Figure 1. Zero growth isoclines for competing species 1 (solid line) and 2 (dotted line) in the Lotka–Volterra model, plotted in a space defined by population numbers of the two species, N₁ and N₂. If N₁ and N₂ are such that the system lies to the right of both isoclines, then both N₁ and N₂ will tend to decrease (shown by thin solid and dotted arrows), resulting in the system moving in a direction indicated by the thick arrows. If the system lies to the left of both isoclines, then both N₁ and N₂ will tend to increase. If the system is to the right of the isocline for species 2, but to the left of the species 1 isocline, then N₁ will increase, whereas N₂ will decrease. The two isoclines in this example thus divide the relevant system space into three sections with different predicted trajectories.

Figure 2. A graphical depiction of the dynamic consequences of different placements of zero growth isoclines in N₁–N₂ space in the Lotka–Volterra model of two‐species competition. As in Figure 1, isoclines for species 1 and 2 are shown by solid and dotted lines, respectively. Arrows represent the system trajectories in different parts of the system space. Empty and solid circles represent unstable and stable equilibria, respectively. (a) The only stable equilibrium in this case is at N₁ = r₁/s₁₁, N₂ = 0, implying that whatever the initial relative abundance of the two species, species 1 will eventually drive species 2 to extinction. (b) The only stable equilibrium in this case is at N₁ = 0, N₂ = r₂/s₂₂, implying that species 2 will eventually drive species 1 to extinction. (c) In this case the system has a stable equilibrium at the intersection of the isoclines for the two species, and long‐term coexistence is, therefore, possible. Both equilibria representing the extinction of one or the other species are unstable. (d) In this case, the intersection of the isoclines is an unstable equilibrium, whereas both equilibria involving extinction of one of the species are stable. Which species eventually becomes extinct depends on the initial relative abundance of the two species (or where in the system space the trajectory starts).