American Institute of Mathematical Sciences

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2007, 4(1): 1-13. doi: 10.3934/mbe.2007.4.1

Response of equilibrium states to spatial environmental heterogeneity in advective systems

Roger M. Nisbet 1, , Kurt E. Anderson 2, , Edward McCauley 2, and  Mark A. Lewis 3,

1. 

Department of Ecology, Evolution and Marine Biology, University of California at Santa Barbara, CA 93106-9610, United States
2. 

Department of Biological Sciences, University of Calgary, Calgary, Alberta, Canada, T2N 1N4, Canada, Canada
3. 

Department of Mathematical and Statistical Sciences, and Department of Biological Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

Received  April 2006 Revised  August 2006 Published  November 2006

Much ecological research involves identifying connections between abiotic forcing and population densities or distributions. We present theory that describes this relationship for populations in media with strong unidirectional flow (e.g., aquatic organisms in streams and rivers). Typically, equilibrium populations change in very different ways in response to changes in demographic versus dispersal rates and to changes over local versus larger spatial scales. For populations in a mildly heterogeneous environment, there is a population ''response length'' that characterizes the distance downstream over which the impact of a point source perturbation is felt. The response length is also an important parameter for characterizing the response to non-point source disturbances at different spatial scales. In the absence of density dependence, the response length is close to the mean distance traveled by an organism in its lifetime. Density-dependent demographic rates are likely to increase the response length from this default value, and density-dependent dispersal will reduce it. Indirect density dependence, mediated by predation, may also change the response length, the direction of change depending on the strength of the prey's tendency to flee the predator.
Keywords: response length, population dynamics, advection, integro-differential equation., dispersal.
Mathematics Subject Classification: 92D40, 34K2.
Citation: Roger M. Nisbet, Kurt E. Anderson, Edward McCauley, Mark A. Lewis. Response of equilibrium states to spatial environmental heterogeneity in advective systems. Mathematical Biosciences & Engineering, 2007, 4 (1) : 1-13. doi: 10.3934/mbe.2007.4.1
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