Seminar in PSA 102 at 3:40p.m.

ABSTRACT:

Ecoystems inhabit hundreds, sometimes even thousands of different
species. Some of these species can be toxic, whereas others are harmless.
Some of these species provide food, shelter, or other valuable goods,
whereas other species seem to contribute very little to the benefit of
other organisms or to mankind. Can we predict which of these species will
become dominant?
Here, we use a classic competition model to demonstrate that
there are limits on the predictability of multi-species competition.
Competition between one or two species in a constant, homogeneous
environment is highly predictable. However, more intricate competitive
interactions may exhibit cyclic and even chaotic dynamics. The
non-equilibrium conditions generated by chaotic competition may enhance
opportunities for a high biodiversity, but simultaneously reduces
predictability at the species level. In particular, competition models
with multiple species may have several alternative outcomes of
competition. We show that these alternative outcomes of competition can
be intermingled in the form of a fractal structure. (In more formal
words, multi-species models may have multiple basins of attraction
separated by fractal basin boundaries). As a result of this fractal
geometry, it can be fundamentally impossible to predict the winners of
multi-species competition in advance.