Open AccessThe perfect mixing paradox and the logistic equation: Verhulst vs. Lotka
Author(s) -
Arditi Roger,
Bersier LouisFélix,
Rohr Rudolf P.
Publication year - 2016
Publication title -
ecosphere
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.255
H-Index - 57
ISSN - 2150-8925
DOI - 10.1002/ecs2.1599
Subject(s) - intraspecific competition , logistic function , mathematics , population , quadratic equation , statistical physics , theoretical ecology , carrying capacity , competition (biology) , statistics , mixing (physics) , scale (ratio) , invariant (physics) , ecology , physics , biology , demography , geometry , quantum mechanics , sociology , mathematical physics
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 (m 2 ·individual −1 ·d −1 ), which is rarely the case.