Figure 3.

Effects of immigration timing on coexistence. (a) When the immigration timing of species 2 is early and the maximum growth rate (per capita fecundity) of species 2 is large, coexistence occurs (i.e. ecological character displacement, ECD). On the other hand, when the immigration timing of species 2 is late and the maximum growth rate of species 2 is small, extinction of species 2 is more likely (i.e. evolution-mediated priority effect, EPE). Two vertical dashed lines show the immigration timings (t = 25 and 50) in figures 2 and 3b. (b) Alternative stable states emerge when the maximum strength of interspecific resource competition (α_ij,max) is large and the maximum per capita fecundities of species 1 (λ_1,max) and species 2 (λ_2,max) are almost equivalent (white and black regions). The black region indicates parameter conditions where immigration of species 2 at t = 25 results in coexistence (ECD as figure 2a), whereas immigration of species 2 at t = 50 results in extinction of species 2 (EPE as figure 2b). The white region above the black region shows extinction of species 2 even when species 2 arrives at t = 25. The white region below the black region shows coexistence even when species 2 arrives at t = 50. See electronic supplementary material, figure S7, for the shape of the black region with different immigration timings. When α_ij,max is small and the fecundity ratio is large (the red region), extinction of species 2 occurs irrespective of the initial condition (i.e. the stable equilibrium of coexistence disappears, but the stable equilibrium without species 2 remains). When α_ij,max and the fecundity ratio are both small (the blue region), coexistence occurs irrespective of the initial condition (i.e. the stable equilibrium without species 2 disappears, and there is the stable equilibrium of coexistence). The other parameters are the same as in figure 2.