First I should say that I assume that analysis made by David MacKay is correct, given its assumptions. Any conflict is only with hasty conclusions that might be drawn from it.

For background, I’m not concerned with biological realism here, but about constraints that might be incorrectly be thought to apply to all evolutionary systems, including computational systems designed to evolve their information quickly.

For simply dividing and re-merging a population, let’s substitute ongoing partial division: We have one big, gene-mixing population when viewed on a long time scale, but not with the fastest and most uniform possible mixing.

Now consider “epistasis”, that is, non-additive gene effects. It is both reasonable and permissible for present purposes to postulate that many mutations produce a small benefit that becomes large only when combined with a second mutation which (for example) fixes a problem created by the first, and would be disadvantageous in itself. The second mutation can’t spread until the first becomes common, and in a small population, this will happen in fewer generations. The story from there involves mixing from one small population to another, or perhaps favorable linkage disequilibrium when mixing into a larger population. This example is enough to show that conclusions drawn from a mathematically simple, idealized population model need not hold in general. (Note that GAs are often coded with structured populations of the sort I described.)

There is also the question of what the question is. If (as tends to happen) “rate of information gain” is tacitly regarded as meaning “rate of evolution”, there is another problem, because conclusions about the former don’t necessarily tell us much about the latter. (“Rate of evolution” is clearly a meaningful concept, even if it lacks a unique metric).

Here, the argument is simple: It is permissible for present purposes to postulate a mapping from genotype to phenotype such that very rare mutations are very important; if so, then for a given mutation rate, a large population will find them faster, simply because there are more mutations in total. In this model, for a given rate of information gain, a larger population would achieve a faster increase in information value.

Here again, I am not saying that this is (or isn’t) a good description of biology, merely that it’s unwise to leap quickly from a theorem about information gain to a conclusion about the rate of significant evolutionary change.

Although I originally thought that an error rate of 10^-8 would imply a maximum genome size of around 10^8, a simple Python simulation failed to validate this. Although it takes one death to remove one mutation from the gene pool, more than one mutation can be removed by the same death. And this indeed gets you an info bound that goes as the square root of genome size, not just selection pressure.

The simulation was written for perfect selection on an entire gene pool (the exact bottom half being eliminated, and such) and it’s not clear to me what happens when you start introducing more realistic assumptions like stochastic selection on small bands or families.

It’s at least worth noting that in real life the genome seems to be mostly junk, and even if it’s not, it still contains vastly less info than it “could” according to MacKay’s bound and the age of life on Earth.

Merging subpopulations is not a trustworthy argument against various attempted speed limits, because the combined population doesn’t instantly get the best of every subpopulation. If you split up into a million subpopulations, then, after merging, every beneficial adaptation promoted in them goes to a frequency of 1 in a million. That’s going to take some time to rise to universality, and any collisions will lose information, and any complex adaptations will be fragmented.

See this discussion on Overcoming Bias for much more.