Neighborhood functions alter unbalanced facilitation on a stress gradient in an alpine treeline simulation

The stress-gradient hypothesis states that individual and species competitive and facilitative effects change in relative importance or intensity along environmental gradients of stress. The importance of the number of facilitators in the neighborhood of a potential beneficiary has not been explored. Evenly distributed and stress-correlated facilitation and the increase in the intensity of facilitation with neighbors as linear, logarithmic, and unimodal functions is simulated for two species such as Pinus albicaulis and Abies lasiocarpa. The mutualism is unbalanced in that the establishment of one species is enhanced by neighbors more than the other. Compared to no facilitation or evenly distributed facilitation, the stress gradient produces more edges in the spatially advancing population, more overall intensity of facilitation, and more individuals further advanced into the area of higher stress; the more enhanced species has increased population relative to the other - to the point where they are equal. Among three neighborhood functions, little difference exists in outcomes between the linear and logarithmic functions, but the unimodal function, which shifts peak facilitation intensity to fewer neighbors, increases the above state variables more than the differences between the even and stress gradient facilitation scenarios. The unbalanced mutualism may be important at treeline ecotones where the spatial pattern becomes central to facilitation.