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 journalArticle

11 Citations (Scopus)

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.

LanguageEnglish
Pages1522-1565
JournalBulletin of Mathematical Biology
Volume76
Issue number7
Early online date3 Jun 2014
DOIs
StatusPublished - Jul 2014

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Ratchet
Invasion
Rivers
Population Dynamics
Hydrodynamics
Hybrid Modeling
Population dynamics
rivers
Caricatures
river
Hydraulics
hydrodynamics
Biological Phenomena
Biological Models
population dynamics
fluid mechanics
Water
Spreading Speed
hydraulics
Spatial Heterogeneity

Cite this

Seasonal invasion dynamics in a spatially heterogeneous river with fluctuating flows. / Jin, Yu; Hilker, Frank M.; Steffler, Peter M.; Lewis, Mark A.

In: Bulletin of Mathematical Biology, Vol. 76, No. 7, 07.2014, p. 1522-1565.

Research output: Contribution to journalArticle

Jin, Yu ; Hilker, Frank M. ; Steffler, Peter M. ; Lewis, Mark A. / Seasonal invasion dynamics in a spatially heterogeneous river with fluctuating flows. In: Bulletin of Mathematical Biology. 2014 ; Vol. 76, No. 7. pp. 1522-1565.
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