Extended Data Fig. 3: Simulation results for competition with Allee effects, in which competitors cannot grow when rare.

This system exhibits multistability in all cases (half-points at the bottom of each graph signal trajectories that resulted in extinctions). Despite the fact that the model contains cubic terms (while our method can deal only with quadratic terms), the in-fit is excellent, in all cases fitting the location of the endpoints perfectly. Experiments in which the species do not coexist are however misclassified—while there exist equilibria close to the prediction, they are unstable, rather than stable as predicted by our method.