Figure 2.

Example of changes in the density of the focal species (shaded region) and the competitor (light gray line) along a portion of the study region in one of our simulations. (a) In the absence of other mechanisms, each species' density gradually changes in response to the abiotic environment. The focal species' density increases with increasing values of x. Parameter values: m ₁ = 1, m ₂ = −2, b ₁ = 0, b ₂ = 1.075. (b) When competition is added to the simulation, each species may be eliminated from a portion of the study region. In this case, the focal species is eliminated when x is small, while the competitor is eliminated when x is large. Parameter values in addition to those used in panel (a): α₁₂ = 0.75, α₂₁ = 1. (c) Dispersal can allow each species to be present in habitats that would otherwise be unsuitable. Parameter values in addition to those used in panel (b): D _a = 10. (d) It is often impossible to know the density of each species in nature with absolute certainty, to reflect this; we simulate sampling of population densities at locations across the study region resulting in the jagged density lines in panel (d)