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 : 002609The 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 :
- Acta Biotheoretica [ 0001-5342 ] ; 1983-06-01.
English descriptors
- Teeft :
- Acta biotheoretica, Aggressive interference, Antagonistic behaviour, Bare maintenance, Biological interpretation, Biological terms, Biophysical specifications, Certain time, Coefficient, Competition coefficients, Competitive exclusion, Competitive replacement, Complementary resources, Compound term, Constant coefficients, Consumer species, Death rate, Different consumer species, Different resources, Direct effects, Ecology, Feedback term, Gause, Geographical ecology, Graphical representation, Growth process, Growth rate, Growth rates, Ideal territorialism, Individual maintenance, Initial conditions, Integral resources, Intrinsic growth rate, Inverse values, Lower equation, Maintenance level, Maintenance quantities, Maintenance quantity, Mathematical modifications, Maximum number, Mere maintenance, Original competition equations, Original equations, Original volterra competition system, Original volterra equations, Other species, Other words, Parallel lines, Particular instant, Physical dimension, Population ecology, Population equilibrium, Population growth, Population number, Population numbers, Population regulation, Positive constants, Positive quadrant, Possible cases, Possible population equilibria, Potential growth, Prey organisms, Random fluctuations, Randomized system, Resource, Resource depletion, Resource flow, Resource flux, Resource increment, Resource quantity, Resource unit, Resource units, Resource utilization, Same resource, Same value, Single line, Single point, Single value, Slower growth, Social interference, Straight line, Such modifications, Sufficient specifications, Theoretical ecology, Time structure, Total quantity, Total resource, Toxic effects, Traditional form, Traditional literature, Volterra, Volterra equations, Volterra equations need, Weaker competitor, Whole term.
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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<front><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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