  We evaluate the implication and outlook of an unanticipated simplification in
the macroscopic behavior of two high-dimensional sto-chastic models: the
Replicator Model with Mutations and the Tangled Nature Model (TaNa) of
evolutionary ecology. This simplification consists of the apparent display of
low-dimensional dynamics in the non-stationary intermittent time evolution of
the model on a coarse-grained scale. Evolution on this time scale spans
generations of individuals, rather than single reproduction, death or mutation
events. While a local one-dimensional map close to a tangent bifurcation can be
derived from a mean-field version of the TaNa model, a nonlinear dynamical
model consisting of successive tangent bifurcations generates time evolution
patterns resembling those of the full TaNa model. To advance the interpretation
of this finding, here we consider parallel results on a game-theoretic version
of the TaNa model that in discrete time yields a coupled map lattice. This in
turn is represented, a la Langevin, by a one-dimensional nonlinear map. Among
various kinds of behaviours we obtain intermittent evolution associated with
tangent bifurcations. We discuss our results.
