title: Desertification by front propagation?
abstract: Understanding how desertification takes place in different ecosystems is an important step in attempting to forecast and prevent such transitions. Dryland ecosystems often exhibit patchy vegetation, which has been shown to be an important factor on the possible regime shifts that occur in arid regions in several model studies. In particular, both gradual shifts that occur by front propagation, and abrupt shifts where patches of vegetation vanish at once, are a possibility in dryland ecosystems due to their emergent spatial heterogeneity. However, recent theoretical work has suggested that the final step of desertification - the transition from spotted vegetation to bare soil - occurs only as an abrupt shift, but the generality of this result, and its underlying origin, remain unclear. We investigate two models that detail the dynamics of dryland vegetation using a markedly different functional structure, and find that in both models the final step of desertification can only be abrupt. Using a careful numerical analysis, we show that this behavior is associated with the disappearance of confined spot-pattern domains as stationary states, and identify the mathematical origin of this behavior. Our findings show that a gradual desertification to bare soil due to a front propagation process can not occur in these and similar models, and opens the question of whether these dynamics can take place in nature.
authors.affiliation: Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990, Israel. Electronic address: zelnik@post.bgu.ac.il.
authors.forename: Yuval R
authors.initials: YR
authors.lastname: Zelnik
authors.affiliation: Institute for Mathematics, Carl von Ossietzky University Oldenburg, P.F 2503, 26111 Oldenburg, Germany.
authors.forename: Hannes
authors.initials: H
authors.lastname: Uecker
authors.affiliation: Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University Oldenburg, PF 2503, 26111 Oldenburg, Germany.
authors.forename: Ulrike
authors.initials: U
authors.lastname: Feudel
authors.affiliation: Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990, Israel; Department of Physics, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel.
authors.forename: Ehud
authors.initials: E
authors.lastname: Meron
mesh_terms: D017753:Ecosystem; D008954:Models, Biological; D063245:Plant Development / Q000502:physiology*; D010944:Plants
keywords: Desertification; Homoclinic snaking; Regime shifts; Spatial transitions; Vegetation patterns