John Baez

Perimeter Institute Colloquium, September 15, 2021

Statistical Physics and Complexity Webinar Series, University of Edinburgh, September 27, 2022

The Fundamental Theorem of Natural Selection

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 videos here:

• Perimeter Institute talk.
• University of Edinburgh talk.

The first covers more material, the second gives the proofs more carefully. 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.

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