Bifurcation analysis can unify ecological and evolutionary aspects of ecosystems
Troost, T.A., Kooi, B.W. and Kooijman, S.A.L.M. 2007
Bifurcation analysis can unify ecological and evolutionary aspects of
ecosystems.
Ecol. Mod. 204: 253 - 268
Abstract
Bifurcation theory is commonly used to study the dynamical behaviour
of ecosystems. It involves the analysis of points in the parameter
space where the stability of the system changes qualitatively.
Generally, such changes are related only to changes in environmental
parameters, while the organism's trait values are assumed to be
constant. In reality, however, these trait values also change, though
on a longer (evolutionary) time scale. On an ecological time scale,
such evolutionary changes often come down to mutants invading a
resident population. Points in the trait space where invasibility
changes correspond to transcritical bifurcations. Therefore,
bifurcation theory may also be used to study the evolutionary dynamics
of ecosystems. First, the bifurctation approach is explained by
analyzing a simple and well known Lotka-Volterra competition model
where the competition coefficients and the carrying capacity are
trait-dependent. However, the bifurcation approach is especially
suitable for the analysis of more complex models. Therefore, the
advantages and differences with the Adaptive Dynamics (AD) approach
are discussed in more detail by means of the analysis of a more
realistic and complex ecosystem model consisting of mixotrophic
organisms.