Shalmali Bandyopadhyay, University of Tennessee at Martin
Coexistence in Fragmented Habitats: How Dispersal-Competition Tradeoffs Shape Species Survival Across Patch Sizes
Understanding how habitat fragmentation affects species coexistence is critical for conservation in increasingly fragmented landscapes. We study the diffusive Lotka-Volterra competition model with realistic boundary conditions that capture organismal behavior at patch edges and differential matrix hostility between species. Using nonlinear analysis tools including sub-supersolution methods, eigenvalue problems, and numerical techniques, we establish conditions for coexistence across competition regimes. While weak and strong competition cases yield results similar to classical isolated or hostile matrix scenarios, we discover a striking phenomenon in semistrong competition: when species face differential matrix effects, coexistence becomes possible only within an intermediate range of patch sizes – both very small and very large patches cannot sustain both species. Our results provide the first rigorous mathematical support for the long-theorized dispersal-competition tradeoff, showing that a species disadvantaged in direct competition can coexist with a superior competitor if it possesses a dispersal advantage (through higher growth-to-diffusion ratio or lower effective matrix mortality). These findings have important implications for conservation strategies and challenge conventional wisdom about optimal reserve design.
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