodgen's post is yet another example of that misconstrual.

2. Models with local fitness calculations. These are models in which the algorithm does not "know" what a target phenotypic state might be, but "knows" only what is better or worse in the local environment, where "local environment" means the values of relevant environmental variables in the volume of phenotype space actually occupied by the current population. The fitness equation of the algorithm can calculate relative fitness among the replicators in the population, based on some defined properties of the replicators in that environment. Most GAs are of this nature. If I want to evolve a population of artificial stock traders, I cannot write down the specific target phenotype -- if I could, I wouldn't bother to use a GA, I'd just write it down and trade on it. However, I know some properties a good artificial trader should have, and I can write a fitness function that tests for values of those properties. For example, I might use risk-adjusted return over some historical data as the relevant property. All members of the population paper trade over that period, and the algorithm calculates each artificial trader's risk-adjusted return and ranks the traders on that measure to determine which survive to replicate, their probability of entering into recombination, and so on. The algorithm "knows" a property of artificial traders -- relative risk-adjusted return, where better traders are higher -- but "knows" neither what an excellent trader's phenotype would look like nor what the global maximum risk-adjusted return might be. It "knows" only how risk-adjusted return differs among the members of the current population.

Biological evolution is an algorithm of the second sort. The algorithm does not "know" a target phenotype in order to determine fitness on the basis of similarity to that target phenotype. Rather, the algorithm of biological evolution "knows" only locally determined fitness, where fitness is "calculated" implicitly as survival and relative reproductive success of the actual replicators in the population in a specific environment composed of physical variables and biological variables (conspecifics and other species).

As a consequence, any algorithm that incorporates a fitness calculation that refers to some phenotype (or genotype) not currently in the population is not a model of biological evolution. Biological evolution "knows" what's better or worse in the current population only by virtue of the differential survival and reproduction of the members of that population; it does not "know" an optimal phenotype or genotype toward which it should evolve.

RBH

What is the probability of arriving at our Hello World program by random mutation and natural selection?

METHINKS is a representation of biological evolution; it's just that it explicitly defines what the environment will favor. Other simulations implicitly define this by generating environments in which certain traits will prove more robust.

From a mathematical and theoretical perspective, it makes no difference if you set up the fitness space explicitly or implicitly. The best solutions within the fitness space will be the states which the simulation will tend towards either way.

Writing Computer Programs by Random Mutation and Natural Selection The first computer program every student writes is called a "Hello World" program. It is a simple program that prints "Hello World!" on the screen when executed. In the course of writing this bit of code one learns about using the text editor, and compiling, linking and executing a program in a given programming environment. Here's a Hello World program in the C programming language: (code stuff) This program includes 66 non-white-space text characters. The C language uses almost every character on the keyboard, but to be generous in my calculations I'll only assume that we need the 26 lower-case alpha characters. How many 66-character combinations are there? The answer is 26 raised to the 66th power, or 26^66. That's roughly 2.4 x 10^93 (10^93 is 1 followed by 93 zeros).

To get a feel for this number, it is estimated that there are about 10^80 subatomic particles in the known universe, so there are as many 66-character combinations in our example as there are subatomic particles in 10 trillion universes. There are about 4 x 10^17 seconds in the history of the universe, assuming that the universe is 13 billion years old.

What is the probability of arriving at our Hello World program by random mutation and natural selection? How many simpler precursors are functional, what gaps must be crossed to arrive at those islands of function, and how many simultaneous random changes must be made to cross those gaps? How many random variants of these 66 characters will compile? How many will link and execute at all, or execute without fatal errors? Assuming that our program has already been written, what is the chance of evolving it into another, more complex program that will compile, link, execute and produce meaningful output?

I can't answer these questions, but this example should give you a feel for the unfathomable probabilistic hurdles that must be overcome to produce the simplest of all computer programs by Darwinian mechanisms.

Now one might ask, What is the chance of producing, by random mutation and natural selection, the digital computer program that is the DNA molecule, not to mention the protein synthesis machinery and information-processing mechanism, all of which is mutually interdependent for function and survival? The only thing that baffles me is the fact that Darwinists are baffled by the fact that most people don't buy their blind-watchmaker storytelling. Filed under: Intelligent Design --- GilDodgen @ 7:34 pm

Then I would decry the decreasing standards of our graduate schools. One of the most common ID arguments is that the specific attributes of living creatures could not have arisen through natural selection. This experiment is a quick way of demonstrating what has been proven again and again in more sophisticated and decisive ways: with the right selection pressures, any specified structure can be produced quite easily.

— caledonian

If Dembski was serious about having an intellectually respectable blog, he'd fire all those idiots and get somebody who had some familiarity with science. A guy with a degree in some kind of actual science.

I presume he doesn't do this because he enjoys the comedy as much as I do.

Avida, Weasel and other simulations are desperate attempts of Darwinists to prove evolutionary mechanisms of RM+NS using computer simulations. In heart of all these simulations you see a fitness functions that *intelligently* selects what should be selected and what should be not. The *designers* of all of these softwares subtly feed their system with external intelligence which normally is not available in the nature.

