Species Interaction Phase Portrait

Every pairwise ecological relationship — competition, predation, parasitism, mutualism, commensalism, amensalism — is classified purely by the sign of two coupling terms in the generalized Lotka–Volterra equation. This 2D companion to the 3D swarm simulator drops the population-as-crowd metaphor and shows the real mathematical object ecologists actually study: a phase portrait. A vector field fills the (A, B) plane with the instantaneous direction each population pair would move, two nullcline curves mark where each population's growth stalls, and the live trajectory traces exactly how the current populations evolve through that field — while a synchronized time-series strip below shows the same numbers unfold against elapsed time. Switch interaction types to watch the equilibrium jump between a stable coexistence point, an unstable saddle that tips into extinction, or no finite equilibrium at all.