An eigenvalue optimization problem in Mathematical Ecology

Alan Lindsay (August 31, 2011)

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Abstract

Determining whether a habitat with fragmented or concentrated resources is a benefit or hindrance to a species' well-being is a natural question to ask in Ecology. Such fragmentation may occur naturally or as a consequence of human activities related to development or conservation. In a certain mathematical formulation of this problem, one is led to study an indefinite weight eigenvalue problem, the principal eigenvalue of which is a function of the habitat's makeup and indicates the threshold for which the species either persists or becomes extinct. For a particular but general class of fragmentation profiles, this threshold can be calculated implicitly and optimized to reveal an definitive strategy for minimizing the persistence threshold and thereby allowing the species to persist for the largest range of physical parameters.

This relates to work contained in the publication: A.E. Lindsay, M.J.Ward, (2010) An Asymptotic Analysis of the Persistence Threshold for the Diffusive Logistic Model in Spatial Environments with Localized Patches Discrete and Continuous Dynamical Systems Series B, Volume: 14, Number: 3, pp.1139-1179