The notion of problem and solution may only exist in intelligent minds, the goal to solve the problem may exist only in intelligent minds, but the problem itself exists in nature. It is a fact that in an environment with a high concentration of an antibiotic, bacteria will die unless they evolve resistance to it.

— Todd

So would it be correct to say that theistic evolutionists picture their god as surreptitiously diddling with the environment, manipulating the fitness function so as to direct RM+NS to produce the desired lineages? Would this manipulation be sufficient in and of itself, or would this flavor of god also be required to interfere in other ways, such as drift control, or directing mutations according to the biase required to get the target results?

In any case, it's quite an elegant technique if the target result isn't known in advance, but its capabilities are.

METHINKS is a representation of biological evolution; it's just that it explicitly defines what the environment will favor. Other simulations implicitly define this by generating environments in which certain traits will prove more robust.

I'm going to have to disagree with RBH. Models that involve a global optima can be models of biological evolution. They are not going to approximate a complete biological fitness function, but they can approximate parts of fitness functions, i.e. areas with optima. I've used them to look at adaptation to environmental distrubance and stochasticity. I have a friend who's used them to look at domestication and recombination.

I should also point out that the WEASLE program is not a model of mutation and selection, but rather of substitution and selection.

One can take a goal-oriented fitness function and cast it in terms that are goal-less.

The optimal phenotype is 1111.

versus

Each 1 adds 1/4 to the fitness.

It's like these chuckleheads don't understand what the word "MODEL" means.

So would it be correct to say that theistic evolutionists picture their god as surreptitiously diddling with the environment, manipulating the fitness function so as to direct RM+NS to produce the desired lineages?

Caledonian left out a phrase in the first sentence: "... and calculates fitness as a function of distance from the most favored state." But that's precisely what biological evolution does not do.

jeannot says,

"Torbjörn, you didn't understand me. But my English might not be perfect.
Evolution doesn't have any specific objective nor problem to resolve. A fitness increase is not a specific objective, contrary to the program described here."

No, it is my english that is failing. "Objective" implies teology, so I shouldn't have used that, it is antropomorhising of software.

However, the software or algorithmn solves a problem and finds a solution (at least if we naively think of the fitness function as constant) since it can find a local maxima of fitness. This is what it's called in math, physics or software, so it should preferably be possible to say so without confusing it with antropomorphic purpose.

"Therefore, I concluded that this computer program is totally irrelevant to evolutionary biology."

I see that you resolved this later.

"DaveScot wrote:

"The way this is accomplished is not disclosed and if it were disclosed I'm sure we'd find the program is cheating by sneaking information in via the filter which ranks the "fitness" of the intermediate outputs.""

IDiots still doesn't understand peer review! The paper should not pass peer review if not enough information is disclosed for repetition of experiments. If it does anyway, an attempted repetition with the help of the authors will resolve the issue, or it is easily refuted, perhaps even deemed a fake. This makes it desirable for the authors to save the information they feel is redundant or too complex to put in the paper for a reasonable time.

Perhaps this explain why ID so easily claim 'peer review' on some of their papers.

""Objective" implies teology"

"Objective" implies teleology. (Not that the difference matters much. :-)

I'm going to have to disagree with RBH. Models that involve a global optima can be models of biological evolution. They are not going to approximate a complete biological fitness function, but they can approximate parts of fitness functions, i.e. areas with optima. I've used them to look at adaptation to environmental distrubance and stochasticity. I have a friend who's used them to look at domestication and recombination.

One can take a goal-oriented fitness function and cast it in terms that are goal-less. The optimal phenotype is 1111. versus Each 1 adds 1/4 to the fitness.

Perhaps this explain why ID so easily claim 'peer review' on some of their papers.

Astrophysicists program astrophysics models.
Chemists program chemistry models.
Biologists program biology models.

The IDists try to dismiss any computer simulations of evolution with hand waving garbage like "Well, a programmer acted intelligently on the system, thereby injecting information, so it's not really evolution."

Take that stupidity to it's conclusion--it can only be a computer model of evolution if nobody set up the model. If that were true, evolution would be uniquely prohibited from ever being modeled by scientists on a computer.

That's the kind of Grade A thinking you can only get from The Short Bus on the Information Superhighway, Uncommonly Dense®.

It is that models that employ knowledge of a global optimum in the fitness function to calculate the fitnesses of current members of an existing population for purposes of determining relative reproductive success of those members are not models of biological evolution.

"The way this is accomplished is not disclosed and if it were disclosed I'm sure we'd find the program is cheating by sneaking information in via the filter which ranks the "fitness" of the intermediate outputs.""

RBH, I agree that in biological evolution fitnesses are not determined by the distance to an optimal genotype. That does not mean that they can't in some way correlate with distance from an optimal genotype. (Phages are an example where optimal genotypes have been observed.) Model builders can exploit such correlation when employing simple fitness functions in their research.

In a corporation, the CEO always has an advantage on his engineers because they are judged by how well they meet their goals while the CEO can always claim that whatever happened was what he had in mind. Natural selection has the same kind of executive edge. Just as the Big Cheese in a company only cares about profits, evolution only searches for higher levels of fitness. To that end, anything goes, including becoming a blind parasite in the bladder of an octopus.

