Non-spatial models of competition between floating aquatic vegetation (FAV) and submersed aquatic vegetation (SAV) predict a stable state of pure SAV at low total available limiting nutrient level, N, a stable state of only FAV for high N, and alternative stable states for intermediate N, as described by an S-shaped bifurcation curve. Spatial models that include physical heterogeneity of the waterbody show that the sharp transitions between these states become smooth. We examined the effects of heterogeneous initial conditions of the vegetation types. We used a spatially explicit model to describe the competition between the vegetation types. In the model, the FAV, duckweed (L. gibba), competed with the SAV, Nuttall's waterweed (Elodea nuttallii). Differences in the initial establishment of the two macrophytes affected the possible stable equilibria. When initial biomasses of SAV and FAV differed but each had the same initial biomass in each spatial cell, the S-shaped bifurcation resulted, but the critical transitions on the N-axis are shifted, depending on FAV:SAV biomass ratio. When the initial biomasses of SAV and FAV were randomly heterogeneously distributed among cells, the vegetation pattern of the competing species self-organized spatially, such that many different stable states were possible in the intermediate N region. If N was gradually increased or decreased through time from a stable state, the abrupt transitions of non-spatial models were changed into smoother transitions through a series of stable states, which resembles the Busse balloon observed in other systems.
Citation: Linhao Xu, Donald L. DeAngelis. Effects of initial vegetation heterogeneity on competition of submersed and floating macrophytes[J]. Mathematical Biosciences and Engineering, 2024, 21(10): 7194-7210. doi: 10.3934/mbe.2024318
Non-spatial models of competition between floating aquatic vegetation (FAV) and submersed aquatic vegetation (SAV) predict a stable state of pure SAV at low total available limiting nutrient level, N, a stable state of only FAV for high N, and alternative stable states for intermediate N, as described by an S-shaped bifurcation curve. Spatial models that include physical heterogeneity of the waterbody show that the sharp transitions between these states become smooth. We examined the effects of heterogeneous initial conditions of the vegetation types. We used a spatially explicit model to describe the competition between the vegetation types. In the model, the FAV, duckweed (L. gibba), competed with the SAV, Nuttall's waterweed (Elodea nuttallii). Differences in the initial establishment of the two macrophytes affected the possible stable equilibria. When initial biomasses of SAV and FAV differed but each had the same initial biomass in each spatial cell, the S-shaped bifurcation resulted, but the critical transitions on the N-axis are shifted, depending on FAV:SAV biomass ratio. When the initial biomasses of SAV and FAV were randomly heterogeneously distributed among cells, the vegetation pattern of the competing species self-organized spatially, such that many different stable states were possible in the intermediate N region. If N was gradually increased or decreased through time from a stable state, the abrupt transitions of non-spatial models were changed into smoother transitions through a series of stable states, which resembles the Busse balloon observed in other systems.
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Linhao Xu, Donald L. DeAngelis. Effects of initial vegetation heterogeneity on competition of submersed and floating macrophytes[J]. Mathematical Biosciences and Engineering, 2024, 21(10): 7194-7210. doi: 10.3934/mbe.2024318
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