title: Seasonal invasion dynamics in a spatially heterogeneous river with fluctuating flows.
abstract: A key problem in environmental flow assessment is the explicit linking of the flow regime with ecological dynamics. We present a hybrid modeling approach to couple hydrodynamic and biological processes, focusing on the combined impact of spatial heterogeneity and temporal variability on population dynamics. Studying periodically alternating pool-riffle rivers that are subjected to seasonally varying flows, we obtain an invasion ratchet mechanism. We analyze the ratchet process for a caricature model and a hybrid physical-biological model. The water depth and current are derived from a hydrodynamic equation for variable stream bed water flows and these quantities feed into a reaction-diffusion-advection model that governs population dynamics of a river species. We establish the existence of spreading speeds and the invasion ratchet phenomenon, using a mixture of mathematical approximations and numerical computations. Finally, we illustrate the invasion ratchet phenomenon in a spatially two-dimensional hydraulic simulation model of a meandering river structure. Our hybrid modeling approach strengthens the ecological component of stream hydraulics and allows us to gain a mechanistic understanding as to how flow patterns affect population survival.
authors.affiliation: Centre for Mathematical Biology, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB , T6G 2G1, Canada, yjin6@unl.edu.
authors.forename: Yu
authors.initials: Y
authors.lastname: Jin
authors.forename: Frank M
authors.initials: FM
authors.lastname: Hilker
authors.forename: Peter M
authors.initials: PM
authors.lastname: Steffler
authors.forename: Mark A
authors.initials: MA
authors.lastname: Lewis
mesh_terms: D003198:Computer Simulation; D017753:Ecosystem; D008962:Models, Theoretical; D011157:Population Dynamics; D045483:Rivers; D012621:Seasons; D014872:Water Movements