Dynamics of a competitive rock-scissors-paper community under invasion

Nathan Muyinda^1*, Hsin-Yao Feng¹, Ritwika Mondal¹, Wei-Hsiang Lin¹

¹Institute of Molecular Biology, Academia Sinica, Taipei, Taiwan

* Presenter:Nathan Muyinda, email:muyinda@as.edu.tw

The coexistence mystery, designated “the paradox of the plankton”, remains an open question in ecology. Under competitive Lotka-Volterra (CLV) model, modern coexistence theory (MCT) delineates the problem of coexistence between two competitors: two species coexist if their niche overlap is low enough to offset their relative fitness differences. May and Leonard (ML), using a CLV model, showed that three competitors whose competition dynamic is cyclic, like in the game of rock-scissors-paper (RSP), can stably coexist even when each pair cannot coexist in isolation. In this work, an extension of the ML model is used to study the effect of a single invader on the coexistence of a stable RSP community. Assuming the invader interacts with one, two or all three species among RSP, we analytically identify parameter regimes where invasion fails or succeeds. After successful invasion, and depending on the strength of competition between the invader and resident species, invader can either coexist with RSP or exclude at least one species from the triplet. We also identify parameter regimes where invader-RSP coexistence occurs via stable limit and/or heteroclinic cycles. Overall, our results show that the four-species CLV model can exhibit very rich dynamics ranging from limit cycles to multiple heteroclinic cycles to strange nonchaotic attractors. We further show that results from the ODE model remain consistent even when spatial stochasticity is added to the model.

Keywords: cyclic competition, invasion criterion, Lotka-Volterra model, species coexistence, heteroclinic cycles