title: Changes in habitat of fish populations: An inverse problem.
abstract: Mathematical modelling applies to a wide variety of application areas, and is an active area of research in many disciplines. It is often the case that accurate depiction of real-world phenomena require increasingly complex models. Unfortunately, this increased complexity in a model causes great difficulty when seeking solutions. What is more, developing a model with known parameters that produces results consistent with observed behaviors may prove to be a difficult or even impossible task. These difficulties have brought about an interest in inverse problems. In this paper we utilize a collage-based approach to solve an inverse problem for a model for the migration of three fish species through floodplain waters. A derivation of the mathematical model is presented and a generalized collage method is discussed and applied to this model to recover diffusion parameters. Theoretical and numerical particulars are discussed and results are presented.
authors.affiliation: Department of Mathematics & Statistics, University of Guelph, 50 Stone Road East, Guelph, Ontario N1G 2W1, Canada. Electronic address: klevere@uoguelph.ca.
authors.forename: Kimberly M
authors.initials: KM
authors.lastname: Levere
mesh_terms: D000818:Animals; D017753:Ecosystem; D005399:Fishes / Q000502:physiology*; D008962:Models, Theoretical
keywords: Fish populations; Inverse problems; Nonlinear; Optimization; Parameter estimation; Partial differential equations