Yesterday, I wrote:

Science has a very exact idea of the capabilities of evolution. If you praise evolution one millimeter higher than this, you're not "fighting on evolution's side" against creationism. You're being scientifically inaccurate, full stop.

In this post I describe some well-known inefficiencies and limitations of evolutions. I say "evolutions", plural, because fox evolution works at cross-purposes to rabbit evolution, and neither can talk to snake evolution to learn how to build venomous fangs.

So I am talking about limitations of evolution here, but this does not mean I am trying to sneak in creationism. This is standard Evolutionary Biology 201. (583 if you must derive the equations.) Evolutions, thus limited, can still explain observed biology; in fact the limitations are necessary to make sense of it. Remember that the wonder of evolutions is not how well they work, but that they work at all.

Human intelligence is so complicated that no one has any good way to calculate how efficient it is. Natural selection, though not simple, is simpler than a human brain; and correspondingly slower and less efficient, as befits the first optimization process ever to exist. In fact, evolutions are simple enough that we can calculate exactly how stupid they are.

Evolutions are slow. How slow? Suppose there's a beneficial mutation which conveys a fitness advantage of 3%: on average, bearers of this gene have 1.03 times as many children as non-bearers. Assuming that the mutation spreads at all, how long will it take to spread through the whole population? That depends on the population size. A gene conveying a 3% fitness advantage, spreading through a population of 100,000, would require an average of 768 generations to reach universality in the gene pool. A population of 500,000 would require 875 generations. The general formula is

Generations to fixation = 2 ln(N) / s

where N is the population size, and (1 + s) is the fitness. (If each bearer of the gene has 1.03 times as many children as a non-bearer, s = 0.03.)

Thus, if the population size were 1,000,000—the estimated population in hunter-gatherer times—then it would require 2763 generations for a gene conveying a 1% advantage to spread through the gene pool. $^{1}$

This should not be surprising; genes have to do all their own work of spreading. There's no Evolution Fairy who can watch the gene pool and say, "Hm, that ...

The Simple Math of Evolution