For each combination of the four competitors (c1 to c4, colours), we ran 96 simulations starting from different initial conditions. Each panel shows the location of the simulations’ endpoints (solid circles), as well as the true location of the equilibria for the system (crosses, computed analytically). Experiments resulting in a lack of coexistence are represented as half-points at the bottom of the graph. The predictions obtained using our method are reported using open symbols. There are two cases: we use circles for predictions of (locally) stable endpoints, and triangles for unstable ones; the stability is calculated under the assumption of Lotka-Volterra dynamics and equal growth rates. For this system, as expected, we recover a perfect fit for the positive densities. We can also correctly predict the lack of coexistence among triplets. We predict perfectly the position of the four-species equilibrium, and correctly classify it as unstable, despite having used growth rates that differ substantially from each other.