The American philosopher C.S.Pierce made a similar point about human creativity, which involves a search of what Pierce called "the Sea of Musement" for results that fit vague and ambiguous goals such as Beauty, Goodness, or Truth. Whenever people have to find something specific, they automatically become stupider since the probabilities of locating the desired result are so small. Finding something interesting and then retroactively declaring it's what you wanted is much easier. Unfortately, in most areas of human endeavor only a minority of individuals have the right to operate in this fashion. As Mel Brooks pointed out, "It's good to be the king."

RBH, I agree that in biological evolution fitnesses are not determined by the distance to an optimal genotype. That does not mean that they can't in some way correlate with distance from an optimal genotype. (Phages are an example where optimal genotypes have been observed.

It doesn't matter one whit whether the slope of the fitness function is calculated by referencing a known strategy, or whether it's generated by a specific equation that doesn't explicitly refer to any particular strategy, if the shapes of the functions are identical.

As long as the fitness function is continuous, there are going to be local regions where the surrounding terrain slopes towards optima. The size of the regions depends on how steep that slope is, granted, but the slope remains.

Claiming that a simulation with such slopes doesn't speak about biological evolution not only incorrect, but almost certainly disingenuous.

It doesn't matter one whit whether the slope of the fitness function is calculated by referencing a known strategy, or whether it's generated by a specific equation that doesn't explicitly refer to any particular strategy, if the shapes of the functions are identical.

— Caledonian

Claiming that a simulation with such slopes doesn't speak about biological evolution not only incorrect, but almost certainly disingenuous.

Astrophysicists program astrophysics models. Chemists program chemistry models. Biologists program biology models. The IDists try to dismiss any computer simulations of evolution with hand waving garbage like "Well, a programmer acted intelligently on the system, thereby injecting information, so it's not really evolution." Take that stupidity to it's conclusion---it can only be a computer model of evolution if nobody set up the model. If that were true, evolution would be uniquely prohibited from ever being modeled by scientists on a computer. That's the kind of Grade A thinking you can only get from The Short Bus on the Information Superhighway, Uncommonly Dense®.

— Steve S

I'm curious as to what is considered "optimal". Seems like a highly relative and subjective term.

What if they are not?

I'm curious if you or Jean have actually seen whether models have correctly predicted the direction a trait will take in the field.

— Sir_T

Nuclear reactors could be built more efficiently using supercomputers to artificially "evolve" designs, say engineers from the US Department of Energy's Oak Ridge National Laboratory in Tennessee. They have found they can speed up the extremely complex process of designing a reactor and generate novel designs from scratch by simulating natural selection.

— NewScientist

Qualls and his colleagues were looking for a more efficient design approach and found inspiration in biological evolution. They used software tools known as genetic algorithms to evolve different reactor designs.

— NewScientist

"[Simulated evolution] will come up with some systems we would just never have thought of," Qualls says. "It won't replace the experts or come up with a finished design, but it makes it possible to consider options they wouldn't have had otherwise."

— NewScientist

It seems like we're arguing about the shape of the container when the important point is that the fluid flows in such a way to fill it.

The given criterion, spell "Hello World", is a simple random filter and the fact that some intelligent force picked it out with the highly technical method of "hmm, that's kinda funny, I think I'll test this one" doesn't mean anything significant.

There are endless possible "fitness criteria". I have a bowl of M&M's on my desk and it seems in that particular species the red M&Ms die young and dark brown M&M's live into old age.

Even in a single environment there may be many possible survival strategies competing at the same time. You can stay away from the lions by getting faster (gazelle) growing bigger (elephants) learning to climb trees (monkeys) or out-thinking them (h.erectus).

The real important point isn't that the fitness criterion draws you to a pre-arranged solution, it's that it it makes you move in the first place.

Secondly, the date on the paper we're talking about is 1995. That's at least a century and a half ago in computer years. Isn't there follow-on data available about this kind of experiments that shows their strengths and weaknesses?

I'm not saying that models specifying an optimum can not be compared to some kind of biological process nor that they can't produce predictions (I wasn't clear on this). After all, the highly disputed Optimal Foraging Theory produced models whose predictions have been validated.

From RBH: "It is that models that employ knowledge of a global optimum in the fitness function to calculate the fitness of current members of an existing population for purposes of determining relative reproductive success of those members are not models of biological evolution." That statement is wrong.

— Caledonian

Re #105001: Jim Harrison --- You state something to the effect that circuits which have been artificially evolved are more robust than designed circuits. I would greatly appreciate a reference. Thanks.

As long as the fitness function is continuous, there are going to be local regions where the surrounding terrain slopes towards optima. The size of the regions depends on how steep that slope is, granted, but the slope remains. Claiming that a simulation with such slopes doesn't speak about biological evolution not only incorrect, but almost certainly disingenuous.

David Bensen asks: Re #105001: Jim Harrison ---- You state something to the effect that circuits which have been artificially evolved are more robust than designed circuits. I would greatly appreciate a reference. Thanks.

