Dispersal of an organism plays an important role in its individual fitness, population dynamics, and species distribution. Typically, dispersal is loosely applied to movement over different spatial scales, e.g. movement between habitat patches separated in space from other areas. Recently, empirical studies have indicated that interacting organisms can affect one another’s dispersal, known as interaction-mediated dispersal. Little is known regarding the patch-level consequences of habitat fragmentation on interacting species in the presence of interaction-mediated dispersal. In this study, we explore effects of habitat fragmentation and interaction-mediated dispersal on patch-level population dynamics of two interacting species through development and study of a model built on the reaction diffusion framework. The model is capable of incorporating essential information about edge-mediated effects such as patch preference, movement behavior, and matrix-induced mortality at the patch/matrix interface. We mathematically analyze the model’s predictions of coexistence with a one-dimensional patch, general logistic-type growth terms, and three types of interactions: asymmetric competition, symmetric competition, and mutualism. In order to isolate effects of interaction-mediated dispersal, we assume that the interactions occur only on the boundary of the patch. Our analysis is based upon study of the structure and stability of steady state solutions of the model.
Results/Conclusions
Mathematical analysis of the model provides insight into effects of habitat fragmentation and interaction-mediated dispersal on coexistence of two interacting species. We determine ranges of patch sizes based on the given parameters in which coexistence, competitive exclusion, extinction, and an interacting species analog of an Allee effect occur. In all three types, patches with smaller size are more sensitive to the effects of interaction, whereas patches with a sufficiently large size are insulated from them. For example, in both competition cases we find a scenario in which neither species can exist for patch sizes below a critical threshold, only the first competitor can persist in sizes in a range larger than this threshold, coexistence is guaranteed for a range of patch sizes larger than the previous, the second competitor excludes the first in a range of patch sizes larger than the previous, and coexistence is again guaranteed for patch sizes larger than this previous range. Interestingly, for a patch size falling within the first of the two coexistence regimes, increasing patch size actually has a negative effect on the first competitor, even to the point that the second will exclude the first by increasing the size into the next regime.