The effect of landscape fragmentation on Turing-pattern formation

<abstract><p>Diffusion-driven instability and Turing pattern formation are a well-known mechanism by which the local interaction of species, combined with random spatial movement, can generate stable patterns of population densities in the absence of spatial heterogeneity of the underlying medium. Some examples of such patterns exist in ecological interactions between predator and prey, but the conditions required for these patterns are not easily satisfied in ecological systems. At the same time, most ecological systems exist in heterogeneous landscapes, and landscape heterogeneity can affect species interactions and individual movement behavior. In this work, we explore whether and how landscape heterogeneity might facilitate Turing pattern formation in predator–prey interactions. We formulate reaction-diffusion equations for two interacting species on an infinite patchy landscape, consisting of two types of periodically alternating patches. Population dynamics and movement behavior differ between patch types, and individuals may have a preference for one of the two habitat types. We apply homogenization theory to derive an appropriately averaged model, to which we apply stability analysis for Turing patterns. We then study three scenarios in detail and find mechanisms by which diffusion-driven instabilities may arise even if the local interaction and movement rates do not indicate it.</p></abstract>

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Species interactions and spatial heterogeneity: predicting cascading predator effects on landscape biogeochemistry

10.32942/osf.io/ya892 ◽

2020 ◽

Author(s):

Julia D. Monk ◽

A. Carla Staver ◽

Oswald J. Schmitz

Keyword(s):

Spatial Heterogeneity ◽

Predation Risk ◽

Species Interactions ◽

Animal Movement ◽

Landscape Heterogeneity ◽

Ecological Systems ◽

General Will ◽

Positive Feedbacks ◽

Predator Prey ◽

Risk Effects

Spatial heterogeneity in ecological systems can result from top-down processes, but despite some theoretical attention, the emergence of spatial heterogeneity from feedbacks with consumers is not well understood empirically. Interactions between predators and prey influence animal movement and associated nutrient transport and release, generating spatial heterogeneity that cascades throughout ecological systems. In this review, we synthesize the existing literature to evaluate the mechanisms by which terrestrial predators can generate spatial heterogeneity in biogeochemical processes through consumptive and non-consumptive effects. Overall, we propose that predators increase heterogeneity in ecosystems whenever predation is intense and spatially variable, whereas predator-prey interactions homogenize ecosystems whenever predation is weak or diffuse in space. This leads to several testable hypotheses: (1) that predation and carcass deposition at high-predation risk sites stimulate positive feedbacks between predation risk and nutrient availability; (2) that prey generate nutrient hotspots when they concentrate activity in safe habitats, but instead generate nutrient subsidies when they migrate daily between safe and risky habitats; (3) that herbivore body size mediates risk effects, such that megaherbivores are more likely to homogenize ecosystems; and 4) that predator loss in general will tend to homogenize ecosystems. Testing these hypotheses will advance our understanding of whether predators amplify landscape heterogeneity in ecological systems.

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