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Open AccessArticle

Continuum Modeling of Discrete Plant Communities: Why Does It Work and Why Is It Advantageous?

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Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
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Department of Physics, Ben-Gurion University, Beer Sheva 84105, Israel
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Complex Systems Group, Facultad de Ingenieria y Ciencias Aplicadas, Universidad de los Andes, Av. Mon. Alvaro del Portillo 12.455, Santiago 7620086, Chile
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Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, CNRS and Paul Sabatier University, 09200 Moulis, France
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French Associates Institute for Agriculture and Biotechnology of Drylands, Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(10), 987; https://doi.org/10.3390/math7100987
Received: 16 September 2019 / Revised: 9 October 2019 / Accepted: 15 October 2019 / Published: 17 October 2019
(This article belongs to the Special Issue Partial Differential Equations in Ecology: 80 Years and Counting)
Understanding ecosystem response to drier climates calls for modeling the dynamics of dryland plant populations, which are crucial determinants of ecosystem function, as they constitute the basal level of whole food webs. Two modeling approaches are widely used in population dynamics, individual (agent)-based models and continuum partial-differential-equation (PDE) models. The latter are advantageous in lending themselves to powerful methodologies of mathematical analysis, but the question of whether they are suitable to describe small discrete plant populations, as is often found in dryland ecosystems, has remained largely unaddressed. In this paper, we first draw attention to two aspects of plants that distinguish them from most other organisms—high phenotypic plasticity and dispersal of stress-tolerant seeds—and argue in favor of PDE modeling, where the state variables that describe population sizes are not discrete number densities, but rather continuous biomass densities. We then discuss a few examples that demonstrate the utility of PDE models in providing deep insights into landscape-scale behaviors, such as the onset of pattern forming instabilities, multiplicity of stable ecosystem states, regular and irregular, and the possible roles of front instabilities in reversing desertification. We briefly mention a few additional examples, and conclude by outlining the nature of the information we should and should not expect to gain from PDE model studies. View Full-Text
Keywords: continuum models; partial differential equations; individual based models; plant populations; phenotypic plasticity; vegetation pattern formation; desertification; homoclinic snaking; front instabilities continuum models; partial differential equations; individual based models; plant populations; phenotypic plasticity; vegetation pattern formation; desertification; homoclinic snaking; front instabilities
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Meron, E.; Bennett, J.J.R.; Fernandez-Oto, C.; Tzuk, O.; Zelnik, Y.R.; Grafi, G. Continuum Modeling of Discrete Plant Communities: Why Does It Work and Why Is It Advantageous? Mathematics 2019, 7, 987.

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