期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1974
卷号：71
期号：8
页码：3041-3044
DOI：10.1073/pnas.71.8.3041
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：The conservative model of Volterra for more-than-two predator-prey species is shown to be generated as extremals that minimize a definable Lagrange-Hamilton integral involving half the species and their rates of change. This least-action formulation differs from that derived two generations ago by Volterra, since his involves twice the number of phase variables and it employs as variables the cumulative integrals of the numbers of each species that have ever lived. The present result extends the variational, teleological formulations found a decade ago by the author to the more-than-two species case. The present result is anything but surprising, in view of the works by Kerner, Montroll, and others which apply Gibbs' statistical mechanics to the all-but-canonical equations of the standard Volterra model. By a globally linear transformation of coordinates, the Volterra equations are here converted into a completely canonical system isomorphic with the classical mechanics models of Newton, Lagrange, Hamilton, Jacobi, Boltzmann, Gibbs, Poincare, and G. D. Birkhoff. The conservative nature of the Lotka-Volterra model, whatever its realism, is a crucially necessary condition for the applicability of the variational formalisms, microscopically and macroscopically.
