We present a hierarchy of four dynamical models for the investigation of coevolutionary systems. The necessity of stochastic treatment is demonstrated and deterministic approximations are derived where appropriate. The mathematical framework advanced here is the first to combine the individual-based, stochastic perspective with a fully dynamical analysis of the phenotypic coevolutionary process.
Deductions are given to derive various well-known equations from the literature of (co)evolutionary modeling as special cases of our approach. In particular, equations central to the fields of evolutionary game theory, adaptive dynamics (in the narrow sense), replicator dynamics and reaction- diffusion systems are recovered. In consequence, the different domains of validity for these models are delineated and several ad-hoc assumptions can be removed.