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Abstract Despite the well known scale‐dependency of ecological interactions, relatively little attention has been paid to understanding the dynamic interplay between various spatial scales. This is especially notable in metacommunity theory, where births and deaths dominate dynamics within patches (the local scale), and dispersal and environmental stochasticity dominate dynamics between patches (the regional scale). By considering the interplay of local and regional scales in metacommunities, the fundamental processes of community ecology—selection, drift, and dispersal—can be unified into a single theoretical framework. Here, we analyze three related spatial models that build on the classic two‐species Lotka–Volterra competition model. Two open‐system models focus on a single patch coupled to a larger fixed landscape by dispersal. The first is deterministic, while the second adds demographic stochasticity to allow ecological drift. Finally, the third model is a true metacommunity model with dispersal between a large number of local patches, which allows feedback between local and regional scales and captures the well studied metacommunity paradigms as special cases. Unlike previous simulation models, our metacommunity model allows the numerical calculation of equilibria and invasion criteria to precisely determine the outcome of competition at the regional scale. We show that both dispersal and stochasticity can lead to regional outcomes that are different than predicted by the classic Lotka–Volterra competition model. Regional exclusion can occur when the nonspatial model predicts coexistence or founder control, due to ecological drift or asymmetric stochastic switching between basins of attraction, respectively. Regional coexistence can result from local coexistence mechanisms or through competition‐colonization or successional‐niche trade‐offs. Larger dispersal rates are typically competitively advantageous, except in the case of local founder control, which can favor intermediate dispersal rates. Broadly, our models demonstrate the importance of feedback between local and regional scales in competitive metacommunities and provide a unifying framework for understanding how selection, drift, and dispersal jointly shape ecological communities.
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Global dynamics of a Lotka–Volterra competition patch model*
Abstract The global dynamics of the two-species Lotka–Volterra competition patch model with asymmetric dispersal is classified under the assumptions that the competition is weak and the weighted digraph of the connection matrix is strongly connected and cycle-balanced. We show that in the long time, either the competition exclusion holds that one species becomes extinct, or the two species reach a coexistence equilibrium, and the outcome of the competition is determined by the strength of the inter-specific competition and the dispersal rates. Our main techniques in the proofs follow the theory of monotone dynamical systems and a graph-theoretic approach based on the tree-cycle identity.
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- PAR ID:
- 10333070
- Date Published:
- Journal Name:
- Nonlinearity
- Volume:
- 35
- Issue:
- 2
- ISSN:
- 0951-7715
- Page Range / eLocation ID:
- 817 to 842
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1361-6544/ac3c2e
