User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/02/02

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 * style="background-color: #EEE"|[[Image:owwnotebook_icon.png|128px]] Stochastic Population Dynamics
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 * style="background-color: #F2F2F2" align="center"|  |Main project page


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Stochastic Population Dynamics Goes Open

 * This is the first entry in my lab notebook, but not the beginning of the project. I have been exploring demographic and colored environmental noise since beginning my graduate program at UC Davis.  Much of that time has been spent in building the appropriate tool set though, so now it's time to dive in.


 * A good starting point is Denis et. al. (2001) Ecological Monographs 71.2. In this paper they reconsider the LPA model for Tribolium and determine that most of the variation can be attributed to demographic noise rather than chaos, limit cycles or environmental noise, contrary to their earlier work.


 * Thus far I've implemented a continuous time individual-based stochastic population model with four age classes. Currently demographic stochasticity is the only source of variation, though the age structure creates large shocks.  Analytic treatment is difficult in a continuous time framework since having fixed ages of maturity makes the model time heterogeneous.


 * Code for the project is hosted open source through Google code and managed with subversion.

Early Warning Signals

 * I've also done some work towards the early warning signal modeling. I've implemented a simple population individual-based model with saddle-node bifurcation in both C and netlogo.  The netlogo implementation allows for a better visualization with slider-bars that change the parameters and dynamic plotting, the C code allows larger numbers, longer times, and replicates (ensemble) simulation.  The C code is also in continuous time (via Gillespie method), while netlogo is in discrete time.  Both need some modification.


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