# User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/05/13 Stochastic Population Dynamics Main project page Previous entry      Next entry ## Beetles workshop Day 2

### Goals

• van Kampen expansion of LPA model, maximize noise in L while keeping A robust?
\displaystyle{ \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• Kendall (yet unpublished)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.