The complete references are in a late chapter of Andreas Wagner's book Robustness and Evolvability in Natural Systems (2005)---I'd give you page numbers, but I think I've loaned out my copy of the book.

Jim, thanks. I check it out of my library.

Phages are one example where "optima" have been observed, defined as a genotype or groups of genotypes that have maximal growth rate. Phages are small viruses that attack bacteria.

Warning: Well-adjusted people should just skip this.

The problem faced by the PT-linked program is much simpler than the one posed by UD. AIUI, the PT program simulates a computer which uses a subset of a Z80 machine in which a sequence of 8 bit bytes represents instructions and/or data. Any 256 8-bit byte value represents a hexadecimal number and most will also also represent a valid instruction of some sort depending on context.

[ Warning the follow may contain a lot of errors in detail, especially
with interpreting byte ordering 0102hex as 258Dec or 513Dec) or the
order in which bytes get loaded into a register]

For instance the sequence: 21 11 01 65 66, occupying consecutive memory locations from 0100 to 0104 can be interpreted rather differently depending on which of those bytes you look at first.

[geeky aside]
The Z80 has several 8 bit registers (which each can hold a number from 00 to FF (hex) or 0-255 (unsigned decimal), or -128-127 (signed decimal), or a character such as "A", depending on how you are looking at them).

These registers are labeled A, B, C, D, E, F, H, and L. Some of the registers are combined to form 16 bit numbers by some instructions. Eg AF, BC, DE, HL. In such a case, if D=1F and E=03, then DE=1F03 (or 7939 decimal).

There are some other 16 bit registers IX, IY which I'll skip, and one called PC (Program Counter) which contains the memory address of the next instruction. Generally 16 bit values can be numbers from 0-65536 (or -32768 to +32767) or can reference any single byte of memory in a computer with 65536 bytes of RAM (=64k).

If your Program Counter (PC) contains 0100, those numbers will be interpreted as

0100 21 11 01 LD HL, 1101 (21 means load register pair H and L with the next two bytes,
17 and 1 respectively [11Hex represents the decimal 16*1 + 1],
Alternatively HL combined =273 decimal)
0103 65 LD H,L (65 means copy the number in register L to register H,
so now both H and L contain 01)
0104 66 LD H, (HL) (66 means take the 16 bit value of H and L combined,
use that to form an address. 0101 in hex is 257 in decimal
so we take whatever 8-bit value is stored in memory location
257 and copy that to register H)

and would have the effect of setting L to 01, and H to whatever was in memory location 257.

If, OTOH, the program counter started at 0101, these instructions would be interpreted as

0101 11 01 65 LD DE, 0165 (Or load register D with 1 and E with 65(hex)=101(decimal)='e' (Ascii)
0104 66 LD H, (HL) (As in previous example)

and if PC was 0102 you'd get

0102 01 65 66 LD BC, 6566 (BC=25216 decimal or B=101/'e' and C=102/'f')

if you swap 21 and 11 you get
0100 11 21 01 LD DE, 2101
0103 65 LD H,L
0104 66 LD H, (HL)
[/geeky aside][resume slightly less geeky mode]

Almost any input is valid to the computer, but the results vary in usefulness to its human owner.

OTOH, if you write "rpintf("Hello World");" or mis-spell printf in any way in a c program you get a link error (function 'rpintf' not found) and your program doesn't run. If you forget the ";" or either of the quote characters you get a compiler error and your program doesn't run. In fact, almost any mistake not inside the string "Hello World" will result in your program failing to compile. This is because high level compilers are designed to trap common human errors - that is, really designed, not just "I don't understand it therefore it was designed"-designed. They allow us to write human-friendly programs which free the programmer from a lot of tedious detail. One mistake anywhere in a 10000 line program
and the program prevents the program from working. This gives the human programmer a change to fix the program before it causes any damage; A program which doesn't run is better than a program which introduces subtle errors. Conversely, in simple machine code almost any input causes something to happen, but often not what was intended.

DNA is rather different from high level computer language; Everyone's DNA contains some replication errors. These errors are not
caught by any compiler or any programming tool - instead you live your life and then maybe one day you get some "access violation" or infinite loop and you die (and maybe get submitted for analysis), or you're just constantly sick. There's no friendly "'G' expected but got 'T' at location 1F374C47" message or "some quote was unmatched" from the compiler which the midwife corrects.

But that's not to say that any DNA sequence will produce something - I just don't know - but is by no means clear to me that DNA is better represented by a high level langauge computer language (which I think was chosen to inflate the numbers) or a low-level one, if indeed it's a formal language at all and not just a part of a really complex series of chemical reactions.

And of course, I am not arguing that the Z80 was not designed; It was, and by humans.

