Seasonal Invasion Dynamics in a Spatially Heterogeneous River with Fluctuating Flows

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.

[1]  Henri Berestycki,et al.  Analysis of the periodically fragmented environment model: II—biological invasions and pulsating travelling fronts , 2005 .

[2]  Frank M. Hilker,et al.  Predator–prey systems in streams and rivers , 2010, Theoretical Ecology.

[3]  Jerome A. Goldstein,et al.  Partial Differential Equations and Related Topics , 1975 .

[4]  G. Petts,et al.  Classifying the hydraulic performance of riffle–pool bedforms for habitat assessment and river rehabilitation design , 2003 .

[5]  Xiao-Qiang Zhao,et al.  Asymptotic speeds of spread and traveling waves for monotone semiflows with applications , 2007 .

[6]  J. Yen,et al.  Putting the “Ecology” into Environmental Flows: Ecological Dynamics and Demographic Modelling , 2012, Environmental Management.

[7]  Hans F. Weinberger,et al.  On spreading speeds and traveling waves for growth and migration models in a periodic habitat , 2002, Journal of mathematical biology.

[8]  Frithjof Lutscher,et al.  Population persistence in the face of advection , 2010, Theoretical Ecology.

[9]  David M. Merritt,et al.  HYDROLOGIC REGIMES AND RIPARIAN FORESTS: A STRUCTURED POPULATION MODEL FOR COTTONWOOD , 2004 .

[10]  Xiao-Qiang Zhao,et al.  Spreading speeds and traveling waves for abstract monostable evolution systems , 2010 .

[11]  D. J. Booker,et al.  Hydraulic modelling of fish habitat in urban rivers during high flows , 2003 .

[12]  Mark A. Lewis,et al.  The Effect of Dispersal Patterns on Stream Populations , 2005, SIAM J. Appl. Math..

[13]  G. Janauer.  Ecohydrology: fusing concepts and scales , 2000 .

[14]  P. Chesson.  Mechanisms of Maintenance of Species Diversity , 2000 .

[15]  R. Naiman,et al.  Freshwater biodiversity: importance, threats, status and conservation challenges , 2006, Biological reviews of the Cambridge Philosophical Society.

[16]  F. Lloyd,et al.  Microhabitat associations of three species of Dryopoidea (Coleoptera) in an Ozark stream: a comparison of substrate, and simple and complex hydraulic characters , 2000, Hydrobiologia.

[17]  Julio L. Betancourt,et al.  Ecology and the ratchet of events: Climate variability, niche dimensions, and species distributions , 2009, Proceedings of the National Academy of Sciences.

[18]  Kimberly A. With.  The Landscape Ecology of Invasive Spread , 2002 .

[19]  G. Smart,et al.  Drag coefficients of stream bryophytes: experimental determinations and ecological significance , 2000 .

[20]  B. Biggs,et al.  HYDRAULIC HABITAT OF PLANTS IN STREAMS , 1996 .

[21]  John R. Post,et al.  Instream flow needs in streams and rivers: the importance of understanding ecological dynamics , 2006 .

[22]  K. Fausch,et al.  Landscapes to Riverscapes: Bridging the Gap between Research and Conservation of Stream Fishes , 2002 .

[23]  Fleur Visser,et al.  A framework for evaluating the spatial configuration and temporal dynamics of hydraulic patches , 2012 .

[24]  M. Chadwick.  Stream Ecology: Structure and Function of Running Waters , 2008 .

[25]  Angela H. Arthington,et al.  Environmental flows and water governance: managing sustainable water uses , 2013 .

[26]  Yu Jin,et al.  Seasonal influences on population spread and persistence in streams: spreading speeds , 2012, Journal of mathematical biology.

[27]  Nicholas F. Hughes,et al.  Process-based modelling of invertebrate drift transport, net energy intake and reach carrying capacity for drift-feeding salmonids , 2007 .

[28]  Brian Richter,et al.  ECOLOGICALLY SUSTAINABLE WATER MANAGEMENT: MANAGING RIVER FLOWS FOR ECOLOGICAL INTEGRITY , 2003 .

[29]  Brian Richter,et al.  River flows and water wars: emerging science for environmental decision making , 2003 .

[30]  K. Bovee,et al.  IMPORTANCE OF THE TEMPORAL ASPECTS OF HABITAT HYDRAULICS TO FISH POPULATION STUDIES , 1996 .

[31]  J. Gore,et al.  Hydraulic Stream Ecology: Observed Patterns and Potential Applications , 1988, Journal of the North American Benthological Society.

[32]  L. Peletier,et al.  Nonlinear diffusion in population genetics , 1977 .

[33]  M. Hanif Chaudhry,et al.  Open-Channel Flow , 2007 .

[34]  M. Uriarte,et al.  Moving forward in global-change ecology: capitalizing on natural variability , 2013, Ecology and evolution.

[35]  S. Levin,et al.  Diffusion and Ecological Problems: Modern Perspectives , 2013 .

[36]  David Zilberman,et al.  Spatially explicit tools for understanding and sustaining inland water ecosystems , 2005 .

[37]  Yu Jin,et al.  Seasonal Influences on Population Spread and Persistence in Streams: Critical Domain Size , 2011, SIAM J. Appl. Math..

[38]  C. Revenga,et al.  Fragmentation and Flow Regulation of the World's Large River Systems , 2005, Science.

