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

Ehud Meron, Jamie J. R. Bennett, Cristian Fernandez-Oto, Omer Tzuk, Yuval R. Zelnik and Gideon Grafi
Additional contact information
Ehud Meron: Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
Jamie J. R. Bennett: Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
Cristian Fernandez-Oto: Complex Systems Group, Facultad de Ingenieria y Ciencias Aplicadas, Universidad de los Andes, Av. Mon. Alvaro del Portillo 12.455, Santiago 7620086, Chile
Omer Tzuk: Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
Yuval R. Zelnik: Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, CNRS and Paul Sabatier University, 09200 Moulis, France
Gideon Grafi: 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

Mathematics, 2019, vol. 7, issue 10, 1-22

Abstract: 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.

Keywords: continuum models; partial differential equations; individual based models; plant populations; phenotypic plasticity; vegetation pattern formation; desertification; homoclinic snaking; front instabilities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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