Also, a lot of the posts at the UD site are going on about the additional complexity required by the operating system and the BIOS and the etc, but the PT paper doesn't need those. Operating systems,
assemblers and compilers came later in the '(non-biological) evoltion' of computers in order to make life easier for humans, but the computer does fine without them. C is easier for humans but harder for machines or evolution models. To a computer, the horrible hex stuff is a given, and it doesn't matter if it was preprogrammed, random, entered bit by bit using electrical switches, paper tape or
fancy compiler program. Output is produced by executing an OUT instruction or by copying the number representing output into a memory location mapped to the display unit, etc. The paper dealt with a simple virtual computer chip using a subset of Z80 with no operating system or BIOS. Their VM writes output by writing to 'physical' ports directly. The chances of hitting an "OUT" instruction and producing some sort of output on the Z80 are better than 1 in 256 whereas your chance of stumbling
upon 'printf("X") is much worse (1 in 256^8). Also they didn't implement block transfers which would allow the output of whole strings with one two-byte sequence and a few bytes of setup.

Granted, the Z80 architecture itself was no accident, but we are taking that as a given.

One thing that bugs me. Many IDers and creationists often describe DNA as a computer code. So, OK you guys, what are the basic instructions in DNA? How many bits are used to represent
them. Does the architecture have registers, busses, stacks, formal syntax, debugging tools, formal methadologies, data structures, standard algorithms? What's the DNA equivalent of a GOTO, or a CALL/RETURN or indirect or indexed addressing mode, or, at the level of 'C', formal function parameters, preprocessor directives, loops, conditionals, BNF. What library functions are available (and what arguments do they take)?

We've known about DNA for about half a century now, and the ID/creationist side argue that an inability to produce a full mutation by mutation history is proof that science is bogus and the
desiIMeanGoddidit, so I think it's only fair that I ask for a detailed blow by blow account of the DNA based computer architecture.
When we have that, we can look of how a mutation in an instruction affects the program, and how that affects the individual, and, ultimately, how individual mutations affect the individual's survival in a complex environment of interactive DNA machines. After that, we can decide of the required step by step mutation history of any given life form makes it impossible or not.

Granted, the Z80 architecture itself was no accident, but we are taking that as a given.

The question of how fitness is calculated for members of a population is separate from questions about the topography of the fitness landscape.

— RBH

I can fully concede (indeed, I can proclaim, as I have done in a number of venues) that 'natural' fitness landscapes are chock full of slopes and gradients leading to local optima --- they display locally autocorrelated surfaces --- while simultaneously insisting that a model purporting to represent biological evolution cannot use knowledge of properties of the topography outside the specific region occupied by members of a population at a given moment.

The program isn't "using" knowledge of the optimum strategy in any way other than determining the shape of the fitness space.

— Caledonian

In short, your point is incorrect, your argument in incorrect, and your position in the context of this experiment is specious. Do not bother with further questions --- you have already been recategorized as a fool, and I will not waste my time further attempting to educate you.

— Caledonian

This reply appears to be entirely disproportionate.... Not to mention the fact that I don't think you've understood what RBH is saying.

There's the spot where you seem to become more than usually confused. The program isn't "using" knowledge of the optimum strategy in any way other than determining the shape of the fitness space. The pressures on the populations are determined only by the fitness space that is calculated. The fact that the slope of the space depends upon the predefined, correct strategy is irrelevant.

One of the most common ID arguments is that the specific attributes of living creatures could not have arisen through natural selection. This experiment is a quick way of demonstrating what has been proven again and again in more sophisticated and decisive ways: with the right selection pressures, any specified structure can be produced quite easily.

If we accept the inherent premises of your argument, then no fitness space model could ever be considered to demonstrate evolution...

These registers are labeled A, B, C, D, E, F, H, and L. Some of the registers are combined to form 16 bit numbers by some instructions. Eg AF, BC, DE, HL. In such a case, if D=1F and E=03, then DE=1F03 (or 7939 decimal). There are some other 16 bit registers IX, IY which I'll skip, and one called PC (Program Counter) which contains the memory address of the next instruction. Generally 16 bit values can be numbers from 0-65536 (or -32768 to +32767) or can reference any single byte of memory in a computer with 65536 bytes of RAM (=64k).

— steve_h

Aw, man! You forgot the alternate register set!

Aw, man! You forgot the alternate register set! And the stack pointer! And the flags and the interrupt page and the refresh registers! If I were a creationist/IDer, I'd say that these oversights completely disprove your analogy and thus God Did It (but that my complete lack of programming prowess is entirely insignificant).

— RupertG

One thing that bugs me. Many IDers and creationists often describe DNA as a computer code. So, OK you guys, what are the basic instructions in DNA? How many bits are used to represent them. Does the architecture have registers, busses, stacks, formal syntax, debugging tools, formal methadologies, data structures, standard algorithms? What's the DNA equivalent of a GOTO, or a CALL/RETURN or indirect or indexed addressing mode, or, at the level of 'C', formal function parameters, preprocessor directives, loops, conditionals, BNF. What library functions are available (and what arguments do they take)?

— steve_h

Andreas,
Re "that grew to one of those long posts nobody ever reads anyway..."

Oops, guess that makes me nobody? ;) Course, being a software engineer myself I found that analysis interesting. If it's computer code, it's not the traditional sequential. Either multiple CPU's or multiple threads on one CPU.

I wonder though if recipe might be a better analogy than computer code (and never mind that my idea of "cooking" is punching buttons on a microwave), since at least a large part of the function seems to be adding of "ingredients" when they're called for.

