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Introducing Mathematical Modeling in an Undergraduate Ecology Laboratory

Introducing Mathematical Modeling in an Undergraduate Ecology Laboratory. Mathematical Biology Modeling Group School of Mathematical Sciences & School of Biological Sciences. J. Fielder. The Ecology Class. 4 credits ; 3 hours/week lecture, 1 three-hour lab/week Juniors and Seniors

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Introducing Mathematical Modeling in an Undergraduate Ecology Laboratory

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  1. Introducing Mathematical Modeling in an Undergraduate Ecology Laboratory Mathematical Biology Modeling Group School of Mathematical Sciences & School of Biological Sciences J. Fielder

  2. The Ecology Class • 4 credits; 3 hours/week lecture, 1 three-hour lab/week • Juniors and Seniors • 25-30 students • Mostly biology majors • Our modeling lab supplemented the population dynamics unit

  3. Why Math Modeling in Ecology? Historically important role of math in ecology Our group focuses on math applications in ecology Models of invasive species en.wikipedia.org http://www.chthonic.f9.co.uk/b3ta/underage.jpg

  4. The Problem of Feral Cats: Kerguelen Islands (Chapuis 1995) • 60 winter inhabitants • up to 120 summer inhabitants • 5 founder cats?... • 25 years later…30,000 cats Birds killed per year? > 3 million per year! glennmci.brinkster.net en.wikipedia.org/wiki/Port-aux-Français

  5. Control of Feral Cats • Culling & trapping are expensive • Time-consuming • Labor intensive • Controversial • Disease • Feline Immunodeficiency Virus (FIV) • Feline Leukemia Virus (FeLV) • Retrovirus found worldwide • Spread by coming in contact with saliva, urine, feces, and nasal secretions (American Association of Feline Practitioners and Cornell Feline Health Center, 2006) www.wildliferesearchmanagement.com.au

  6. Introducing Predator-Prey Models: Logistic Growth Birds Cats

  7. Trying an Example Starting Values

  8. Graph of (Cat, Bird) Trajectory Birds Cats

  9. What happens if a cat disease is introduced to the system? Birds Cats

  10. Differential equations for FeLV

  11. Mathematica Simulator • Can run from any computer (with Mathematica Player download) • 12 parameters (run by sliders) • Initial populations controlled by pointer. http://www.unco.edu/NHS/mathsci/facstaff/Champion/Math/AlienCats/

  12. Benefits of the Collaboration • Mathematicians learned about applications of mathematics in Ecology • Learned that technology made the mathematics more accessible • Extended depth of mathematics that the Biologists could be involved with • More efficient, saved time • Feedback from the students was positive

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