Some strange properties of the logistic equation defined withr andK: Inherent defects or artifacts?
In some situations the logistic equation in the usual expression, dN/dt=r(1−N/K)N, exhibits properties that are biologically unrealistic. For example, whenr≦0 the population can no longer show any normal, negative response in per-capita growth rate to increasing density. Also, when the equation is employed in the Volterra's competition model, a familiar but incredible conclusion is derived which says that the outcome of competition is entirely independent of the reproductive potentialr of each species. It is shown that all such strange properties are mere artifacts arising peculiarly in thisr-K model from its misleading implicit supposition thatK could be independent ofr, and they can be readily removed by alternative use of a plainer, classical form of the model, dN/dt=(r−hN)N.
Key WordsLogistic equation carrying capacity competition theory K-selection
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