Henry

hmm, I can't recall seeing a "fitness space model" that actually WAS used "to demonstrate evolution". All the models I've ever seen were used to test general assumptions and predictions, not to specifically model and predict the evolution of a specific trait within a real-world population.

I'm not really sure what else needs to be said.

This reply appears to be entirely disproportionate.... Not to mention the fact that I don't think you've understood what RBH is saying.

For example, if in an algorithm the fitness of individual X = (optimum body size - current body size), where \x{201C}optimum body size\x{201D} is the value of some peak on the fitness landscape distant from the point currently occupied by the individual, then that algorithm does not veridically represent biological evolution. It may illustrate some aspect of evolution \x{2014} e.g., the power of cumulative selection to transform tiny probabilities into large probabilities, as in Dawkins\x{2019} METHINKS illustration \x{2014} but it does not represent biological evolution with anything like the necessary fidelity to do serious work on most questions in evolution.

— RBH

Conversely, any functional relation between fitness and the distance to an optimal body size can be expressed in ways that does not refer to the optimal body size. The distinction between calculations of fitness that do and do not refer to optimal body size is therefore entirely subjective and I cannot see any significance in it. In particular, the choice of one of several equivalent expressions for fitness has no effect on the predictions that follow from the model.

I agree with RBH. Even if an optimum exists, estimations of fitness using this optimum as a parameter are approximations, which may be usefull and precise enough in many cases, but may not be applicable in others.
It reminds me of the comparison between Newton's mechanics and relativity.

Mathematical equivalence does not necessarily translate to equally valid mappings of reality.

Then perhaps Erik or Caledonian would kindly supply me with the equivalent of "optimal body size" for the GAs I use to model financial markets and drive derivatives trading. It would be so much easier and more efficient than having to evolve those damned artificial traders.

— RBH

Mathematical equivalence does not necessarily translate to equally valid mappings of reality.

— RBH

Even if an optimum exists, estimations of fitness using this optimum as a parameter are approximations,

— jeannot

Obviously, we could model --- represent --- the input-output relationships predicted by both hypotheses with the counting procedure; they are equivalent in that respect. However, if we actually do an experiment and find that the reaction time to produce an answer to each of a set of single-digit multiplication problems varies linearly --- or at least monotonically --- in the cardinality of the product, we have strong reason to prefer one representation (the counting procedure) over the other equivalent representation, the lookup table. Different system dynamics are predicted by the two different-but-equivalent representations (models). That's a non-trivial issue in doing the science, as distinguished from doing the math.

— RBH

So if I take Burger & Lande's distance-to-optimum-form of their fitness function and rewrite it into something which is completely equivalent, so that all of Burger & Lande's predictions remain unaffected, I might end up with something that is either a better or worse mapping of reality?

These objections leveled against the example are inane.

IDists frequently claim that because the statistical likelihood of producing a pattern through raw chance is small, that pattern could not have evolved. This simulation does not need to reproduce fitness spaces commonly found in nature to refute that claim, nor does it need to attempt to emulate the development of any organism, nor does it need to utilize randomly generated fitness spaces.

All it has to do is have a defined fitness algorithm and a system for "reproducing" with occasional mutations programs to which the fitness algorithm can be applied. It fulfils both of those criteria, and in the process, nicely demonstrates how natural selection can very quickly produce seemingly improbable results.

This is a trivially simple point, and for a person not to have grasped it by now requires either a hostile agenda, a lack of abstract reasoning, or both.

— Caledonian

Or more likely, the fact that you are talking about two different things. RBH seems to be talking about evolution modeling in general; you are talking about this experiment in particular.

— Rilke's Grandmother

As a consequence, any algorithm that incorporates a fitness calculation that refers to some phenotype (or genotype) not currently in the population is not a model of biological evolution.

— RBH

Determining the global optimum or optima of a function defined on a many-dimensional space is typically very difficult for a mere human. That we cannot in practice determine them does not mean they do not exist. Rewriting the function in terms of distances to such optima is typically also a daunting task in practice. That we cannot in practice do the rewriting does not mean that it is in principle impossible. For one-dimensional cases it is easy to do it practice.

— Erik

That* is what I have been arguing against; this experiment in particular is just an example of the much larger set RBH misrepresents.

— Caledonian

His point is that the algorithm does not have visibility (in the case of 'veridical modeling of evolution') to the landscape in order to determine such an optimum.

— Rilke's Granddaughter

The landscape is timewise dimensional, for example, and determining a global optimum on that would require the ability to 'forsee things' (Sybil Trewlaney eat your heart out). The algorithm used by evolution does not, cannot by the nature of the problem, incorporate global maxima or minima on the fitness landscape.

— Rilke's Granddaughter

On a first reading, Burger & Lande's specific predictions appear to be math-form-insensitive.

— RBH

Even if they are, however, other properties of the system --- e.g., the specific system dynamics --- may be sensitive to the form of the fitness function and those properties may interact with the specific properties under examination in Burger & Lande's context to produce differences in outcomes.

