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Biological entities are inherently dynamic. As such, various ecologicaldisciplines use mathematical models to describe temporal evolution. Typically,growth curves are modelled as sigmoids, with the evolution modelled by ordinarydifferential equations. Among the various sigmoid models, the logistic andGompertz equations are well established and widely used in fitting growth datain the fields of biology and ecology. This paper suggests a statisticalinterpretation of the logistic equation within the general framework. Thisinterpretation is based on modelling the population environment relationship,the mathematical theory of which we discuss in detail. By applying this theory,we obtain stochastic evolutionary equations, for which the logistic equation isa limiting case. The prospect of modifying logistic population growth isdiscussed. We support our statistical interpretation of population growthdynamics with test numerical simulations. We show that the Gompertz equationand other related models can be treated in a similar way.

A statistical interpretation of biologically inspired growth models