User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/03/31

Stochastic Population Dynamics

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Research Writing up work just on ensemble vs single instance detection of regime shifts. See this entry Outline Title On the ability to detect leading indicators of catastrophe in unreplicated time series Introduction Background on Warning Signals literature Saddle Node bifurcation Detecting decreasing stabilization -- gradual vs changepoint estimation Reasons detection can fail: Ergodicity: ensembles vs single instances Sufficient statistical power Appropriate dynamics Methods Defining an indicator -- significant Kendall rank correlation coefficient [math]\displaystyle{ \tau }[/math] as in doi:10.1073/pnas.0802430105 Simulation approach Analytic limits accounting for delay? Figures Saddle node bifurcation example -- should discuss difference between stochastic and deterministic edge? Single replicates using standard detection statistics Results/Discussion Misleading indicators Need for further exploration