  It is well known that low-dimensional nonlinear deterministic maps close to a
tangent bifurcation exhibit intermittency and this circumstance has been
exploited, e.g. by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to
develop a general theory of 1/f spectra. This suggests it is interesting to
study the extent to which the behavior of a high-dimensional stochastic system
can be described by such tangent maps. The Tangled Nature (TaNa) Model of
evolutionary ecology is an ideal candidate for such a study, a significant
model as it is capable of reproducing a broad range of the phenomenology of
macroevolution and ecosystems. The TaNa model exhibits strong intermittency
reminiscent of Punctuated Equilibrium and, like the fossil record of mass
extinction, the intermittency in the model is found to be non-stationary, a
feature typical of many complex systems. We derive a mean-field version for the
evolution of the likelihood function controlling the reproduction of species
and find a local map close to tangency. This mean-field map, by our own local
approximation, is able to describe qualitatively only one episode of the
intermittent dynamics of the full TaNa model. To complement this result we
construct a complete nonlinear dynamical system model consisting of successive
tangent bifurcations that generates time evolution patterns resembling those of
the full TaNa model in macroscopic scales. In spite of the limitations of our
approach, that entails a drastic collapse of degrees of freedom, the
description of a high-dimensional model system in terms of a low-dimensional
one appears to be illuminating.
