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Abstract:
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The classic, widely used logistic growth model is based on the mechanistic model N'=(r-sN)N, where N denotes population size, N' its derivative, and r,s>0 birth and death rate coefficients. The positive root, r/s, is called the carrying capacity. Letting F(t) denote the integral of N(t), we develop the new mechanistic model N'=(r-sF)N. The death rate in this model is a function of F, the cumulative past population size, which results in eventual population collapse. The analytical solution of the model may be expressed with parameters having natural physical interpretation. We have fitted the model successfully to numerous data sets on the local abundance of mustard, pecan, cotton, corn leaf and greenbug aphids. We show that a 'model-based' statistical analysis, based on the estimated kinetic rates r and s, has advantages over a standard 'model-free' analysis.
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