Two-patch model of spatial niche segregation

Spatial niche segregation between two habitats and the related adaptive dynamics are investigated. Independent population regulations operate in the two patches by a single resource in each. The populations migrate between the habitats with a constant rate. In line with a general mathematical concept published elsewhere, the niche of a species is described by the measures of the two-way interactions between the species and the resources. Increasing migration rate tends to equalize the population sizes between the habitats and diminish the dependence of the niches on the environmental tolerances of the species. In line with the expectations, when two species coexist, their realized niches are more segregated than their fundamental ones. We demonstrate that robust coexistence requires sufficient niche segregation. That is, the parameter range that allows coexistence of the two species shrinks to nil when the niche-differences between the species disappear. In turn, niche segregation requires separation of tolerances and sufficiently low migration rate. For the evolutionary study we assume a continuous, clonally inherited character that has different optima at the two patches. Evolution of this trait may end up in an intermediate “generalist” optimum, or it can branch and leads to a dimorphic population. The condition of the latter outcome is in line with the conditions that allow niche segregation: the patches have to be sufficiently different and the migration has to be sufficiently low.