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The physical dimensions and biological meaning of the coefficients in the Volterra competition equations and their consequences for the possibility of coexistence

Identifieur interne : 002608 ( Main/Exploration ); précédent : 002607; suivant : 002609

The physical dimensions and biological meaning of the coefficients in the Volterra competition equations and their consequences for the possibility of coexistence

Auteurs : I. Walker [Brésil]

Source :

RBID : ISTEX:BC3A17C2D58AF8DA1D0B21ACBEA9E433A382A83A

English descriptors

Abstract

Abstract: Exact definitions in physical and biological terms of the coefficients in Volterra's (1926, 1931) original competition equations are indispensable for the understanding of the system. In agreement with Volterra's own, but not quite sufficient specifications, it is tried in this paper to give more precise definitions of the parameters used by Volterra. This leads to some consequences; i.a. that there does not exist a “principle of competitive exclusion”. In order to allow for competitive exclusion — or for stabilization — the Volterra equations need additional biophysical specifications and mathematical modifications. Some such modifications are proposed, for instance for aggressive interference as a function of population numbers.

Url:
DOI: 10.1007/BF02045063


Affiliations:


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Le document en format XML

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<term>Biological interpretation</term>
<term>Biological terms</term>
<term>Biophysical specifications</term>
<term>Certain time</term>
<term>Coefficient</term>
<term>Competition coefficients</term>
<term>Competitive exclusion</term>
<term>Competitive replacement</term>
<term>Complementary resources</term>
<term>Compound term</term>
<term>Constant coefficients</term>
<term>Consumer species</term>
<term>Death rate</term>
<term>Different consumer species</term>
<term>Different resources</term>
<term>Direct effects</term>
<term>Ecology</term>
<term>Feedback term</term>
<term>Gause</term>
<term>Geographical ecology</term>
<term>Graphical representation</term>
<term>Growth process</term>
<term>Growth rate</term>
<term>Growth rates</term>
<term>Ideal territorialism</term>
<term>Individual maintenance</term>
<term>Initial conditions</term>
<term>Integral resources</term>
<term>Intrinsic growth rate</term>
<term>Inverse values</term>
<term>Lower equation</term>
<term>Maintenance level</term>
<term>Maintenance quantities</term>
<term>Maintenance quantity</term>
<term>Mathematical modifications</term>
<term>Maximum number</term>
<term>Mere maintenance</term>
<term>Original competition equations</term>
<term>Original equations</term>
<term>Original volterra competition system</term>
<term>Original volterra equations</term>
<term>Other species</term>
<term>Other words</term>
<term>Parallel lines</term>
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<term>Physical dimension</term>
<term>Population ecology</term>
<term>Population equilibrium</term>
<term>Population growth</term>
<term>Population number</term>
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<term>Positive quadrant</term>
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<term>Potential growth</term>
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<term>Random fluctuations</term>
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<term>Resource</term>
<term>Resource depletion</term>
<term>Resource flow</term>
<term>Resource flux</term>
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<term>Resource quantity</term>
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<term>Resource units</term>
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<term>Same resource</term>
<term>Same value</term>
<term>Single line</term>
<term>Single point</term>
<term>Single value</term>
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<term>Social interference</term>
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<term>Total quantity</term>
<term>Total resource</term>
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<term>Traditional form</term>
<term>Traditional literature</term>
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<div type="abstract" xml:lang="en">Abstract: Exact definitions in physical and biological terms of the coefficients in Volterra's (1926, 1931) original competition equations are indispensable for the understanding of the system. In agreement with Volterra's own, but not quite sufficient specifications, it is tried in this paper to give more precise definitions of the parameters used by Volterra. This leads to some consequences; i.a. that there does not exist a “principle of competitive exclusion”. In order to allow for competitive exclusion — or for stabilization — the Volterra equations need additional biophysical specifications and mathematical modifications. Some such modifications are proposed, for instance for aggressive interference as a function of population numbers.</div>
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