Note on the mathematical theory of population dynamics and a recent fallacy.

Abstract

Principles are outlined for the construction of a consistent theoretical treatment of the various problems of population dynamics. Three types of interspecific competition are distinguished, "imperfect", "perfect", and "hyperperfect", depending on whether the product aß in the Lotka-Volterra equations is less than, equal to, or greater than unity. It is shown that perfect competition, which is of especial relevance to the problems of natural selection and evolution, leads to a much simpler set of inequalities and limits than those commonly quoted as resulting from the Lotka-Volterra equations. It is shown that in perfect competition the surviving species is not necessarily superior in "reproductive efficiency". "Metabolic efficiency" is equally important. This restatement of the problems of population dynamics is used to demonstrate the falsity of the recent claim of Andrewartha and Birch (1953) that a fundamental contradiction exists in the Lotka-Volterra equations for interspecific competition.