Lotka-Volterra Population Models

In almost every field of science, and nowhere than in biology, a tension has existed constantly between the experimentalists and the theorists; the tension is particularly strong in biology because there the theorists have not produced the kinds of advances that have come from the theoretical physicists and chemists. Among the biological theorists, the sub-class of mathematical modellers has often suffered the most from the onslaughts of their more practical brethren. To some extent, this tension has been the result of misunderstandings on the part of both groups. The experimentalists have often been almost innocent of the mathematical techniques needed for mOdel-building. The modellers, often recruited from either physics or mathematics, have plunged directly into some of the most difficult biolog­ ical problems with an impressive array of mathematical skills and an equally impres­ sive innocence of biological principles. The reading required for this paper has led me to believe that the ex-mathematicians in particular display an almost cavalier disregard for the biological literature. When a faulty citation in one paper, involving an inversion in the order of authors, is repeated in a series of papers by at least three other authors, I am led to wonder whether the later authors bothered to look up the original paper, much less read it. A result of this lack of care has been the rediscovery of the wheel at regular intervals. Certainly some of the difficulties between the two groups stem from basic misun­ derstandings, on both sides, of the nature and function of mathematical models. Models are too often considered simply as predictors, and any inability to predict accurately is accepted as prima facie evidence of the uselessness of the technique. Actually, only those engineering models designed to fit a particular set of circum­ stances are even moderately successful as predictors. The general models of theoretical biology are used to deduce the form of possible solutions, rather than to predict future states of the system being modelled.