User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/04/20

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Alan Meeting

From 03/31, see below for more!



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

Towards a better approach

  • Estimating the linear system directly:
  1. estimating the exponential coefficient [math]\displaystyle{ \lambda }[/math] of the autocorrelation function directly. Contrast to the autocorrelation. Estimating spectral width.
  2. estimating variance directly: [math]\displaystyle{ \frac{\sigma^2}{2\lambda } }[/math]
  • Changepoint analysis vs gradual trends.
    • i.e. web example,
    • book,
    • Bayesian / Dirchelet Process Prior analysis,
    • model selection.
  • Examples from software:
    • correlation C executable
    • R: source("warning_signals.R") example.

Other topics

  • F1000
  • Workstation order
  • Adaptive Dynamics manuscript
  • Labrids Manuscript

Updated Outline

  1. Warning Signals intro (Alan)
  2. Scope & previous work -> 1D (Alan)
  3. Reasons Detection can fail (Carl)
  4. Methods -> defining an indicator (Carl)
  5. Simulation approach (Carl)
  6. Analytic limits (Carl -- still to do)
  7. Accounting for delay (Carl -- still to do)
  8. Results -- saddle node (Carl -- still to do)
  9. Results -- single replicate (Carl -- still to do)
  10. Conclusions (Alan / both)

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