In 1930, the famous statistician and geneticist Ronald Fisher claimed to have proved a "fundamental theorem of natural selection". He compared this result to the second law of thermodynamics, and described it as holding "the supreme position among the biological sciences". But others found it obscure, and in its most obvious interpretation it is simply false. Luckily there is a true result closely resembling Fisher's claim: a general theorem connecting dynamical systems and information theory. I'll explain this, give the very simple proof, and draw a few conclusions.

You can see the slides for this talk here, and a video here.

For more, read:

- John Baez, The fundamental theorem of natural selection.
- John Baez, Fisher's fundamental theorem.
- John Baez, Information geometry.
- John Baez and Blake Pollard, Relative entropy in biological systems.
- Marc Harper, The replicator equation as an inference dynamic.
- Marc Harper, Information geometry and evolutionary game theory.

© 2021 John Baez except the picture by John Tenniel.

baez@math.removethis.ucr.andthis.edu