Species exclusion and coexistence in a noisy voter model with a competition-colonization tradeoff

We introduce an asymmetric noisy voter model to study the joint effect of immigration and a competition-dispersal tradeoff? in the dynamics of two species competing for space on a one-dimensional lattice. Individuals of one species can invade a nearest-neighbor site in the lattice, while individuals of the other species are able to invade sites at any distance but are less competitive locally, i.e., they establish with a probability $g\leq 1$. The model also accounts for immigration, modeled as an external noise that may spontaneously replace an individual at a lattice site by another individual of the other species. This combination of mechanisms gives rise to a rich variety of outcomes for species competition, including exclusion of either species, mono-stable coexistence of both species at different population proportions, and bi-stable coexistence with proportions of populations that depend on the initial condition. Remarkably, in the bi-stale phase, the system undergoes a discontinuous transition as the intensity of immigration overcomes a threshold, leading to an irreversible loop dynamics that may cause the loss of the species with shorter dispersal range.