  In biology, information flows from the environment to the genome by the
process of natural selection. But it has not been clear precisely what sort of
information metric properly describes natural selection. Here, I show that
Fisher information arises as the intrinsic metric of natural selection and
evolutionary dynamics. Maximizing the amount of Fisher information about the
environment captured by the population leads to Fisher's fundamental theorem of
natural selection, the most profound statement about how natural selection
influences evolutionary dynamics. I also show a relation between Fisher
information and Shannon information (entropy) that may help to unify the
correspondence between information and dynamics. Finally, I discuss possible
connections between the fundamental role of Fisher information in statistics,
biology, and other fields of science.
