Correcting the (genetic) record

I screwed up the basic math on the post about evolution. I’m not too proud to admit that. Correctness is more important. Yes, I’m weird that way. No, I have no idea what I was thinking when I wrote the original post. Past me is not accountable to present me.

Let’s start over. In carefully controlled experiments, e. coli bacteria, which have 4, 639,221 base pairs in their DNA, showed 25 fixed mutations after 40,000 generations. That establishes a baseline for asexual organisms at (40,000 generations / 25 fixed mutations) * 4.639221 = 7422.75 generations per fixed mutation per million base pairs. The bacteria in the experiment were exposed to environmental pressures to encourage rapid mutation, so we must assume this is as fast as the process can go.

Human DNA contains about 3.1 billion base pairs. Using the same rate as bacteria (most people are, fortunately, not bacteria), that gives humans a rate of 7422.75 / 3,100 = 2.39 generations per fixed mutation. This is how fast science says genetic mutations can, on average, fix across the entire species. Notice we are ignoring how many members of the species there are, and whether that number is static, growing, declining, or varying somewhat randomly. This is a simple average.

There has been at most 9 million years (6-7 million is more likely) since the last human-chimp common ancestor. There are 40,000,000 base pair differences between modern humans and modern chimps. Splitting the difference and assuming parallel evolution, we must assume humans have 20,000,000 fixed mutations from that common ancestor. Let us assume a human generation is 20 years. (It varies a lot, and humans are not bacteria - generations overlap.) That gives us (9,000,000 years / 20 years/generation) = 450,000 generations. That gives us an average rate of mutation fixing of (450,000 generations / 20,000,000 fixed mutations) = 0.0225 generations per fixed mutation, or 44.44 fixed mutations per generation.

44.44 fixed mutations per generation. Look at that again. Now remember that is an average over 450,000 generations. In the last 7,000 years (350 generations), we have seen exactly zero mutations fix across the entire human species. That’s what fixation requires. Every member of the species has the mutation.

So, science says the maximum rate of fixed mutations for humans is 2.39 generations per fixation. Science also says humans must have an average rate of 0.0225 generations per fixation. These numbers are different. Wildly different. Different by a factor of (2.39 / 0.0225) = 106. To account for the observed differences between humans and chimps, humans (and chimps) must have an average rate of mutation fixing more than two orders of magnitude higher than seen in the fastest lab experiments with bacteria.

To extend these calculations to the Cichlids of Lake Victoria, we first observe their DNA has about a billion base pairs. That gives a laboratory rate of 7422.75 / 1,000 = 7.423 generations per fixed mutation. The Cichlids have been isolated there for at most 20,000 years (15,000 years is more likely), and breed at age two. So that gives us, at most, 10,000 generations. Doing the math, (10,000 generations / 7.423 generations per fixed mutation) = 1347 fixed mutations.

Cichlids show a genetic spread of about 750,000 base pairs. (There are over 500 species, but that’s an overall average.) Let’s divide that by two to show change from a common ancestor. That gives us 375,000 base pairs of mutation over 10,000 generations. This gives us an observed rate of (10,000 generations / 375,000 fixed mutations) = 0.0267 generations per fixed mutation. (That’s 37.5 fixed mutations per generation.) Again, that is wildly different from the laboratory rate of 7.423 generations per fixation. By a factor of (7.423 / 0.0267) = 278.

DNA mutation rates?

Vox Day has a couple new books out about how fast DNA can fix mutations. It’s based upon well-established science following the evolution of e. coli in the lab. These asexual bacteria split every half hour or so, so it’s fairly easy to track how many generations it takes for a captive population to fix a mutation. The answer, established by multiple experiments and just a touch of very simple math, is one mutation fixed per 1,600 generations. That includes parallel fixation, by the way.  (40,000 generations / 25 fixed mutations = 1,600 generations per fixed mutation on average.)

How many base pairs does e. coli bacteria DNA have? 4,639,221. Do the math, and that gives a fixed mutation rate of 7423 generations per million base pairs. Let’s call it 7,500.

So, let’s extrapolate that to a much more complex, multicellular creature - the cichlid fish of Lake Victoria. Their DNA has about a billion base pairs, and they breed sexually. Sexual reproduction doubles the chances of mutation in offspring (there being two parents, each of which may pass a mutation). So we have a sexual reproduction mutation fixation rate of 3750 generations per million base pairs.

Cichlids have a billion base pairs. That’s 1,000 million. So we expect a total of 3.75 fixed mutations per generation. Cichlids breed at two years of age. Lake Victoria has been an isolated breeding ground for at most 100,00 years. That’s 50,000 cichlid generations. 50,000 times 3.75 = 187,500 fixed mutations in that time. The average DNA spread between each of the over 400 different species of cichlids is about 750,000 base pairs. So there has been, at best, 1/4 the time needed to produce such biodiversity, given the DNA experiments with e. coli.

You’ll notice I have made no attempt to explain how 3.75 mutations would fix across an entire population in one generation. I’m just doing the math.

By the way - humans have a little over 3 billion base pairs. That would result in 11.25 fixed mutations per generation. (This obviously does not happen in modern humans.  We would have noticed.  But let’s ignore that simple observation.) There are 20 million mutations between humans and chimp common ancestry. That evolution happened in at most 9 million years. Assume one generation to be 20 years, and that’s 450,000 generations. Multiple by 11.25, and you get 5,062,500 fixed mutations. Again, one quarter of what’s necessary.

Does sexual reproduction result in a rate of beneficial (or at least neutral) mutation fixing at least 8 times faster than asexual reproduction?

(Vox's error is, in a computing metaphor, to assume that the number of cores working to parallel process information is irrelevant.  He assumes that 4 cores process the exact same amount of information as 3,000 cores.)