Evolution.

Society for Experimental Biology

Date:: 1953

Licence: Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

Credit: Evolution. Source: Wellcome Collection.

32/484 (page 8)

$8 THE ORIGIN OF LIFE circulation (Brunt, 1939) and to adaptive changes in this structure in relation to the synoptic conditions. The analogy between these different systems rests ultimately on the similarity of mathematical formulation adequate to describe their dynamic properties. Mathematical formulations of biological and other complex equilibria are usually much over-simplified, but the Verhulst-Pearl logistic equation (I) at describes one such steady-state equilibrium of a single unit involving a divergent and a convergent process. Volterra (1931) has extended the study of equations of this type to cover some of the simpler types of inter¬ specific interaction in ecology, and his equations for competitive interaction are the ones which are important in this context. If M and N are two units which compete in a manner defined by the equations ^ = аМ-ЬМ{сМ+ dN), ^=a'N-b'N{cM+dN), (2) some interesting results emerge. There is no steady-state solution of equations (2) with non-zero values of either N or M unless a a' b b' This special case gives an unstable equilibrium liable to be upset by any change in the relative 'success' of M and N. In other words, if conditions change so that a a b^b M increases to an amount ajbc replacing completely unit N which dis¬ appears from the system. The result holds good for any initial values of M and N not zero, and under suitable conditions therefore ^ single unit (individual or molecule) of M appearing in a system previously con¬ taining only N produces a change in the macroscopic steady state of the system. This mathematical formulation of the concept of the 'survival of the fittest' of two dynamically stable units when they compete for certain features of their common environment has much wider application in nature than the ecological example which it was originally devised to explain. Spiegelman (1948) has proposed a treatment of the competitive$

Evolution.

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