Using Dynamical Systems to
Understand History
Peter Kauphusman
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This presentation will include a brief look into utilizing dynamical systems for the testing historical conjectures. I will introduce two proposed models – the single polity and two polity model. I will discuss the behavior of each model in this presentation, as well as some overall discussion of the merit of introducing more complex mathematics to historical areas of interest.
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Intergral Projection Model of the Gizzard Shad (Dorosoma cependianum) Incorporating Winter
Temperature
Mya Austin
(co-author: Avery Kanel)
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The American gizzard shad (Dorosoma cependianum) is an important prey species for popular game fish. Winter kill is a survival bottleneck for shorter gizzard shad and can cause massive die-offs. Our goal was to incorporate winter temperature into an Integral Projection Model (IPM) to predict future population trends in gizzard shad. The survival function’s inflection point for shad populations in pool four and twenty-six of the Mississippi River was found using the least square error method. A linear function was fitted to the pools and used to predict the inflection point of other pools based on early-spring average temperature. It was found that colder, more northern, pools had a higher inflection point than warmer, more southern, pools. Colder pools had a lower frequency of longer length fish suggesting that first year fish weren’t able to survive the winter. Our results suggest gizzard shad in colder pools must reach longer lengths than individuals in warmer pools to survive winter.
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