Spatiotemporal dynamics in variable population interactions with density-dependent interaction coefficients

In this article, I present a two-patch metapopulation model with locally explicit dynamics to study the effect of spatial heterogeneity and dispersal upon population interactions with variable or conditional outcomes. These are interactions that may be either detrimental or beneficial for each species depending on the balance of the density-dependent costs and benefits involved. The local dynamics respond to density-dependent α-interaction functions that may change sign, thus yielding a diversity of possible local outcomes for the association in terms of type of interaction and in the number of stable solutions. The spatiotemporal model predicts that the fragmentation of space and dispersal between patches may cause further variation in these outcomes. First, the demographic performance of a species in the association is enhanced if migrations cause a proportional increase of individuals of its own species; being so, a victim may become a mutualist or an exploiter, an excluded species may invade, and a good competitor may overcome its own carrying capacity: the 'enhancement effect of dispersal'; a sort of rescue effect in source-sink dynamics. The underlying mechanisms involve an interplay between density-dependent effects of dispersal per se and the relative local and global average α-interaction functions, which involve costs and benefits at both the local and regional level that may either counteract or reinforce each other; thus, localities and/or populations may change dynamically their sink or source role in the spatial dynamics. A significant insight arises herewith: in the context of variable or conditional interactions the concept of the role of a species does not make strict sense; it becomes a spatiotemporal dynamic quality. Second, regardless of which species disperses, bifurcation of equilibria may occur in those patches that receive the migrating individuals, and annihilation of equilibria in those from where migration leaves; thus, the number of equilibria increases or decreases accordingly.