— RBH

What, in general, does it mean for an algorithm to "have visibility to the landscape"? And which algorithm do you have in mind? It is customary to split evolutionary algorithms into two parts, a fitness evaluation part and a part taking care of the population dynamics. The fitness evaluation part is essentially a black box as far as the rest of the evolutionary algorithm is concerned. Is it the fitness evaluation part or the population dynamics part that must not "have visibility to the landscape" in order to be veridical?

— Erik

So what is your view of population genetics models that incorporate global maxima in the fitness landscape? What do you make of Burger & Lande's computer simulation using a distance-to-optimum fitness function?

I think they are using a local, rather than an global value in the equation you reference.

— Rilke's Granddaughter

Do you say this because you think that all estimations of fitness are inaccurate? Or because you think that estimations of fitness using some optimum are particularly inaccurate?

— Erik

The sample problem in the OP is not a sample problem in evolution - evolution simply doesn't work that way. That's what RBH is trying to point out.

— Reikili's Granddaughter

So you don't think the fitness algorithm used by Burger & Lande has access to the landscape optimum phenotype value? What do you think the term kt in the Gaussian-type exponential of Eq. (16) represents?

— Erik

But it can and does work that way --- that's what you've both been failing to comprehend.

— Caledonian

This is pointless. Welcome to the list, Granddougher.

I wonder though if recipe might be a better analogy than computer code (and never mind that my idea of "cooking" is punching buttons on a microwave), since at least a large part of the function seems to be adding of "ingredients" when they're called for.

— Henry J

The local optima; not the optima for the entire space.

— Rilke's Granddaughter

1) Darwinian logic is quite simple and clear. Here's a short summary: * If heritable variation exists, (which, of course, it does) * if excess reproduction occurs, (also obviously true, or we'd be up to our ears in mice) * if variants differ in their likelihood of survival and reproduction, (a little trickier, but still fairly obvious) * then the relative frequencies of the variants must change.

— PZ Myers

Andreas,

Re "the genome is equivalent to a chip."
Except that evolution of the gene pool can rewire that "chip" a whole lot easier than a hardware chip can be rewired. ;)

Come to think of it, I guess some aspects of that "chip" would get rewired during development of the organism, as well.

Henry

The fact of the matter remains: Random mutation and natural selection as an explanation for all of life's complexity, functionally integrated machinery, and information content is wishful speculation, unsupported by convincing hard evidence. This should simply be admitted.

Oh, don't worry, Gil. In a week or so, Paul Nelson's going to be presenting Ontogenetic Depth v 2.0 at the Society of Developmental Biology meeting, and I'm sure that will obliterate Darwinism, you know, like the Explanatory Filter did, and the NFL theorems, and your analogies to computers, and Irreducible Complexity, and Sal's plane anecdotes, and the last 400-500 dumb things you guys have said, and Intelligent Evolution will in the future, &c, &c, &c....

Dear Steve,

I appreciate your intellectually satisfying refutation of my thesis.

The fact of the matter remains: Random mutation and natural selection as an explanation for all of life's complexity, functionally integrated machinery, and information content is wishful speculation, unsupported by convincing hard evidence.

Glad you simply admitted it.

And I look forward to all the analogies I'm sure you'll present in the future, and the concomitant incredulity.

The fact of the matter remains: Random mutation and natural selection as an explanation for all of life's complexity, functionally integrated machinery, and information content is wishful speculation, unsupported by convincing hard evidence. This should simply be admitted.

— Gil

I suppose this is old-fashioned of me, but

optimum == the best

hence, 'global optimum' is redundant whilst 'local optima' is at best confusing. For the latter, 'local maxima' is certainly to be preferred.

Then where is global optimum of the fitness function defined by Eq. (16), if not at z = kt?

— Erik

To me, the use of an optimum in order to determine an adaptive landscape and/or simulate evolution is based on the assumptions: - that an optimum exists - that it can define alone the fitness of suboptimal replicators (individuals, alleles\x{2026}).

— jeannot

Evolution by natural selection is not based on these assumptions, at least not in the books or papers I\x{2019}ve read.

For instance, you want to simulate the evolution of beak size in a population of finches, by setting the optimum as the adapted size for consumption of the more frequent seeds: you make those two assumptions. But you\x{2019}re not sure the optimum is correct of even exists. As the population evolves, different (and extreme) beak sizes may be favored by instra-specific competition for resources (or whatever), resulting in an unstable polymorphism or even speciation. Can this be modeled with a program à la METHINKS?

I suppose this is old-fashioned of me, but optimum == the best hence, \x{2018}global optimum\x{2019} is redundant whilst \x{2018}local optima\x{2019} is at best confusing. For the latter, \x{2018}local maxima\x{2019} is certainly to be preferred.

— David B. Benson

Then where is global optimum of the fitness function defined by Eq. (16), if not at z = kt?

— Erik

There isn\x{2019}t one. There is an optimum at that particular node, because one can determine based on the fitness algorithm suggested/black boxed that such an optimum must exist.

— Rilke's Granddaughter

Evolutionary fitness in the real world is determinable only from the actual factors that affect a specific individual member of a population.

