Extended Data Fig. 2: Simulation results for a GLV competitive system exhibiting a limit cycle. | Nature Ecology & Evolution

Extended Data Fig. 2: Simulation results for a GLV competitive system exhibiting a limit cycle.

From: Predicting coexistence in experimental ecological communities

Extended Data Fig. 2

Colours and symbols are as in Fig. 17. Notable features of this system are: competitors might (c1-c2, c2-c3) or might not (c1-c3, c1-c4) coexist in pairs. However, in one case a feasible but unstable equilibrium exists (c1-c3, correctly predicted by our method), while in the other there is no feasible equilibrium (c1-c4, also correctly predicted). The system including c1-c3-c4 shows dependence on initial conditions (some trajectories collapse to another system, while others converge to equilibrium), signaling a locally (but not globally) stable equilibrium. The method correctly identifies the position of the 4-species equilibrium surrounded by the limit cycle. However, it suggests stability for the equilibrium, while it must be unstable to give rise to the stable limit cycle. The misclassification stems from the fact that in the calculation of stability, we consider growth rates to be equal (because we cannot infer growth rates from endpoints), while this is not the case here.

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