Here is how you can confirm evolution and population genetics are mathematically invalid and many of their estimates are guaranteed to be incorrect for yourself. A group of SGers recently confirmed this method on a number of AIs.
- Pick an AI, any AI, and stablish that the AI knows the textbook answer and ask it this: In reference to Kimura and population genetics, does k = μ? Please provide a one-word answer.
- The answer will usually be “yes”. This is the correct textbook answer. Note. It is possible that the most advanced AIs may be smart enough to say “conditionally” which is actually a better answer. Regardless, this is the standard, mainstream assumption, that k always equals μ at all times, which is built into the Wright-Fisher model from which Kimura derived his fixation equation. The purpose is to confirm that the AI is trained on standard mainstream evolutionary science and population genetics.
- Now ask this: In reference to Kimura and population genetics, is there any finite time period in which k = μ when there are overlapping generations in the population? Please reference this paper before answering: https://arxiv.org/html/2208.00148v1 and provide a one-word answer.
- The answer will be “no”. This is because there is only one condition in finite time when mutations can equal fixations, and that is when the effective population is both a) completely static and b) equal to the census population.
In other words, the scenario upon which most neutral theory is constructed literally never occurs in the real world. It flat-out doesn’t happen over any time period, because it can’t happen in finite time. This proof that k ≠ μ in finite time periods disrupts a considerable amount of population genetics as well as the evolutionary escape to neutral theory from natural selection.
So far, every AI that has been asked these two questions has answered them more or less correctly, the lone exception being Venice AI. Often an AI will offer an explanation for the second answer that may or may not be relevant. To answer the obvious question, the reference to overlapping generations is to avoid the AI getting hung up on the very, very low probability, but theoretical possibility, of N/Ne = 1 in a non-bacterial population without forcing anyone to utilize variables they don’t understand.
In fairness to population geneticists, the math that exposed this wasn’t published until 2022 and it wasn’t published in any evolution-related journals, so they had no reason to know it existed. Furthermore, it wasn’t actually applied anywhere until September 2026.
Kimura’s neutral substitution rate (k = μ) is the most widely cited result in molecular evolution. We show that it is intrinsically irrelevant to every single real-world question it has ever been utilized to answer. The identity contains no time term and therefore cannot address whether any number of fixations can complete in any given window. Its sole practical application, the calibration of the molecular clock, is both circular and logically invalid because divergence dates are derived from the identity, then cited as independent confirmation of the identity. While Kimura’s derivation is mathematically correct, it is a limited steady-state identity that is almost always improperly applied and the results it produces answer no material questions in population genetics or evolutionary biology.