User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/05/13

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Beetles workshop Day 2

Goals

  • van Kampen expansion of LPA model, maximize noise in L while keeping A robust?

\begin{align}
\frac{d \langle \xi^2 \rangle}{d t} &= 2 \frac{\partial \alpha_{1,0}}{\partial \phi} \langle \xi^2 \rangle + 2 \frac{\partial \alpha_{1,0} }{\partial \psi} \langle \xi \eta \rangle + \alpha_{2,0}  \\
\frac{d \langle \xi \eta \rangle}{d t} &= \left( \frac{\partial \alpha_{1,0}}{\partial \phi} + \frac{\partial \beta_{1,0} }{\partial \psi} \right)\langle \xi \eta \rangle+ \frac{\partial \alpha_{1,0} }{\partial \psi} \langle \eta^2 \rangle \\
\frac{d \langle \xi^2 \rangle}{d t} &= 2 \frac{\partial \beta_{1,0}}{\partial \psi} \langle \eta^2 \rangle + \beta_{2,0}
\end{align}
  • Indiv. heterogeneity issue: dividing larval class into a smaller, highly-cannibal and remainder of more weakly cannibalistic.
  • Pulse dynamics -- interspike interval, magnitude?

Potential Data

  • 1995 Dennis et al. -- 5 replicate populations (2-cycle dataset), 5 age-cycles.
  • eight-year chaotic time series
  • Strawbridge daily samples (single replicate), occasional disease in lines though.

Literature

  • Caswell 2009 Sensitivity of density dependent dynamics
  • Kendall (yet unpublished)
  • Vindenes 2008 Individual heterogeneity & demographic stochasticity.
  • Ludwig 1996 Failure of diffusion approximation in small populations.

Next Steps

  1. Analytic description of large demographic noise systems
  2. Comparisons to beetle datasets
  3. Paper Outline. Skype meeting May 28th.


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