Nonlinear Physics of Ecosystems

Abstract

Introduction An emerging new scientific discipline Pattern formation-a missing link in ecological research Purpose and scope of the book OVERVIEW Spatial Self-Organization Natural and laboratory realizations of pattern formation Pattern-forming systems as dynamical systems A glimpse into pattern formation theory Spatial Ecology The complexity of ecological systems Outstanding problems The relevance of pattern formation theory to spatial ecology Modeling Ecosystems Why model? The modeling process Model output PATTERN FORMATION THEORY Pattern Formation Analysis: Basic Methods Dimensional analysis Two canonical models Linear stability analysis of uniform states Pattern Formation Analysis: Advanced Methods Amplitude equations Linear stability analysis of periodic states Singular perturbation theory Basic Mechanisms of Pattern Formation Nonuniform instabilities of uniform states Multiplicity of stable states and localized structures Instabilities of localized structures External Modulations of Pattern Forming Systems The interplay between intrinsic and extrinsic periodicities Multistability of phase states and fronts Symmetry-breaking instabilities APPLICATIONS TO ECOLOGY Modeling Water-Limited Vegetation Basic biomass-water feedbacks A mathematical model for water-limited vegetation Vegetation Pattern Formation Uniform and periodic vegetation states along environmental gradients Nonperiodic patterns Regime Shifts and Desertification The common view Spatial aspects of regime shifts Regime shifts in water-limited landscapes Species Coexistence and Diversity in Plant Communities Modeling plant communities Species coexistence induced by ecosystem engineers Savanna-like forms of species coexistence Linking pattern formation and biodiversity Bibliography Index