If biology is the study of self-replicating entities, and we want to understand the role of information, it makes sense to see how information theory is connected to the 'replicator equation' — a simple model of population dynamics for self-replicating entities. The relevant concept of information turns out to be the information of one probability distribution relative to another, also known as the Kullback–Liebler divergence. Using this we can get a new outlook on free energy, see evolution as a learning process, and give a clearer, more general formulation of Fisher's fundamental theorem of natural selection.

You can see the the slides for this talk, and also this video:

In the video there's a typo which I fixed later in the slides: \( \exp(-kE_i/T) \) should be \(\exp(-kE_i/T) \). For more, read:

- Marc Harper, The replicator equation as an inference dynamic.
- Marc Harper, Information geometry and evolutionary game theory.
- Barry Sinervo and Curt M. Lively, The rock-paper-scissors game and the evolution of alternative male strategies,
*Nature***380**(1996), 240–243. - John Baez, Diversity, entropy and thermodynamics.
- John Baez, Information geometry.

© 2017 John Baez except the photo is by Christian Ziegler.

baez@math.removethis.ucr.andthis.edu