  The now classical replicator equation describes a wide variety of biological
phenomena, including those in theoretical genetics, evolutionary game theory,
or in the theories of the origin of life. Among other questions, the permanence
of the replicator equation is well studied in the local, well-mixed case.
Inasmuch as the spatial heterogeneities are key to understanding the species
coexistence at least in some cases, it is important to supplement the classical
theory of the non-distributed replicator equation with a spatially explicit
framework. One possible approach, motivated by the porous medium equation, is
introduced. It is shown that the solutions to the spatially heterogeneous
replicator equation may evolve to equilibrium states that have a bounded
support, and, moreover, that these solutions are of paramount importance for
the overall system permanence, which is shown to be a more commonplace
phenomenon for the spatially explicit equation if compared with the local
model.
