Recently in EvoMath Category

A couple of months ago, I finished a first reading of Stephen Meyer’s new book, Signature in the Cell. It was very slow going because there is so much wrong with it, and I tried to take notes on everything that struck me.

Two things struck me as I read it: first, its essential dishonesty, and second, Meyer’s significant misunderstandings of information theory. I’ll devote a post to the book’s many mispresentations another day, and concentrate on information theory today. I’m not a biologist, so I’ll leave a detailed discussion of what’s wrong with his biology to others.

In Signature in the Cell, Meyer talks about three different kinds of information: Shannon information, Kolmogorov information, and a third kind that has been invented by ID creationists and has no coherent definition. I’ll call the third kind “creationist information”.

Intelligent design creationists love to talk about information theory, but unfortunately they rarely understand it. Jonathan Wells is the latest ID creationist to demonstrate this.

In a recent post at “Evolution News & Views” describing an event at the University of Oklahoma, Wells said, “I replied that duplicating a gene doesn’t increase information content any more than photocopying a paper increases its information content.”

Wells is wrong. I frequently give this as an exercise in my classes at the University of Waterloo: Prove that if x is a string of symbols, then the Kolmogorov information in xx is greater than that in x for infinitely many strings x. Most of my students can do this one, but it looks like information expert Jonathan Wells can’t.

Like many incompetent people, Wells is blissfully unaware of his incompetence. He closes by saying, “Despite all their taxpayer-funded professors and museum exhibits, despite all their threats to dismantle us and expose us as retards, the Darwinists lost.”

We don’t have to “expose” the intelligent design creationists as buffoons; they do it themselves whenever they open their mouths.

A few people (actually, a lot of people) have written to me asking me to address Kirk Durston’s probability argument that supposedly makes evolution impossible. I’d love to. I actually prepared extensively to deal with it, since it’s the argument he almost always trots out to debate for intelligent design, but — and this is a key point — Durston didn’t discuss this stuff at all! He brought out a few of the slides very late in the debate when there was no time for me to refute them, but otherwise, he was relying entirely on vague arguments about a first cause, accusations of corruption against atheists, and very silly biblical nonsense about Jesus. So this really isn’t about revisiting the debate at all — this is the stuff Durston sensibly avoided bringing up in a confrontation with somebody who’d be able to see through his smokescreen.

If you want to see Durston’s argument, it’s on YouTube. I notice the clowns on Uncommon Descent are crowing that this is a triumphant victory, but note again — Durston did not give this argument at our debate. In a chance to confront a biologist with his claims, Durston tucked his tail between his legs and ran away.

Creationists think information theory poses a serious challenge to modern evolutionary biology – but that only goes to show that creationists are as ignorant of information theory as they are of biology.

Whenever a creationist brings up this argument, insist that they answer the following five questions. All five questions are based on the Kolmogorov interpretation of information theory. I like this version of information theory because (a) it does not depend on any hypothesized probability distribution (a frequent refuge of scoundrels) (b) the answers about how information can change when a string is changed are unambiguous and agreed upon by all mathematicians, allowing less wiggle room to weasel out of the inevitable conclusions, and (c ) it applies to discrete strings of symbols and hence corresponds well with DNA.

All five questions are completely elementary, and I ask these questions in an introduction to the theory of Kolmogorov information for undergraduates at Waterloo. My undergraduates can nearly always answer these questions correctly, but creationists usually cannot…

According to Rotten Tomatoes, the movie WΔZ starts showing today in the UK. The movie is a psychological thriller/horror movie and has been compared to Se7en. What makes this movie interesting is the fact that the screenplay was inspired by Price’s Equation:

Price’s Equation is a broader version of Fisher’s Fundamental Theorem of Natural Selection. It describes how the change in trait with phenotypes is related to the phenotypes’ fitnesses, . Note that the genetics of the trait (mutation, ploidy, etc.) is contained in the second term. See Wikipedia for more details.

Now according to the Rotten Tomatoes exclusive on WΔZ:

The script comes from City of Vice scribe Clive Bradley, who claims to have come up with the movie’s premise after flicking through a book on Darwinism. “It featured a mathematical equation—W Delta Z—formulated by American population geneticist George R. Price,” he explains. “It supposedly shows that there’s no real altruism in nature; no such thing as selflessness. Price was so upset by his findings that he ended up giving away all his possessions to the poor and, eventually homeless himself, committed suicide with a pair of nail scissors in a filthy London squat.”

The study of the evolution of altruism goes beyond the description above, and I hope moviegoers won’t be seduced by this fictional account of evolutionary theory. (I’m waiting to see what demagoguery that AiG, DI, and the Expelled frauds come up with about this movie.) Now, it is true that according to Price’s Equation, altruistic behavior that benefits a species at the cost of individual fitness is selected against. (Note that a deleterious phenotype can still exist in a population through mutation-selection balance or genetic drift.) However, if the altruism only benefits certain members of the species (e.g. relatives), then altruism can be selected for.

