  We review models of biological evolution in which the population frequency
changes deterministically with time. If the population is self-replicating,
although the equations for simple prototypes can be linearised, nonlinear
equations arise in many complex situations. For sexual populations, even in the
simplest setting, the equations are necessarily nonlinear due to the mixing of
the parental genetic material. The solutions of such nonlinear equations
display interesting features such as multiple equilibria and phase transitions.
We mainly discuss those models for which an analytical understanding of such
nonlinear equations is available.
