Name: Yu Jin
Date: Friday, Dec. 1
Title: Spatial Population Dynamics in Heterogeneous River Environments
Abstract: Natural rivers and streams are important habitats for aquatic species and other species that rely on them. The study of population persistence and spread in river ecosystems is key for understanding river population dynamics and invasions as well as instream flow needs. We develop process-oriented reaction-diffusion-advection equations that couple hydraulic flow to population growth and analyze the models theoretically and numerically to assess the effects of hydraulic, physical, and biological factors on population dynamics. We present a mathematical framework, based on persistence metrics such as the fundamental niche, the source and sink metric, the net reproductive rate and the principal eigenvalue of the associated eigenvalue problem to determine local and global persistence of a population in a spatially heterogeneous one-dimensional or two-dimensional river or river network. We establish asymptotic spreading speeds to understand biological invasions in the upstream and downstream directions in temporally and/or spatially heterogeneous river environments. Furthermore, we present a hybrid modeling approach to explicitly link the flow regime with ecological dynamics, which helps analyze the impact of river morphology on population persistence in a realistic river.