[PAST EVENT] Mathematics Colloquium and EXTREEMS-QED Lecture: Yu Jin (University of Nebraska-Lincoln)
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Mathematics Colloquium and EXTREEMS-QED Lecture: Yu Jin (University of Nebraska-Lincoln)
Title: Persistence measures for populations in river environments
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 reaction-diffusion-advection equations that couple hydraulic flow to population growth and dispersal in the flow, and we analyze them to assess the effect of water flow on population persistence. Then we consider the situation where a population grows on the benthos, drift in water, and transfer between the water column and the benthos, and we use reaction-diffusion-advection equations coupled with ordinary differential equations to describe the dynamics of a single species and of two competitive species. We present a mathematical framework of persistence measures based on the net reproductive rate and related measures as well as eigenvalues of corresponding eigenvalue problems. We derive numerical methods to calculate persistence measures and apply them under various flow regimes to investigate the influences of various factors on population persistence in rivers. The theory developed here provides the basis for effective decision-making tools for water managers.