Abstract
An attempt is made to apply an averaging procedure to a non-linear dynamic model of n species competing for common resources in a single trophic level. We have proved that a model of such a community enables accurate averages to be calculated, at least in the linear approximation near a positive equilibrium state. The weight coefficients of the averaging procedure can be determined as the components of the Frobenius eigenvector for a community matrix; uniqueness of the solution to the problem of averaging is provided by the condition that an average biomass in the equilibrium state concurs with the total biomass of the populations averaged. In the case of two competing species with logistic growth laws, both proximate formulae and approximate ones are obtained for the averaging procedure, which permit description of the average quantity dynamics by a non-linear (logistic) equation. In conclusion some considerations are presented concerning the problems of averaging and aggregation in models with several trophic levels.
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