An Introduction to Mathematical Population Dynamics by Mimmo Iannelli & Andrea Pugliese

Author:Mimmo Iannelli & Andrea Pugliese
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

The conclusions drawn by the analysis of the model constitute the mathematical basis of the ecological principle of exclusion. Condition (7.5) that was written in terms of intrinsic growth rates and resistance to resource depletion can be also written as

(7.10)

in terms of resource consumption and carrying capacities. In particular, (7.10) shows that species 1 wins the competition because, at its carrying capacity, it depletes the resources more than species 2.

In Chap.​ 1, Fig. 1.9, we have already shown Gause data relative to separate culture of Paramecium aurelia and Glaucoma scintillans. Gause also grew the two together, obtaining the results shown in Fig. 7.2 with the eventual exclusion of Paramecium aurelia. Instead, Paramecium aurelia excluded Paramecium caudatum, when grown in co-culture, as shown in Fig. 7.3. These experiments, performed few years after Volterra's theoretical results, lent support to the exclusion principle and its further elaborations.

Fig. 7.2Competition between Paramecium aurelia and Glaucoma scintillans, ending with exclusion of Paramecium aurelia. The upper graph shows data of abundances of the two species as a function of time. In the graph below the same data are shown in the phase-plane (N 1,N 2). From [6]

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