[39]  W. Barthlott,et al.  Biodiversity : structure and function , 2009 .

[40]  Frithjof Lutscher,et al.  Effects of Heterogeneity on Spread and Persistence in Rivers , 2006, Bulletin of mathematical biology.

[41]  Jenny Davis,et al.  Microflow regimes and the distribution of macroinvertebrates around stream boulders , 1998 .

[42]  Allison Kolpas,et al.  Modeling the influence of flow on invertebrate drift across spatial scales using a 2D hydraulic model and a 1D population model , 2013 .

[43]  Gunog Seo,et al.  SPREAD RATES UNDER TEMPORAL VARIABILITY: CALCULATION AND APPLICATION TO BIOLOGICAL INVASIONS , 2011 .

[44]  N. Shigesada,et al.  Biological Invasions: Theory and Practice , 1997 .

[45]  Xiao-Qiang Zhao,et al.  The periodic Ross–Macdonald model with diffusion and advection , 2010 .

[46]  Sebastian J Schreiber,et al.  Interactive effects of temporal correlations, spatial heterogeneity and dispersal on population persistence , 2010, Proceedings of the Royal Society B: Biological Sciences.

[47]  K. Fausch,et al.  DYNAMICS OF INTERMITTENT STREAM HABITAT REGULATE PERSISTENCE OF A THREATENED FISH AT MULTIPLE SCALES , 2000 .

[48]  A. Arthington,et al.  Basic Principles and Ecological Consequences of Altered Flow Regimes for Aquatic Biodiversity , 2002, Environmental management.

[49]  V. B. Pasour,et al.  Computational and Analytic Perspectives on the Drift Paradox , 2010, SIAM J. Appl. Dyn. Syst..

[50]  S. D. Cooper,et al.  Implications of scale for patterns and processes in stream ecology , 1998 .

[51]  Roy A. Walters,et al.  Simulation of solute transport in a mountain pool‐and‐riffle stream: A transient storage model , 1983 .

[52]  R. Fisher.  THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES , 1937 .

[53]  P. McIntyre,et al.  Global threats to human water security and river biodiversity , 2010, Nature.

[54]  K. Gregory,et al.  Stability of the pool-riffle sequence in changing river channels , 1994 .

[55]  S. Schmutz,et al.  The effects of recreated instream and ecotone structures on the fish fauna of an epipotamal river , 1995, Hydrobiologia.

[56]  B. L. Lamb,et al.  The Instream Flow Incremental Methodology: A Primer for IFIM. , 1995 .

[57]  D. Walks.  Persistence of plankton in flowing water , 2007 .

[58]  D. Aronson,et al.  Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation , 1975 .

[59]  John L. Orrock,et al.  Spatial interplay of plant competition and consumer foraging mediate plant coexistence and drive the invasion ratchet , 2010, Proceedings of the Royal Society B: Biological Sciences.

[60]  F. Dyer,et al.  Effects of spatial and temporal variation in hydraulic conditions on metabolism in cobble biofilm communities in an Australian upland stream , 2006, Journal of the North American Benthological Society.

[61]  William Gurney,et al.  POPULATION PERSISTENCE IN RIVERS AND ESTUARIES , 2001 .

[62]  Gunog Seo,et al.  The effect of temporal variability on persistence conditions in rivers. , 2011, Journal of theoretical biology.

[63]  Melissa Parsons,et al.  Identifying spatial and temporal patterns in the hydrological character of the Condamine–Balonne river, Australia, using multivariate statistics , 2003 .

[64]  M A Lewis,et al.  Invasion speeds in fluctuating environments , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[65]  R. Sparks,et al.  THE NATURAL FLOW REGIME. A PARADIGM FOR RIVER CONSERVATION AND RESTORATION , 1997 .

[66]  S. Schmutz,et al.  The effects of recreated instream and ecotone structures on the fish fauna of an epipotamal river , 1995 .

[67]  H. Fischer.  Mixing in Inland and Coastal Waters , 1979 .

[68]  R. Tharme.  A global perspective on environmental flow assessment: emerging trends in the development and application of environmental flow methodologies for rivers , 2003 .

[69]  Xiao-Qiang Zhao,et al.  Spreading speeds and traveling waves for periodic evolution systems , 2006 .

[70]  Wilfried Thuiller,et al.  Predicting potential distributions of invasive species: where to go from here? , 2010 .

[71]  M. Palmer,et al.  Frontiers inEcology and the Environment Climate change and the world ’ s river basins : anticipating management options , 2007 .

[72]  Christian Wissel,et al.  Modelling persistence in dynamic landscapes : lessons from a metapopulation of the grasshopper Bryodema tuberculata , 1997 .

[73]  G. Harvey,et al.  Physical habitat, eco-hydraulics and river design: a review and re-evaluation of some popular concepts and methods , 2006 .

[74]  J. Lancaster,et al.  Linking the hydraulic world of individual organisms to ecological processes: Putting ecology into ecohydraulics , 2010 .

[75]  M A Lewis,et al.  Persistence, spread and the drift paradox. , 2005, Theoretical population biology.

[76]  E. Mccauley,et al.  Spatial heterogeneity and rates of spread in experimental streams , 2008 .

[77]  N. Poff,et al.  Ecological responses to altered flow regimes: a literature review to inform the science and management of environmental flows , 2010 .