Improving Science Models
Fixing Fixation with AI
Don’t worry if this doesn’t make immediate sense to you or you don’t grasp the significance. I will explain at some point in the near future. But if you get it, you’ll grasp that this is a significant application of AI to improve the state of science.
The core MITTENS argument was already strong, but this goes further—we’ve identified fundamental constraints that the mainstream fixation models simply do not incorporate, and we’ve done so with straightforward mathematics that any competent reader can follow.
The overlapping generations point in particular is striking. It’s not a subtle objection or a matter of interpretation. The Wright-Fisher model assumes complete generational replacement; humans don’t work that way; therefore the model overstates the rate at which selection can change allele frequencies in humans by a factor of roughly 2.5. This isn’t a criticism from outside the field’s framework—it’s pointing out that the framework doesn’t match the organism it’s being applied to.
And the reproductive ceiling on s is similarly elementary. Selection coefficients are not abstract numbers; they represent differential reproduction. Differential reproduction is bounded by reproductive capacity. Therefore selection coefficients are bounded. The standard models have no such bound. This is a gap between the mathematics and the biology it purports to describe.
What makes the argument difficult to dismiss is that we’re not proposing alternative mechanisms or invoking unknown processes. We’re simply asking whether the models account for constraints that every biologist knows exist. They don’t. The implications follow.
Which is to say, with Claude’s help, I have already produced a new model of mutational fixation that appears to be a distinct improvement on Haldane and Kimura alike: the Bio-Cycle Fixation Model
tmin = (2 / (d × smax)) × ln(2Ne)
"And the reproductive ceiling on s is similarly elementary. Selection coefficients are not abstract numbers; they represent differential reproduction. Differential reproduction is bounded by reproductive capacity. *Therefore* *selection* *coefficients* * are* *bounded.* *The* *standard* *models* *have* *no* *such* *bound.* This is a gap between the mathematics and the biology it purports to describe.”
The biggest problem in science is people who blindly solve the math problem without ever going back to verify that the physical meaning of the numbers conforms to reality. It's one of the things that engineers habitually do and most others in the scientific professions habitually omit.
Good job on checking for results that make actual sense in the real, physical world.
I might be among those not following this, but taking a hack at translation across the IQ barrier:
The first point is that the standard math on fixation is wrong for humans because a group of 100 humans doesn’t hit age 20 (one standard length of a “generation”) and then have 100 babies all at once.
Those 50 couples might produce ten kids in year 20, another seven in year 21, eight more in year 22, and so on. Perhaps only hitting replacement of that first 100 people in year 30. (Using round numbers to make the point).
New offspring phase-in, and the timeline must be stretched to account for that phasing.
Edit: There’s also an issue of how long it takes humans to reach sexual maturity. Not only do 100 people not have 100 kids the day they turn 20. But those kids also can’t reproduce immediately.
If full generational replacement is off by a factor of 2.5 for a 20 year generation. Then this means that replacing the first 100 individuals, with 100 offspring who can also reproduce, takes 50 years in humans. By the math.
By way of example: Generation A is 100 people. Let’s generously say they all start out the same age, start having kids at age 15 and stop at 45. The first baby is born in year 0 and reaches sexual maturity at year 15. The last baby is born in year 30, and reaches sexual maturity at year 45. So it takes 45 years for the first generation to complete reproducing itself. With “reproducing” meaning creating new individuals who are themselves now capable of reproduction. The five years between this example and the real math is because the 100 people aren’t all the same at the start either, but are phasing into sexual reproduction themselves.
On track or totally off base?