Posted by Reed on August 26, 2004 | Comments (0) | TrackBack (0)

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

Posted by Reed on August 24, 2004 | Comments (10) | TrackBack (0)

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.

Posted by Pim van Meurs on August 12, 2004 | Comments (6) | TrackBack (0)

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.

Continue reading  “A quick explanation of Wasserstein Metric”

Posted by Reed on May 30, 2004 | Comments (0) | TrackBack (9)

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.

Continue reading  “EvoMath 3: Genetic Drift and Coalescence, Briefly”

Posted by Jeff on May 12, 2004 | Comments (58) | TrackBack (0)

Two previous entries on this blog by John Lynch have discussed the scientific output (or lack thereof) of two intelligent design superstars, Jonathan Wells and Michael Behe. Despite claims that both of these ID supporters are actively engaged in research, Lynch documents that they have published little or no scientific research in the last six years. Now let's look at the record of another one of ID's superstars, William Dembski.

Continue reading  “Dembski's mathematical achievements”

Posted by Reed on April 08, 2004 | Comments (0) | TrackBack (0)

In the first installment of EvoMath, I derived the Hardy-Weinberg Principle and discussed its significance to biology. In the second installment I will demonstrate how to test if a population deviates from Hardy-Weinberg equilibrium.

Continue reading  “EvoMath 2: Testing for Hardy-Weinberg Equilibrium”

Posted by Reed on April 04, 2004 | Comments (9) | TrackBack (2)

The Hardy-Weinberg Principle states that a population satisfying certain primary conditions will not evolve. This result is very important because any departure from these conditions will result in an evolving population. Three scientists in the early 20th century (G.H Hardy, Wilhelm Weinberg, and W.E. Castle) independently discovered this principle which is now used as the null model of population biology.

Consider a group of interbreeding organisms (a population). . .

Continue reading  “EvoMath 1: The Hardy-Weinberg Principle”

Posted by Reed on April 02, 2004 | Comments (17) | TrackBack (1)

Occasionally a creationist or an aideeist will make the wild assertion that biologists do not understand math/statistics and that math/statistics actually disproves evolution. This is followed by some random math argument based on ignorance of biology. The irony is that biologists probably understand math better than mathematicians understand biology, for the simple fact that biologists use math in their work more than mathematicians use biology in their work.

Continue reading  “EvoMath 0: An Introduction”

Posted by Timothy Sandefur on March 31, 2004 | Comments (0) | TrackBack (2)

A common charge of anti-evolutionists is to say "but what are the chances of this all happening by mechanistic and unguided processes?" Well, in this article (which I saw on Arts & Letters Daily), Freeman Dyson explains "Littlewood's Law of Miracles," which "states that in the course of any normal person's life, miracles happen at a rate of roughly one per month." Reminds me of how Richard Feynman used to put it. "Today on the freeway, I drove behind a car whose license plate was 3SVD543. Can you imagine how small the chances are of that happening?"

For more on the unremarkability of extremely rare coincidences, see chapter 7 of Richard Dawkins' magnificent Unweaving The Rainbow.