Population dynamics with or without evolution: a physicistʹs approach

Modeling the dynamics of interacting species (or populations) is a long standing problem in sciences which, in the recent years, has attracted a lot of physicists working in statistical physics. The similarities and differences between models of dynamics of population and usual statistical mechanics problems on a lattice are discussed. First the question of the appropriate level of description (ordinary differential equations, reaction–diffusion equations, patches models or individual-based models for extended systems) is considered. Second, the role of the internal degrees of freedom associated to the phenotype of the individuals on the dynamics is discussed.