User:Carl Boettiger/Notebook/Stochastic Population Dynamics
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Stochastic Population Dynamics
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.
See the most recent journal entry for more immediate goals and details.