Seasonal invasion dynamics in a spatially heterogeneous river with fluctuating flows

Yu Jin, Frank M. Hilker, Peter M. Steffler, Mark A. Lewis

Research output: Contribution to journalArticlepeer-review

24 Citations (SciVal)


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.

Original languageEnglish
Pages (from-to)1522-1565
JournalBulletin of Mathematical Biology
Issue number7
Early online date3 Jun 2014
Publication statusPublished - Jul 2014


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