title: Early warning signals of ecological transitions: methods for spatial patterns.
abstract: A number of ecosystems can exhibit abrupt shifts between alternative stable states. Because of their important ecological and economic consequences, recent research has focused on devising early warning signals for anticipating such abrupt ecological transitions. In particular, theoretical studies show that changes in spatial characteristics of the system could provide early warnings of approaching transitions. However, the empirical validation of these indicators lag behind their theoretical developments. Here, we summarize a range of currently available spatial early warning signals, suggest potential null models to interpret their trends, and apply them to three simulated spatial data sets of systems undergoing an abrupt transition. In addition to providing a step-by-step methodology for applying these signals to spatial data sets, we propose a statistical toolbox that may be used to help detect approaching transitions in a wide range of spatial data. We hope that our methodology together with the computer codes will stimulate the application and testing of spatial early warning signals on real spatial data.
authors.affiliation: Institut des Sciences de l'Evolution, CNRS, Université de Montpellier II, Montpellier, France.
authors.forename: Sonia
authors.initials: S
authors.lastname: Kéfi
authors.affiliation: Centre for Ecological Sciences, Indian Institute of Science, Bangalore, India.
authors.forename: Vishwesha
authors.initials: V
authors.lastname: Guttal
authors.affiliation: Department of Economics, University of Wisconsin, Madison, Wisconsin, United States of America; Department of Economics, University of Missouri, Columbia, Missouri, United States of America.
authors.forename: William A
authors.initials: WA
authors.lastname: Brock
authors.affiliation: Department of Economics, University of Missouri, Columbia, Missouri, United States of America; Center for Limnology, University of Wisconsin, Madison, Wisconsin, United States of America.
authors.forename: Stephen R
authors.initials: SR
authors.lastname: Carpenter
authors.affiliation: Harvard Forest, Harvard University, Petersham, Massachusetts, United States of America.
authors.forename: Aaron M
authors.initials: AM
authors.lastname: Ellison
authors.affiliation: National Physical Laboratory, Hampton Road, Teddington, United Kingdom.
authors.forename: Valerie N
authors.initials: VN
authors.lastname: Livina
authors.affiliation: Department of Environmental Sciences, University of Virginia, Charlottesville, Virginia, United States of America.
authors.forename: David A
authors.initials: DA
authors.lastname: Seekell
authors.affiliation: Department of Aquatic Ecology and Water Quality Management, Wageningen University, Wageningen, The Netherlands.
authors.forename: Marten
authors.initials: M
authors.lastname: Scheffer
authors.affiliation: Department of Aquatic Ecology and Water Quality Management, Wageningen University, Wageningen, The Netherlands.
authors.forename: Egbert H
authors.initials: EH
authors.lastname: van Nes
authors.affiliation: Integrative Ecology Group, Estacion Biologica de Donana, Sevilla, Spain.
authors.forename: Vasilis
authors.initials: V
authors.lastname: Dakos
mesh_terms: D004463:Ecology / Q000379:methods*; D017753:Ecosystem; D005583:Fourier Analysis; D008954:Models, Biological; D008962:Models, Theoretical; D013997:Time Factors