I believe what he's trying to say is that any perceived difference between the model and real life, no matter how trivial or irrelevant, will be seized upon as rhetorical evidence that evolutionary theory is false.

"Fitness is taken to be determined entirely by Gaussian stabilizing viability selection on the phenotypic value of the trait. The relative fitness of individuals of genotypic value G arises from an average of viability over environmental effects (see e.g. Turelli, 1984 or Bulmer, 1989) and is given by w(G) = exp[-(G - Zopt)^2 / (2 Vs)], where Vs^{-1} (>0) is a direct measure of the intensity of selection on genotypic values of the trait and Zopt is the optimal phenotypic value (and also the optimal genotypic value)." quoted from Y. Bello and D. Waxman, Near-periodic substitution and the genetic variance induced by environmental change, Journal of Theoretical Biology, 239(2):152-160, 2006 http://dx.doi.org/10.1016/j.jtbi.2005.08.044 "In Fisher's and Kimura's analyses, it was assumed that all traits are under stabilizing selection of identical intensity. In particular, it was assumed that the fitness of a phenotype is a monotonically decreasing function of its Euclidean distance from the optimal phenotype. Geometrically, this corresponds to a "fitness landscape" that is spherically symmetric. "Surfaces" of constant fitness are hyperspheres (i.e., circles when n = 2, spheres when n = 3, ...) that are centered on the optimal phenotype. If we choose to measure each trait in such a way that its optimal value is 0, then the optimal phenotype will lie at the coordinate origin, z = 0 = (0,0,...,0). Fitness is then a function of ||z|| = (z_1^2+z_2^2+...+z_n^2)^{1/2}." quoted from D. Waxman and J.J. Welch, Fisher's Microscope and Haldane's Ellipse, American Naturalist, 166:447-457, 2005, http://www.lifesci.sussex.ac.uk/home/David_Waxman/Papers/Microscope.pdf

I apologize in advance for what will surely turn out to be a totally clueless question:

since in reality organisms do not appear to be "assessed for fitness" by reference to an abstract Platonic ideal, isn't there something fundamentally wrong with doing so in modelling?

since in reality organisms do not appear to be \x{201C}assessed for fitness\x{201D} by reference to an abstract Platonic ideal, isn\x{2019}t there something fundamentally wrong with doing so in modelling?

— Aureola Nominee

Thank you, Erik.

First, I don't see those two equations as different; I see them as the same equation, written in two different ways. Therefore they both suffer from the same fundamental flaw (if it is a flaw), or neither does (if it isn't).

Second, my point is that "reproductive fitness", in my layman's eyes, does not depend from how close or how far a given organism is from a theoretical optimum, because it is relative, not absolute.

In other words, if I have a population of organisms, the reproductive success of each individual depends on how much better or worse than the others it is, not on how much worse than the local optimum it is.

So, for instance, if I take the function you mention

w(z) = 1 - (z - 0.17)^2

and use it to calculate a relative fitness

w(z1) - w(z2) = (z2 - 0.17)^2 - (z1 - 0.17)^2

I obtain

w(z1) - w (z2) = (z2)^2 - (z1)^2 - (0.34 * (z2 - z1))

which seems to me to be a very different kettle of fish!

As I said, I do not presume to correct people who have devoted their careers to this stuff; but I would really like to understand why, instead of using relative fitness (which would avoid the whole problem of "comparing to a non-existing ideal", we seem to be using absolute fitness. Where is my mistake?

P.S. Your remark on modelling trajectories seems to me not to address this aspect.

It is not an optimum genotype/phenotype, but rather the difference between it and a genotype/phenotype of interest, that is assumed to determine fitness.

— Erik

You just need a more general form of the fitness function. In Dawkins's METHINKS program the fitness is a function of a single variable, namely the genotype to be evaluated. In the case of your finches, one would probably need a fitness function that depends not only on the genotype to be evaluated, but also on the composition of the rest of the population. That would allow for frequency dependent selection.

— Erik

First, I don't see those two equations as different; I see them as the same equation, written in two different ways. Therefore they both suffer from the same fundamental flaw (if it is a flaw), or neither does (if it isn't).

— Aureola Nominee

So, for instance, if I take the function you mention w(z) = 1 - (z - 0.17)^2 and use it to calculate a relative fitness w(z1) - w(z2) = (z2 - 0.17)^2 - (z1 - 0.17)^2 I obtain w(z1) - w (z2) = (z2)^2 - (z1)^2 - (0.34 * (z2 - z1)) which seems to me to be a very different kettle of fish!

Mathematical equations . . . now my head hurts. Owwwwwwwwwww.

(grin)

Sorry, but I've always been mathematically-challenged. It's why I was an English major and not a science major.

Erik:

My point is precisely that using the difference is not equivalent to using the absolute value. I'm not entirely convinced that the effects of modelling absolute fitness vs. relative fitness are negligible; however, not being a professional in this field, I'll defer to expert opinion.

My point is precisely that using the difference is not equivalent to using the absolute value.

— Aureola Nominee

I'm not entirely convinced that the effects of modelling absolute fitness vs. relative fitness are negligible; however, not being a professional in this field, I'll defer to expert opinion.