It is quite common for ID commenters to argue that it is not possible for evolutionary forces such as natural selection to put Functional Information or Specified Information) into the genome. Whether they know it or not, these commenters are relying on William Dembski’s Law of Conservation of Complex Specified information. It is supposed to show that Complex Specified Information cannot be put into the genome. Many people have argued that this theorem is incorrect. In my 2007 article I summarized many of these objections and added some of my own.

One of the sections of that article gave a simple computational example of mine showing natural selection putting nearly 2 bits of specified information into the genome, by replacing an equal mixture of A, T, G, and C at one site with 99.9% C.

This post is intended to show a more dramatic example along the same lines.

Suppose that we have a large population of wombats and we are following 100 loci in their genome. We will make the wombats haploid rather than diploid, to make the argument simpler (diploid wombats would give a nearly equivalent result). At each locus there are two possible alleles, which we will call 0 and 1. We start with equal gene frequencies 1/2 and 1/2 of these two alleles at each locus. We also assume no association (no linkage disequilibrium) between alleles at different loci. Initially the haploytypes (haploid genotypes) are all combinations from 00000…000 to 11111…111, all equiprobable.

Let’s assume that the 1 allele is more fit than the 0 allele at each locus. The fitness of 1 is 1.01, and the fitness of 0 is 1. We assume that the fitnesses are multiplicative, so that a haploid genotype with M alleles 1 and 100-M alleles 0 has fitness 1.01 raised to the Mth power. Initially the number of 1s and 0s will be nearly 50:50 in all genotypes. The fraction of genotypes that have 90:10 or more will be very small, in fact less than 0.0000000000000000154. So very few individuals will have high fitnesses.

What will happen to these multiple loci? This case results in the gene frequency of the 1 allele rising at each locus. The straightforward equations of theoretical population genetics show that after 214 generations of natural selection, the genotypes will now have gene frequency 0.8937253. The fraction of genotypes having 90:10 or more will then be 0.500711. So the distribution of genotypes has moved far enough toward ones of high fitness that over half of them have 90 or more 1s. If you feel that this is not far enough, consider what happens after 500 generations. The gene frequencies at each locus are then 0.99314, and the fraction of the population with more than 90 1s is then more than 0.999999999.

The essence of the notion of Functional Information, or Specified Information, is that it measures how far out on some scale the genotypes have gone. The relevant measure is fitness. Whether or not my discussion (or Dembski’s) is sound information theory, the key question is whether there is some conservation law which shows that natural selection cannot significantly improve fitness by improving adaptation. My paper argued that there is no such law. This numerical example shows a simple model of natural selection doing exactly what Dembski’s LCCSI law said it cannot do. I should note that Dembski set the threshold for Complex Specified Information far enough out on the fitness scale that we would have needed to use 500 loci in this example. We could do so — I used 100 loci here because the calculations gave less trouble with underflows.

I hope that ID commenters will take examples like this into account and change their tune.

Let me anticipate some objections and quickly answer them:

1. This is an oversimplified model, you were not realistic. Dembski’s theorems were intended to show that even in simple models, Specified (or Functional) Information could not be put into genomes. It is therefore appropriate to check that in such simplified models, where we can do the calculation. For if natural selection is in trouble in these simple models, it is in trouble more generally.

2. You have not allowed for genetic drift, which would be present in any finite population. For simplicity I left it out and did a completely deterministic model. Adding in genetic drift would complicate the presentation enormously, but would still result in the achievement of a population with all 11111…1111 genotypes after only a modest number more of generations.

3. If fitness differences are due to inviability of some genotypes, fitnesses could not exceed 1. Yes, but making the 0 allele have fitness 1/1.01 = 0.9900990099… and the 1 allele have fitness 1 could then be used, and the results would be exactly the same, as long as the ratio of fitnesses of 0 and 1 is still 1:1.01.

4. You just followed gene frequencies — what about frequencies of haplotypes? This case was set up with multiplicative fitnesses so that there would never be linkage disequilibrium, so only gene frequencies need to be followed.

I trust also that people will not raise all sorts of other matters (the origin of life, the bacterial flagellum, the origin of the universe, quantum mechanics, etc.) To do so would be to admit that they have no answer to this example, which shows that natural selection can put functional information into the genome.