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I have nagging doubts that the random genetic mutation process of natural selection is sufficient to explain evolution, even when coupled with sexual selection (Darwin proposed that evolution is driven by both natural selection and sexual selection).

This is because there are billions of base pairs in the genomes of complex creatures like humans, which equate to billions of independent genetic parameters which define these creatures.

It has been calculated that if you seat monkeys in front of typewriters and get them to press random keys, even a whole universe of monkeys furiously typing away since the dawn of time are exceedingly unlikely to write out just by chance the complete works of William Shakespeare. Each letter in Shakespeare is an independent parameter, and a monkey would need to get every single letter right in order to type out Shakespeare's works.

This is roughly what I mean when I say that there are billions of independent parameters in the genomes of complex creatures that the random mutation process of natural selection would have had to get right in order to create such creatures within the 4 billion year timeframe that life has existed on Earth.

Although this typewriter scenario is not a good analogy, as nature's experimental new gene mutations are tested against their environment, so each mutation can be checked for its "truth or falsity", that is to say, whether it aids the survival of the organism or not. Whereas the monkeys have no way of testing whether each letter they type is correct or not.

But the complexity of evolution comes from the fact that many of these mutations are being tested at the same time, which makes it harder for nature to keep track of which mutations are causing the survival benefits.

So my question is, what sort of mathematical formalism could be used to analyse whether natural selection can reliably operate under such conditions of multiple simultaneous mutations?

I am looking for a formalism that could be used to either prove or disprove the idea that natural selection is capable of driving evolution to create complex creatures within a 4 billion year timeframe.

I am not proposing creationism here by the way, I accept complex life came into existence via evolution, it's just that I have some nagging doubts that natural selection alone is capable of being the motor of evolution.

Possibly rather than relying purely on natural selection and sexual selection, evolution might have also made use of certain quantum computational capabilities and optimisation processes naturally present in the universe, things like quantum computation, and quantum entanglement over both spatially and temporally distant points.

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  • $\begingroup$ I don't think random genetic mutations is taken to be the source of evolution. There are far more intrusions in our genetic material than that. Catch a cold? Your DNA may change. Have a particular bacterial infection? Your DNA may change, or at least, in some cells. My impression is there are a wide array of ways for genes to slip into and out of an individuals genome. $\endgroup$
    – Ryan Budney
    Commented Mar 30, 2023 at 7:44
  • $\begingroup$ I recommend Jason Rosenhouse, The Failures of Mathematical Anti-Evolutionism, cambridge.org/core/books/… $\endgroup$
    – Gerry Myerson
    Commented Mar 30, 2023 at 10:25
  • $\begingroup$ A trillion bacteria simultaneously evolve, searching for something random that will aid their survival, and pass on their best answers, so very different from the monkeys, partly because of scale, and partly because, as you say, the answers are tested at every instant in time. The scale is unimaginable $\endgroup$
    – Ben McKay
    Commented Mar 30, 2023 at 12:12
  • $\begingroup$ Since the question is closed, I add this as a comment. I recommend the work of Robert Rosen. He had the idea that biology has a teleological aspect to it. It is not simply random processes blindly moving forward in time, but rather complex systems such as life are moving forward TOWARDS something, a final cause in Aristotelian language. He used category theory to motivate this. $\endgroup$
    – Eoin
    Commented Jul 13, 2023 at 14:43
  • $\begingroup$ "An anticipatory system is a natural system that contains an internal predictive model of itself and of its environment, which allows it to change state at an instant in accord with the model’s predictions pertaining to a later instant." This means the future state can affect the present state, which goes against orthodox viewpoints. researchgate.net/profile/A-Louie/publication/… $\endgroup$
    – Eoin
    Commented Jul 13, 2023 at 14:44

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Your view, that "Darwinism" is insufficient to explain the appearance of all genetic variation, was also exactly the view of M.-P. Schützenberger, one (along with e.g. Noam Chomsky) of the founders of formal language theory as we know it today; his views are elaborated on in this article (in French), although there are no formal mathematical arguments there.

Schützenberger was very much not a creationist, and does not propose anything except for the fact that the current theory is insufficient. Unfortunately, his questioning of Darwinism (whether correct or not!) led to him being branded as a creationist and his ideas therefore rejected without further question, in spite of his vehement opposition to that idea.

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  • $\begingroup$ Very interesting, thank you for that link. $\endgroup$
    – user501885
    Commented Apr 1, 2023 at 4:55
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Recent developments in the development of a mathematical description of evolution are discussed in Quanta, Mathematics Shows How to Ensure Evolution.
You can be certain that quantum mechanical correlations (entanglement) play no role, these are fully degraded to classical correlations at room temperature.

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  • $\begingroup$ Very interesting, thank you. $\endgroup$
    – user501885
    Commented Apr 1, 2023 at 4:58

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