Some Remarks on Animal Population Dynamics

Abstract

T HE PRESENT PAPER is not survey of the vast field of investigation into the dynamics of population change but an attempt to discuss few specific problems in the hope of suggesting some new lines of investigations to those better qualified than the author to carry them out. Any investigation into population dynamics must necessarily involve mathematics in some way or other, and it is convenient and perhaps illuminating to begin by classifying the various ways in which mathematics is applied to biological problems of this kind. Moreover, such classification will be found to hold equally well for the applications of mathematics to economics. Without begging any philosophical questions, we may distinguish between a and a posteriori methods. In priori applications of mathematics to biology, an attempt is made to describe the main features of biological system in terms of mathematical model involving set of equations. From this model, we then try to make deductions which can be verified by observation or experiment. Such deductions need not be numerical (if they are, they are usually very difficult of verification) but they may often be qualitative-e.g., ultimate extinction of population, existence of oscillations, and so on. The difficulty and dangers of taking into account all the factors in situation without making the mathematical model very complicated are obvious, yet the more complicated the model, the more difficult is it of verification. Such models may be further classified according to whether they do or do not involve probability, and are then described as probabilistic and deterministic respectively. Examples of the latter are the equations of Volterra and others describing predator-prey relationships'

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