Seminar on stochastic modeling in ecology and hydrology
Semester Taught - Fall
This course takes a problem-based approach to introduce stochastic modeling in context of ecology and hydrology. The students will be asked to study selected papers in detail, through reading and in-class discussion, such that they understand how to set up the problems and derive some results and mathematical expressions reported therein. In the first few lectures, some basic concepts in probability and stochastic processes will be discussed. During the first part of the course, the instructor will lead the discussion. Afterwards, the students may take turn to lead the discussion. Depending on their interest and progress, the students may suggest papers on stochastic modeling in the field related to their own research during a later phase of the course. Examples of topics to be covered include neutral model of biodiversity (in which birth, death, dispersal, and speciation are stochastic), soil moisture dynamics driven by stochastic (Poisson) rainfall, stochastic models of rainfall (pulse model), etc.
Graduate standing; basic calculus and college-level probability courses
After taking this course, you should:
- Understand and be able to derive the basic results in the papers covered in class.
- Be able to apply these techniques to similar problems.
- Be able to formulate problems and construct models to study the effects of stochastic fluctuation on the resulting outcomes.
Dr. Rachata Muneepeerakul
Office: Room 227 Rogers Hall
Phone: 392-1864 x227
Class Materials Required
(Notes: we would likely not have time to cover all papers listed below; we may cover them in a different order; and we may even switch to different papers, depending on the interest and progress of the class.)
Leigh , E.G. Jr. 2007. Neutral theory: a historical perspective. Journal of Evolutionary Biology 20: 2075-2091.
Volkov, I., J.R. Banavar, S.P. Hubbell, & A. Maritan. 2003. Neutral theory and relative species abundance in ecology. Nature 424: 1035-1037.
McKane, A.J., D. Alonso, & R. V. Solé. 2004. Analytical solution of Hubbell’s model of local community dynamics. Theoretical Population Biology 65: 67-73.
Chave, J. & E.G. Leigh Jr. 2002. A spatially explicit neutral model of b-diversity in tropical forests. Theoretical Population Biology 62: 153-166.
Rodriguez-Iturbe, I., A. Porporato, L. Ridolfi, V. Isham, & D.R. Cox. 1999. Probabilistic modeling of water balance at a point: the role of climate, soil and vegetation. Proceedings of the Royal Society, London, A 455: 3789-3805.
Laio, F., A. Porporato, L. Ridolfi, & I. Rodriguez-Iturbe. 2001. Mean first passage times of processes driven by white shot noise. Physical Review E 63, 036105.
Leigh , E.G. Jr. 1981. The average lifetime of a population in a varying environment. Journal of Theoretical Biology 90: 213-239.
Rodriguez-Iturbe, I., D.R. Cox, & V. Isham. 1987. Some models for rainfall based on stochastic point processes. Proceedings of the Royal Society, London, A 410: 269-288.
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