This is represented by Hamilton’s rule: . This describes under what conditions an altruistic allele will invade a population. is the cost of the allele to the “actor”, is the relatedness of the receiver to the actor, and is the benefit that the receiver receives by the actor being altruistic. The consequence of Hamilton’s rule is that selfish genes can still be altruistic. There is a lot of interesting literature about the evolution of altruism, including how punishment can reinforce altruism. I recommend Sean Rice’s Evolutionary Theory, Chapter 10, as a good starting point.

So if anyone in the UK goes to see this movie this weekend, please send us an overview/review.

As promised, hot off the presses, here is a little tutorial I’ve decided to call Genetic Algorithms for Uncommonly Dense Software Engineers. Given some of the bizarre commentary issuing from the ID community over at Uncommon Descent regarding my past posts on Genetic Algorithms, I’ve developed this guide to help the folks over there figure out if the Genetic Algorithms (GAs) they are working on employ a “fixed-target” approach (like Dawkins’s Weasel), or if they are instead un-targeted, like most GAs used in research and industry are.

They came for a contest that might someday be viewed as a pivotal moment in the eternal conflict between Darwin and Design.

On one side were the Intelligent Designers. They came from California and Alabama, New Mexico and England, Finland and the Netherlands, and from all around the world. They came from academia, and from industry, and from the armed services. They came armed with computer spreadsheets, home-made programs, graph paper and calculators. They applied trigonometry and calculus, intuition and insight, knowledge of minimal soap films and surface tension, database optimizing algorithms and random searches, and other techniques available only to Intelligent Designers. And they strived to answer the tricky question “What is the Steiner Tree (smallest possible network of straight line segments connecting six given points) for the network shown in “Take the Design Challenge!”

On the other side were Evolutionary (or Genetic) Algorithms, in which herds of digital organisms were bred over many generations. Each organism was a string of numbers and letters, which were “transcribed” by fixed rules as representing some of the billions upon billions of possible candidate networks for the given problem. Those organisms whose lengths were smaller gained a slightly better chance at being a parent of one of the organisms of the next generation, and mutations of the strings were allowed to happen occasionally. In this process, no trigonometry or calculus was required. No information about characteristics of Steiner Trees was necessary. But, as the strings competed with each other, marvelous and unexpected designs began to appear.

Although most of the Intelligent Designers were not members of the “Intelligent Design” movement, which had been officially invited to respond, the ID community did indeed weigh in, via the efforts of Salvador Cordova, one of the IDers running the show at William Dembski’s blog Uncommon Descent.

So, what is the Answer? Did Salvador do better than Darwin? Did our team of Intelligent Designers find the True Steiner, or did they, like the evolutionary algorithm, find “MacGyver” (not-quite-perfect-but-extremely-functional) solutions also?

Readers, let’s enter the Design Room and meet our Winners!

In July, I described a Genetic Algorithm that, unlike Dawkins’ “Weasel” experiment, specifies no fixed “Target” for the simulation, but instead rewards those members of the current population which use fewer or shorter segments to connect a fixed set of points. As the algorithm progresses, it finds a multitude of answers for the math problem called “Minimization of Steiner Trees,” i.e. the shortest possible straight-line networks connecting the fixed points.

Last Monday, I posted Take the Design Challenge, wherein I called for solutions to a tricky little 6-point network. Next Monday, I will announce the winners (there are 20 entries already, several with true Steiner Solutions, and others with almost-as-good “MacGyver” solutions).

Imagine my surprise, then, when I found Salvador Cordova at Uncommon Descent spewing blatant falsehoods about this work. I was shocked - shocked, I say - to catch the UD Software Engineers in a lie. And quite a lie it is - with the help of mathematicians like Carl Gauss, I’m going to lift the veil from the obfuscations of IDers, and prove it’s a Lie, much as you would prove a mathematical theorem.

Since posting my essay on Genetic Algorithms, I’ve since developed a brand-new C++ version of my Steiner Networks genetic algorithm, a vast improvement over the old Fortran number-clunker I developed five years ago.

And already, the new code is leading to some very interesting results.

In light of William Dembski’s remarks in No Free Lunch, basically arguing that in all Genetic Algorithms,

… the fitness function … is well-defined and readily supplies the complex specified information that an optimal crooked wire genetic antenna [or any other problem solved with Genetic Algorithms] seems to acquire for free,

I’m giving Intelligent Design proponents (and everyone else!) a chance to actually Design something!

As you recall, my algorithm involves finding Steiner Trees, the shortest networks of straight-line segments connecting a given collection of fixed points. These networks may include additional variable “Steiner Points” where segments may meet.

The Challenge Here is a collection of six fixed points. Designers, send your candidates for the Steiner Solution for this particular 6-point system to me at nmsrdaveATswcp.com (replace the AT with an @ if you please).

I will announce the winners (if any) in a week’s time, and also will present the answer that Evolution came up with. I’m interested in proposed solutions from any and all (you don’t have to be in the ID camp), but am especially interested in solutions by ID advocates, since y’all are saying that the solution is already implicitly defined in the statement of the problem (finding shortest connected networks). Here’s a Hint:

Here follows the guts of my new C++ program for solving Steiner Tree problems with a Genetic Algorithm.

