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

  • 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.

    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

    Related Papers:

  • 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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    [1] T. Andersen (1997) Pelagic nutrient cycles; herbivores as sources and sinks. Springer, Berlin.
    [2] T. Andersen , J. J. Elser and D. O. Hessen, Stoichiometry and population dynamics. Ecol. Lett., 7 (2004), 884–900.
    [3] S. A. Berger, S. Diehl, T. J. Kunz, D. Albrecht, A. M. Oucible and S. Ritzer, Light supply, plankton biomass, and seston stoichiometry in a gradient of lake mixing depths. Limnol. Oceanogr., 51 (2006), 1898–1905.
    [4] E. L. Cussler (1996) Diffusion: Mass Transfer in Fluid Systems. Cambridge University Press.
    [5] S. Diehl, S. Berger and R. W¨ohrl, Flexible nutrient stoichiometry mediates environmental influences on phytoplankton and its resources.
    Ecology , 86 (2005), 2931–2945.
    [6] C. Dissanayake (2016) Finite element simulation of space/time behavior in a two species ecological stoichiometric model. PhD thesis, Texas Tech University.
    [7] C. Dissanayake, L. Juan, K. R. Long, A. Peace and M. M. Rana (under review 2018) Genotypic selection in spatially heterogeneous producer-grazer systems subject to stoichiometric constraints. Bulletin of Mathematical Biology.
    [8] J. Huisman, J. Sharples, J. M. Stroom, P. M. Visser, W. E. A. Kardinaal, J. M. Verspagen and Sommeijer B, Changes in turbulent mixing shift competition for light between phytoplankton species. Ecology, 85 (2004), 2960–2970.
    [9] J. T. Kirk (1994) Light and photosynthesis in aquatic ecosystems. Cambridge University Press.
    [10] D. Kuefler, T. Avgar and J. M. Fryxell, Rotifer population spread in relation to food, density and predation risk in an experimental system. J. Anim. Ecol., 81 (2012), 323–329.
    [11] D. Kuefler, T. Avgar and J. M. Fryxell, Density-and resource-dependent movement characteristics in a rotifer. Funct. Ecol., 27 (2013), 323–328.
    [12] I. Loladze, Y. Kuang and J. J. Elser, Stoichiometry in producer–grazer systems: linking energy flow with element cycling. Bull. Math. Biol., 62 (2000), 1137–1162.
    [13] A. Lorke, Investigation of turbulent mixing in shallow lakes using temperature microstructure measurements. Aquat. Sci.-Research Across Boundaries, 60 (1998), 210–219.
    [14] A. Peace, H.Wang and Y. Kuang, Dynamics of a producer–grazer model incorporating the effects of excess food nutrient content on grazer's growth. Bull. Math. Biol., 76 (2014), 2175–2197.
    [15] F. H. Shu (1991) The Physics of Astrophysics, Vol. 2: Radiation. Univ. Sci. Books, Mill Valley CA.
    [16] R. W. Sterner and J. J. Elser (2002) Ecological stoichiometry: the biology of elements from molecules to the biosphere. Princeton University Press.
    [17] H. Wang, H. L. Smith, Y. Kuang and J. J. Elser, Dynamics of stoichiometric bacteria-algae interactions in the epilimnion. SIAM J. Appl. Math., 68 (2007), 503–522.
    [18] H. Wang, Y. Kuang and I. Loladze, Dynamics of a mechanistically derived stoichiometric producer-grazer model. J. Biol. Dynam., 2 (2008), 286–296.
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