R₀ Analysis of a Spatiotemporal Model for a Stream Population

Authors

H. W. Mckenzie, University of Alberta
Y. Jin, University of Alberta
Jon T. Jacobsen, Harvey Mudd CollegeFollow
M. A. Lewis, University of Alberta

Document Type

Article

Department

Mathematics (HMC)

Publication Date

4-2012

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 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.

Comments

This article is also available from the Society for Industrial and Applied Mathematics at http://dx.doi.org/10.1137/100802189.

Rights Information

© 2012 Society for Industrial and Applied Mathematics

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1137/100802189

Recommended Citation

H. Mckenzie, Y. Jin, J. Jacobsen and M. Lewis. "R0-analysis of a spatiotemporal model for a stream population," SIAM J. Appl. Dyn. Syst (2012), pp. 567-596.