Response of equilibrium states to spatial environmental heterogeneity in advective systems

  • Received: 01 April 2006 Accepted: 29 June 2018 Published: 01 November 2006
  • MSC : 92D40, 34K20.

  • 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.

    Citation: Roger M. Nisbet, Kurt E. Anderson, Edward McCauley, Mark A. Lewis. Response of equilibrium states to spatial environmental heterogeneity in advective systems[J]. Mathematical Biosciences and Engineering, 2007, 4(1): 1-13. doi: 10.3934/mbe.2007.4.1

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  • 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.


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