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R0 Analysis of a Spatiotemporal Model for a Stream Population Open Access

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Author or creator
McKenzie, H.W.
Jin. Y.
Jacobsen, J.T.
Lewis, M.A.
Additional contributors
Subject/Keyword
instream flow needs
next generation operator
drift paradox
positive operator
net reproductive rate
spectral radius
Type of item
Journal Article (Published)
Language
English
Place
Time
Description
Water resources worldwide require management to meet industrial, agricultural, and urban consumption needs. Management actions change the natural flow regime, which impacts the river ecosystem. Water managers are tasked with meeting water needs while mitigating ecosystem impacts. We develop process-oriented advection-diffusion-reaction equations that couple hydraulic flow to population growth, and we analyze them to assess the effect of water flow on population persistence. We present a new mathematical framework, based on the net reproductive rate R0 for advection-diffusion-reaction equations and on related measures. We apply the measures to population persistence in rivers under various flow regimes. This work lays the groundwork for connecting R0 to more complex models of spatially structured and interacting populations, as well as more detailed habitat and hydrological data.
Date created
2011
DOI
doi:10.7939/R36X5X
License information
Rights
© 2012 Society for Industrial and Applied Mathematics
Citation for previous publication
McKenzie, H.W., Jin, Y. Jacobsen, J.T. & Lewis, M.A. (2011). R0 Analysis of a Spatiotemporal Model for a Stream Population. SIAM J. Appl. Dyn. Syst., 11(2), 567–596. DOI: 10.1137/100802189
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File title: $R_0$ Analysis of a Spatiotemporal Model for a Stream Population
File author: Mckenzie, H., Jin, Y., Jacobsen, J., and Lewis, M.
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