CMMB Seminar: Analysis of spatiotemporal models for stream populations

Speaker: Mark Lewis, University of Alberta

Title: Analysis of spatiotemporal models for stream populations

Abstract: 

Human activites change the natural flow regimes in rivers and this impacts river ecosystems. Water managers are tasked with meeting human water needs while mitigating ecosystem impacts. We develop process-oriented advection-diffusion-reaction equations that couple hydraulic flow to population growth, and analyze them to assess the effect of water flow on population dynamics. We present a mathematical framework, based on the net reproductive rate $R_0$ for advection-diffusion-reaction equations and on related measures. We apply the measures to populations in rivers under various flow regimes.

This work lays the groundwork for connecting $R_0$ to more complex models of spatially structured and interacting populations, as well as more detailed habitat and hydrological data. This is achieved through explicit numerical simulation of two dimensional depth-averaged models for river population dynamics.

This talk is is based on recent collaborative work with Frank Hilker, Jon Jacobsen, Yu Jin, Hannah McKenzie, and Peter Steffler as well as earlier collaborative work with Frithjof Lutscher, Ed McCauley, and Roger Nisbet.