Fundamental Unpredictability in Multispecies Competition

Abstract

One of the central goals of ecology is to predict the distribution and abundance of organisms. Here, we show that, in ecosystems of high biodiversity, the outcome of multispecies competition can be fundamentally unpredictable. We consider a competition model widely applied in phytoplankton ecology and plant ecology in which multiple species compete for three resources. We show that this competition model may have several alternative outcomes, that the dynamics leading to these alternative outcomes may exhibit transient chaos, and that the basins of attraction of these alternative outcomes may have an intermingled fractal geometry. As a consequence of this fractal geometry, it is impossible to predict the winners of multispecies competition in advance.

Different types of synchrony in chaotic and cyclic communities

“…Synchronization of biological phenomena, such as periodic dynamics of populations, physiological activities or reproductive behavior, have been shown and one principal conclusion of these studies is that synchronization and phase locking can have a fundamental role 11,13,14 . However, previous studies did not consider more complex dynamics such as chaos and quasiperiodicity that are predicted for complex systems with multi-species interactions as we find them in nature 15,16 .…”

Stability and stabilization for models of chemostats with multiple limiting substrates

“…For example, stable periodic solutions were reported for Monod kinetics [14] and later for interacting resources [4,6,7,42]. There are numerical studies for chemostats with more than two competing species and more than two limiting nutrients that illustrate the possibility of chaotic or oscillatory dynamics [15,16]. See also [3,23,24] for theoretical results on limit cycles in chemostats with multiple competing species and several limiting nutrients, which are very different from our work owing to our stability and stabilization analyses for equilibrium points.…”

Some Discrete Competition Models and the Competitive Exclusion Principle†

“…A natural question to examine, from a mathematical point of view, is whether or not there exist any two species competition models that allow for such a multiple attractor, coexistence/exclusion case. A number of studies involving competition models have, under certain circumstances, found results of non-Lotka/Volterra type or that contradicted the competitive exclusion principle in one way or another [2,[5][6][7][8]10,13,20,[22][23][24]28,29,[31][32][33][34][35][36]41,42]. None of these results, however, involve the multiple attractor scenario described above.…”