R0 Analysis of a Spatiotemporal Model for a Stream Population

Authors

H. W. Mckenzie, University of AlbertaFollow
Y. Jin, University of AlbertaFollow
J. Jacobsen, Harvey Mudd College
M. A. Lewis, University of AlbertaFollow

Date of this Version

2012

Citation

SIAM J. APPLIED DYNAMICAL SYSTEMS

Vol. 11, No. 2, pp. 567–596

Comments

© 2012 Society for Industrial and Applied Mathematics

DOI. 10.1137/100802189

Abstract

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 im- pacts. 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 popula- tion 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.