Drylands showcase fascinating spatial self-organization phenomena involving partial plant mortality and the rearrangement of the remaining plants in regular patterns (Fig. 1). Mathematical models and pattern formation theory have played crucial roles in uncovering the mechanisms that drive vegetation patterning (Meron, Nonlinear Physics of Ecosystems 2015; Physics Today 2019​). 

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These questions can be addressed at different levels of complexity, taking into account the interplay between spatial self-organization – a population-level response – with mechanisms operating at other levels of ecological organization, such as phenotypic changes at the single-plant level or plant-community re-assembly (Fig. 3; Meron, Mathematical Biosciences, 2016; Bera et al., eLife 2021​). Another element of complexity is the interaction of plants with different trophic levels, such as herbivores or soil biota (Inderjit et al., Physics of Life Reviews 2021).

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We address these questions using mathematical models of increasing complexity, importing concepts of nonlinear physics, such as front instabilities (Zelnik and Meron, Ecological Indicators 2018Fernandez-Oto et al. Phys. Rev. Lett. 2019), homoclinic snaking (Zelnik et al., PNAS 2015; Zelnik et al. J. Theor. Biol. 2017); spatial resonances (Mau et al. Phys. Rev. Lett. 2012; Mau et al., Phys. Rev. E 2015) and others, and applying state-of-the-art methods of pattern-formation theory.  This allows us to shed new light on old questions in ecology and ask new questions of ecological interest that have never been asked before. 

We further confront theoretical predictions with empirical observations from satellite images, field studies, and laboratory experiments by collaborating with ecologists (Sheffer et al. Ecology Letters 2013; Getzin et al. Ecography 2015; Getzin et al. PNAS 2016​). Intensive further collaboration with ecologists is expected in the framework of our new ERC-Synergy project RESILIENCE​ on “Pathways of resilience and evasion of tipping in ecosystems,” which will start in 2023 for six years and will focus on savanna and tundra ecosystems.