A reaction–diffusion replicator equation is studied. A novel method to apply the
principle of global regulation is used to write down a model with explicit spatial
structure. Properties of stationary solutions together with their stability are analyzed
analytically, and relationships between stability of the rest points of the
non-distributed replicator equation and the distributed system are shown. In particular,
we present the conditions on the diffusion coefficients under which the non-distributed
replicator equation can be used to describe the number and stability of the stationary
solutions to the distributed system. A numerical example is given, which shows that the
suggested modeling framework promotes the system’s persistence, i.e., a scenario is
possible when in the spatially explicit system all the interacting species survive whereas
some of them go extinct in the non-distributed one.