ELECTIVES > MATHEMATICAL MODELING OF ECOLOGICAL SYSTEMS

The students will first be exposed to the role of models in science and the relationship of models to scientific theories. Then the basics of calculus are reviewed in the context of the mass-balance concept. Next the students are introduced to numerical (as opposed to analytical) solutions of the mass-balance equation; that is, they are taught how to get a computer to do all the hard math. They then apply these techniques to a series of examples including the growth of an individual organism and of a populations of organisms, the interactions within species communities (competition for resources, predator-prey systems), the cycling of elements within ecosystems, the hydrology of a watershed, and an analysis of the CO2 balance of the atmosphere.

The students will use what they learn over the course of the semester to develop their own simulation model of an ecosystem. They are provided with a model shell that includes a Windows™ interface, integrator, and graphical-output package. The student then provides a set of equations describing the ecological processes they want to simulate. These equations are based on the simple concept of a mass balance and can be applied to ecosystem element cycles, population dynamics, or community interactions.

Required Text: Students will be assigned chapters from selected texts and papers from the primary literature.

What to expect:

The students will complete about six programming problems that illustrate the topics covered in lecture. Students will be evaluated predominantly based on a term project. In that project they will develop their own simulation model, address some ecologically significant question with the model, and write a manuscript describing the model and analysis. The manuscript is to be written as if it were to be submitted to a scientific journal (e.g., Ecology) and will undergo the same scientific and editorial review as any manuscript submitted for publication. The manuscript will first be submitted about three weeks before the end of formal classes. It will undergo scientific and editorial review by the instructor and returned. The revised manuscript will be resubmitted on the last day of classes. Students are encouraged to relate their project to topics covered in other courses, and may use the model they develop as part of their independent research project undertaken during the last 4 weeks of the semester. Students will also be encouraged to interact with one another while working on these projects, but the manuscripts are to be individually authored. In addition, each student will make an oral presentation describing their project to the class.

Syllabus (2 sessions per week):

Session 1: Examples of the types of models you'll be building (original MEL)

Session 2: Orientation to computers, software, programming

Session 3: Models in Science

Session 4: Mass balance and a review of calculus

Session 5: Numerical integration

Session 6: The growth of a spherical cell

Session 7: Global C budget

Session 8: Forest N budget

Session 9: Catchment hydrologic budget

Session 10: The Michaelis-Menton equation. (equations due)

Session 11: population logistic and competing populations

Session 12: predator-prey systems

Session 13: parameter estimation and curve fitting

Session 14: In -class help with projects

Session 15: In -class help with projects

Session 16: The Multiple Element Limitation (MEL) Model. (first sub)

Session 17: Island model

Session 18: Forest model

Sessions 19 and 20: Student Presentations. (projects due)

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