Honors College Thesis
 

The Mathematics of Critical Shifts in Ecological Networks with Alternative Stable State Theory, A Potential Framework for Early Warning Indicators

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https://ir.library.oregonstate.edu/concern/honors_college_theses/n583z157d

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  • A long running problem in mathematical biology is the prediction of extinction events, a specialized case of the larger global stability problem found in differential equations and dynamical systems theory. A central technical question is how to introduce the randomness observed in real ecological systems not accounted for in deterministic models. This work introduces the SP-system as a new mathematical object in which ecological parameters are treated as sequences of random variables that attain values over intervals of random lengths of time. The SP-system characterization of ecological networks leads to two different novel approaches for the simulation and extinction prediction. The first approach uses a construct new to modeling literature to describe the probability of a parameter transition event into an extinction event. The second approach utilizes Markov chains for both simulation and extinction prediction. A constructive technique for the associated probability kernel is demonstrated as the basis of the Markov chain approach. An example of each application is presented.
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  • 2019-08-24 to 2020-01-02

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