Atlas home || Conferences | Abstracts | about Atlas
Host: University of British Columbia
Sponsor: PIMS
Homepage: http://www.pims.math.ca/sections/activities/eco.html
Organizers: Marc Mangel
Description:
Ecology is the study of the distribution and abundance of organisms. Mathematical analysis and methods contribute to this study at a number of different levels.
Individual behavior. A generation ago, the computational complexity associated with predicting individual behaviour made it an enormous task. The development of computational power has made behavioural prediction using stochastic dynamic programming, genetic algorithms and other optimization methods feasible. Furthermore, this is an area where collaboration between experiment and mathematical theory is particularly fruitful because the time scale of individual behavior is conducive to rapid collection of data. Even so, many mathematical challenges remain, ranging from problems of numerical analysis of interpolation at boundaries to overcoming the curse of dimensionality in problems with many state variables.
Single population dynamics. The analysis of the population dynamics of single species has contributed to the development of nonlinear differential equations, the theory of chaos (through analysis of discrete maps), nonlinear diffusion theory (through analysis of equations such as the Fisher equation), and stochastic population theory. Many interesting problems remain. These include: i) determining the spectra of time series generated by nonlinear maps (a topic that received much coverage in high profile journals such as Nature, recently), ii) connecting nonlinear stochastic and deterministic models where closure problems similar to the ones in the theory of turbluence arise, and iii) the origins of diffusion models from discrete movement models, particularly when some fraction of the population may make large movements.
Multi-species population dynamics and community ecology. The interactions of two or more species, as in predation, competition, mutualism and disease, present new kinds of mathematical challenges. These include the extension of phase plane analysis to more than two dimensions, the estimation of parameters for complicated nonlinear systems, the possibilities of large excursions (as occur in pest or disease outbreaks) and understanding the stability properties of large multidimensional systems of ordinary, partial, and stochastic differential equations.
Mail Address:
Fred Adler Colin Clark Michael Doebeli Greg Dwyer Steve Ellner Shea Gardner Don Ludwig Bernard Luttbeg Marc Mangel Jonathan Newman
Date received: May 06, 1999
© 2008 Atlas Conferences Inc.