I have eliminated much of the Microsoft Foundation Class support code, focusing mainly on the number-crunching routines. I will be happy to share the complete code with interested parties.

The original FORTRAN version from five years ago is still online at NMSR.

You’ll see that I’ve cleaned up and organized everything quite a bit, and completely re-done the snippet which checks for properly connected solutions.

Dave August 21^st, 2006

Genetic Algorithms are simplified simulations of evolution that often produce surprising and useful answers in their own right. Creationists and Intelligent Design proponents often criticize such algorithms for not generating true novelty, and claim that these mathematical recipes always sneak the “answer” into the program via the algorithm’s fitness testing functions.

There’s a little problem with this claim, however. While some Genetic Algorithms, such as Richard Dawkin’s “Weasel” simulation, or the “Hello World” genetic algorithm discussed a few days ago on the Thumb, indeed include a precise description of the intended “Target” during “fitness testing” on of the numerical organisms being bred by the programmer, such precise specifications are normally only used for tutorial demonstrations rather than generation of true novelty.

In this post, I will present my research on a Genetic Algorithm I developed a few years ago, for the specific purpose of addressing the question Can Genetic Algorithms Succeed Without Precise “Targets”? For this investigation, I picked a math problem for which there is a single, specific answer, yet one for which several interesting “quasi-answers” - multiple “targets” - also exist.

PT readers, you are about to enter the Strange and Curious world of “The MacGyvers.” Buckle up your seat belts, folks - our ride through Fitness Landscapes could get a little bumpy.

I don’t know about you, but whenever I want to learn about information theory, I naturally turn to the creationists. Why, they know so much about geology, biology, and paleontology, it only seems reasonable that their expertise would extend to mathematics and computer science.

Take Nancy Pearcey, for example. Here, for example, we learn that Ms. Pearcey has studied philosophy, German, and and music at Iowa State; that she has a master’s degree in biblical studies; that she is a senior fellow at that temple of truth, the Discovery Institute; and that for nine years she worked with former Watergate conspirator and convicted criminal Charles Colson on his radio show, “Breakpoint”. Why, those seem exactly the sort of credentials one would want in an instructor of information theory…

Read more at Recursivity.

Forget prime numbers in the movie “Contact”, your own last name may be encoded in your DNA, reports Science

Paging Mr. Chromosome Your last name may be encoded in your DNA

A genetic study of British men finds a one in four chance that two strangers with the same last name share an ancestor. The relationship implies that certain surnames have a unique DNA signature–a fact that could help police narrow down suspects in some unsolved cases. But the criminally intent John Smiths of the world need not worry, because the signatures are found predominantly for rare surnames.

Now that’s a ‘Design Inference’

It has been a while since the last EvoMath. In this installment I am going to begin to discuss classical selection theory. Selection occurs when certain alleles are likely to transmit more copies of themselves to the next generation than other alleles at the same locus. The simplest way to think of this is in terms of the viabilitity of individuals. If an individual dies before it can reproduce, then it is not able to transmit its genes. If such a death was influenced by the genes it carried then selection can occur. Classical selection theory assumes that there exists viability selection and that it is constant, i.e. independent of allele or genotype frequencies. There is also theory behind frequency-dependent selection, but it beyond the scope of this article.

Read the rest at De Rerum Natura

I’m working on a new installment of evomath. This one is going to be some simple examples of classical selection theory. I am probably going to post it on my blog because it is using features of a new version of Kwickcode that I haven’t setup on PT. I think I am going to wait until PT makes the switch to MT 3.1 before I install version 2 of my plugins here.

Now to encourage me to keep on track with my series, I want readers to make requests. Is there any particular part of evolutionary theory that you would like me to cover? Is there something you didn’t quite get from your days as an undergraduate that you want to see again? Etc.

Note that Dembski has uploaded a revised manuscript which now correctly attributes the measure to Renyi and thanks the many critics for their contributions

I am not a mathematician but let me give it a try and others can amend and revise my comments.

The Kantorovich/Wasserstein distance metric is also known under such names as the Dudley, Fortet Mourier, Mallows and is defined as follows.

where refers to the expectation of the random variable x and means that the minimum is sought on all random variables X which take a distribution F and random variables Y which take a distribution G.

where is the set of all joint distributions of random variables X and Y whose marginal distributions are F and G.

Genetic Drift

EvoMath is back from a long hiatus. In this edition I will briefly touch on genetic drift and coalescence theory. Genetic drift is the evolutionary force whereby allele frequencies fluctuate due to chance because the alleles in a generation are a random sample of the alleles in previous generation. To help understand what I am talking about, consider a heterozygous father, with genotype Aa. Under Mendelian heredity, he will pass on the A allele 50% of the time and the a allele the other 50% of the time. If he has only one child, then he clearly cannot pass on both of his alleles, and thus one of those alleles–say a–will be lost from his lineage. The remaining allele, A, will then have “drifted” to 100% or “fixation.” If he has more children, then he may pass on both of his alleles, but it is not likely to be exactly at a 50:50 ratio.

Genetic drift occurs whenever a population has a finite size, and since all populations are finite, it occurs in all populations. However, in large populations it can be very weak and thus negligible compared to other evolutionary forces.