Cross-diffusion constraints, complexity, and pattern formation in heterogeneous habitats

Determine whether cross-diffusion terms constrained by ecological sign rules (predator avoidance and prey tracking) versus unconstrained cross-diffusion produce greater metacommunity complexity and alter the prevalence of spatial pattern formation in reaction–diffusion metacommunity models under spatial environmental heterogeneity.

Background

The study analyzes how interspecific dispersal responses (cross-diffusion) affect pattern formation in metacommunities. In homogeneous settings, unconstrained cross-diffusion strongly promotes spatial pattern formation, while ecologically constrained cross-diffusion (prey tracking and predator avoidance) suppresses it across motifs and larger random webs.

The authors note that real metacommunities experience spatial environmental variation, which can influence persistence, complexity, and dispersal. They suggest that environmental heterogeneity may increase community linkages and alter stability and pattern formation, but explicitly state that the comparative effects of constrained versus unconstrained cross-diffusion on complexity and pattern formation in heterogeneous habitats remain unknown.