Early warning signals ofintermediate complexity - PDF document

Early warning signals ofintermediate complexity Steven Lade Early warning signals of intermediate complexity (Detailed simulations)Global circulation modelsIntegrated assessment modelsAgent based modelling ModeldrivenDatadriven(Time series analysis)VarianceAutocorrelationSkewness IntermediateapproachesGeneralised modellingIncorporate data and knowledge with a generalised modelCritical transition as fold bifurcation*; fastslow time separationCalculate eigenvalues � warning signal← complementary → Steven Lade Early warning signals of intermediate complexity OutlineSimple growth model with Allee effect (introduction)Fishery model (realistic)Tritrophic food chain (versatility) Steven Lade Early warning signals of intermediate complexity Allee effectPer capita growth rate increasing with population sizeInteresting population dynamics… including critical transitions Population sizePer capita growth rate Steven Lade Early warning signals of intermediate complexity Generalised model for Allee effect Population size BirthsDeaths Externalparameter These two series of measurements and one assumptionare sufficient to calculate an early warning signal linear in Distinguish processes, but do not specify functional forms Steven Lade Early warning signals of intermediate complexity Early warning signal for Allee effect Steven Lade Early warning signals of intermediate complexity Early warning signal for Allee effect Clear early warning signalSignal from only 15 time points Steven Lade Early warning signals of intermediate complexity Fishery modelPiscivores being harvested. Planktivores also important for dynamics.Fishery managers are concerned that increased harvesting may cause a collapse from highpiscivore regime to lowpiscivore regime Steven Lade Early warning signals of intermediate complexity Fishery model(discrete time) Quadratic in Predationlinear in constant Steven Lade Early warning signals of intermediate complexity Fishery collapseBiggs et al.is a hybrid discretecontinuous modelUse yearend dataPolynomial smoothingSuccessful even with explicitly modelling neither juvenile population nor continuoustime intrayear dynamics Juvenile piscivoresAdult piscivoresPlanktivoresCritical transition thresholdGen. model.eigenvalueBiggs et al.varianceYearvarianceFish catch Steven Lade Early warning signals of intermediate complexity Tritrophic food chain Linear in Linear in Linear in Linear in Linear in Extendable to incomplete conversion effciency Steven Lade Early warning signals of intermediate complexity Tritrophic food chain simulationCritical transitionClear warning signalBifurcation delayWarning of transitionGradientbased method can distinguish some types of critical transition X1 X2 X3 Steven Lade Early warning signals of intermediate complexity Future workBayesian filtering frameworkQuality of prior knowledgeCompare suitability of generalised modelsConfidence in an early warning signalReduce sensitivity to noiseNormal form calculation (Thompson & Sieber)Calculate probabilities over time of future transitionsSpectrum of eigenvaluesObservational data from a past transition? t Steven Lade Early warning signals of intermediate complexity ConclusionsEarly warning signals of intermediate complexityGeneralised modelling framework successfully predicted critical transitionsBased on combining multiple types of data with systemspecific knowledgeComplementary to existing approaches like variance and autocorrelationLade & Gross (2012), PLoS Comp. Biol.8(2) e1002360