Graduate Thesis Or Dissertation
 

Persistence of Populations in Environments with an Interface

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/ws859h80k

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  • We model a fish population in a spatial region comprising a marine protected area and a fishing ground separated by an interface. The model assumes conservation of biomass density and takes the form of a reaction diffusion equation with a logistic reaction term. At the interface, in addition to continuity of biomass density flux, two possible matching conditions are considered: continuity of population density and continuity of biomass density. Neumann conditions are imposed at the physical boundaries. The eigenvalues of the elliptic problem resulting from the linearization of the model are computed. Necessary and sufficient conditions for the largest eigenvalue to be positive are determined. We show that there exist positive eigenfunctions corresponding to this eigenvalue. If the largest eigenvalue is positive, the population persists, whereas if this eigenvalue is negative, the population goes extinct. A simple sufficient condition for persistence when biomass density is continuous is that the spatially averaged net growth rate is positive. Similarly, if the spatially averaged net body mass growth rate is positive, the population persists when population is continuous. A brief introduction is given on connections between parabolic partial differential equations and stochastic processes. Questions relating branching stochastic processes and properties of population models that incorporate interfaces are identified.
  • Keywords: Population Models, Interface, Persistence, Marine Protected Area
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file details RekowJamesA2016.pdf 2017-08-04 Público Descargar