Mechanistically derived spatially heterogeneous producer-grazer model subject to stoichiometric constraints

Md Masud Rana; Chandani Dissanayake; Lourdes Juan; Kevin R. Long; Angela Peace; Md Masud Rana; Chandani Dissanayake; Lourdes Juan; Kevin R. Long; Angela Peace

doi:10.3934/mbe.2019012

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 1: 222-233. doi: 10.3934/mbe.2019012

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Mechanistically derived spatially heterogeneous producer-grazer model subject to stoichiometric constraints

1.
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA
2.
Sri Lanka Technological Campus, Colombo, Sri Lanka

Received: 24 October 2018 Accepted: 24 October 2018 Published: 11 December 2018

Known stoichiometric models of a two species producer-grazer ecosystem have either neglected spatial dynamics or failed to track free phosphorus in the media. In this paper we present a spatially heterogeneous model that tracks phosphorus content in the producer and free phosphorus in the media. We simulate our model numerically under various environmental conditions. Multiple equilibria, with bistability and deterministic extinction of the grazer, are possible here. In conditions that had been previously studied without tracking free phosphorus we find cases where qualitatively different behavior is observed. In particular under certain environmental conditions previous models predict stable equilibria where our model predicts stable limit cycles near the surface. Oscillatory dynamics can have consequences on the population densities, which may spend some time at low values throughout the cycles where they are in danger of stochastic extinction.
- ecological stoichiometry,
- di usion,
- population dynamics
Citation: Md Masud Rana, Chandani Dissanayake, Lourdes Juan, Kevin R. Long, Angela Peace. Mechanistically derived spatially heterogeneous producer-grazer model subject to stoichiometric constraints[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 222-233. doi: 10.3934/mbe.2019012

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Abstract

Known stoichiometric models of a two species producer-grazer ecosystem have either neglected spatial dynamics or failed to track free phosphorus in the media. In this paper we present a spatially heterogeneous model that tracks phosphorus content in the producer and free phosphorus in the media. We simulate our model numerically under various environmental conditions. Multiple equilibria, with bistability and deterministic extinction of the grazer, are possible here. In conditions that had been previously studied without tracking free phosphorus we find cases where qualitatively different behavior is observed. In particular under certain environmental conditions previous models predict stable equilibria where our model predicts stable limit cycles near the surface. Oscillatory dynamics can have consequences on the population densities, which may spend some time at low values throughout the cycles where they are in danger of stochastic extinction.

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