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

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Writing up work just on ensemble vs single instance detection of regime shifts. See this entry



On the ability to detect leading indicators of catastrophe in unreplicated time series

Introduction Background on Warning Signals

  1. literature
  2. Saddle Node bifurcation
  3. Detecting decreasing stabilization -- gradual vs changepoint estimation

Reasons detection can fail:

  1. Ergodicity: ensembles vs single instances
  2. Sufficient statistical power
  3. Appropriate dynamics


  • 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?


  • Saddle node bifurcation example -- should discuss difference between stochastic and deterministic edge?
  • Single replicates using standard detection statistics


  • Misleading indicators
  • Need for further exploration