User:Carl Boettiger/Notebook/Stochastic Population Dynamics

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=Stochastic Population Dynamics=
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This notebook has moved from the native OWW formatted notebook (calendar above) to my new notebook. All new entries can be seen through the embedded frame above. The OWW notebook remains my archive on this topic from the beginning of February 2010 to October 20th, 2010. The new notebook remains open and is interleaved with my Comparative Phylogenetics notebook. The Categories function on the new system make it easy to separate the notebooks. Many improved features, including nice handling of categories and tags, better search, clean rss feeds of posts, easy control over backups, support for mobile devices, and control over format and layout have led me to explore this change. The notebook remains open.

Modeling Uncertainty
Mathematical population models play an essential role in management of natural resources such as fisheries, forecasting disease dynamics or controlling invasive species. Understanding uncertainty and quantifying risk are crucial to effective management decisions -- a plan with a higher expected recovery rate of fish stocks may not be preferable if it also has a higher probability of possible extinction of the stock. Stochasticity is an intrinsic part of natural systems, and rather than view it always as noise that must be filtered out, it can become a source of information about the system itself. I am currently working on two inter-related projects in stochastic population dynamics.

Structured Populations (Github Code)
The assumption of large populations has been a longstanding favorite in ecological and evolutionary theory to avoid many of the challenges of intrinsically stochastic systems. Many natural populations are structured by age or stage in such a way that a small subset of the total population has a significant influence over the population as a whole. We are exploring these dynamics in laboratory populations of Tribolium flour beetles, which are structured by stage (egg, larva, pupa, adult) and in which mobile stages cannibalize the immobile stages. This produces a rich feedback of complicated dynamics sensitive to demographic stochasticity and individual heterogeneity as well as the more commonly assumed source of noise through environmental variation. The goal of this work is to parse the influence of these different sources of variation to provide accurate computer-based replications of the dynamics and analytic approximations thereof.

Early Warning Signals
A particularly tantalizing prospect in stochastic modeling is the ability for stochastic variation to serve as a source of information rather than a noisy nuisance. One of the most ambitious of such attempts is to use characteristics in this variation such as variance, autocorrelation, or skewness as an early warning signal of an impending tipping point or bifurcation.

Completed

 * Program individual-based Gillespie simulation of beetle dynamics with age classes.
 * Program example of tipping point in stochastic simulation due to saddle node bifurcation
 * Analytic treatment of noise in structured populations

Upcoming Goals

 * Analytic treatment of expected distribution for warning signals
 * R package tool for testing significance of potential warning signal, bootstrapping.

See the most recent journal entry for more immediate goals and details.

Collected Literature
 Theoretical Ecology is a group in Biological Sciences on Mendeley.

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