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The perfect mixing paradox and the logistic equation: Verhulst vs. Lotka

  • Arditi, Roger cology and Evolution – Department of Biology, University of Fribourg, Switzerland
  • Bersier, Louis-Félix cology and Evolution – Department of Biology, University of Fribourg, Switzerland
  • Rohr, Rudolf P. cology and Evolution – Department of Biology, University of Fribourg, Switzerland
    01.11.2016
Published in:
  • Ecosphere. - 2016, vol. 7, no. 11, p. e01599
English A theoretical analysis of density-dependent population dynamics in two patches sheds novel light on our understanding of basic ecological parameters. Firstly, as already highlighted in the literature, the use of the traditional r-K parameterization for the logistic equation (due to Lotka and Gause) can lead to paradoxical situations. We show that these problems do not exist with Verhulst's original formulation, which includes a quadratic “friction” term representing intraspecific competition (parameter α) instead of the so-called carrying capacity K. Secondly, we show that the parameter α depends on the number of patches, or more generally on area. This is also the case of all parameters that quantify the interaction strengths between individuals, either of the same species or of different species. The consequence is that estimates of interaction strength will vary when population size is measured in absolute terms. In order to obtain scale-invariant parameter estimates, it is essential to express population abundances as densities. Also, the interaction parameters must be reported with all explicit units, such as (m2·individual−1·d−1), which is rarely the case.
Faculty
Faculté des sciences et de médecine
Department
Département de Biologie
Language
  • English
Classification
Ecology and biodeversity
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https://folia.unifr.ch/unifr/documents/306022
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