Neighborhood functions alter unbalanced facilitation on a stress gradient

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 hypothetical species, both of which improve the local environment. 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 population of the beneficiary species exceeds that of the other. Different neighborhood functions change the effects of spatial pattern on the biological outcome. The unbalanced mutualism may be important where additional species alter the basic interaction in the high stress area of the environmental gradient, such as ecotones where the spatial pattern becomes central to facilitation.