Fig. 3: A graphical method to explain coexistence of multiple species.

a Numerical simulation of the dynamic system shows that the four coexisting species (black lines) persist while the two go extinct (gray lines). b Graphical method to determine which species from the metacommunity stably coexist in the forest mosaic. Each black curve represents a species-specific \({LRS}\). A competitively excluded species (light gray) cannot persist either because: (1) it has a break-even time (light gray dot) that is greater than \({t}_{0}\), which means that its expected \({LRS}\) is less than one, even without any competitors present, or (2) it cannot reach its break-even time (gray dot) before a taller species has already closed the canopy over it (at the vertical red line immediately to the left of the gray dot).