# Mathematical Biology Seminar

### Mark Lewis

Canada Research Chair in Mathematical Biology, University of Alberta

#### Mathematics behind stream population dynamics

#### Wednesday, October 8, 2014, at 3:05pm

LCB 219

Human activities change the natural flow regimes in streams and rivers and this impacts
ecosystems. In this talk I will mathematically investigate the impact of changes in water
flow on biological populations. The approach I will take is to develop process-oriented
advection-diffusion-reaction equations that couple hydraulic flow to population growth,
and then to analyze the equations so as to assess the effect of impacts of water flow on
population dynamics. The mathematical framework is based on new theory for the net
reproductive rate Ro as applied to advection-diffusion-reaction equations. I will then
connect the theory to populations in rivers under various flow regimes.

This work lays the groundwork for connecting Ro 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.