Fig. 5

Insights from a stochastic spatial model. A Markov chain describing the transitions of our model; colonization rates are dependent on the state of neighboring sites. B Long-term behavior of our model with nearest neighbor (\(r=1\)) interaction. Three phases as a function of \((1-\Delta \beta )\times \gamma\) depict differences in colonization \(\Delta \beta\) and priority effects \(\gamma\). Average colonizer fractional abundance \((1-\tilde{\theta }) =\langle \rho _E \rangle /(\langle \rho _E \rangle +\langle \rho _P \rangle )\) is shown as magenta-to-green color map. Here, \(\Delta \beta = \beta _1-\beta _2\), \(\alpha =4\), \(\beta _1\equiv 1\) and \(\delta =0.1\). C For a fixed value of colonization difference, \((1-\Delta \beta )=0.8\), metacommunity dynamics, \((1-\tilde{\theta }_t)=\rho _E(t)/(\rho _E(t)+\rho _P(t))\), are shown for different values of \(\gamma\) (cyan gradient bar) with other parameter values same as in B. D, E Three landscapes where we observe regimes of coexistence (D) or dominance (E) behavior. F, G 1D spatial transects of 2D simulations with parameter values shown as stars in the phase space shown in (B) (\(r=1\); left) and for higher interaction range (\(r=4\); right). Simulations correspond to coexistence phase (II) for \(\gamma =0.3\) (F) and interference phase (III) for \(\gamma =0.8\) (G). Both scenarios \((1-\Delta \beta )=0.8\)