  This review is an introduction to theoretical models and mathematical
calculations for biological evolution, aimed at physicists. The methods in the
field are naturally very similar to those used in statistical physics, although
the majority of publications appeared in biology journals. The review has three
parts, which can be read independently. The first part deals with evolution in
fitness landscapes and includes Fisher's theorem, adaptive walks, quasispecies
models, effects of finite population sizes, and neutral evolution. The second
part studies models of coevolution, including evolutionary game theory, kin
selection, group selection, sexual selection, speciation, and coevolution of
hosts and parasites. The third part discusses models for networks of
interacting species and their extinction avalanches. Throughout the review,
attention is paid to giving the necessary biological information, and to
pointing out the assumptions underlying the models, and their limits of
validity.
