Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-24T17:32:58.242Z Has data issue: false hasContentIssue false
  • English
  • Français

Notes on the Volterra Equations

Published online by Cambridge University Press:  31 May 2012

W. R. Thompson
W. R. Thompson
Affiliation:
Ottawa, Ontario
Get access Rights & Permissions [Opens in a new window]

Extract

According to one of the popular ecological theories, populations are self-governing systems, which maintain themselves in existence by utilizing “density-dependent factors”, whose effect becomes more intense as the population increases and less intense as it decreases. This theory is connected with a mathematical model developed by V. A. Bailey and A.J. Nicholson, 1935, to represent the results of the interaction of predator and prey populations. According to the theory, as expressed verbally, a disturbance of the conditions of stability – the “steady state” – produces oscillations which tend to re-establish the stable conctition. In fact, however, when numbers are inserted in the equations, the population values, at the end of one or more cycles – which increase in amplitude if there are more than one – fall below unity, which, on a common sense view may be considered to mean the extermination of the prey, followed by that of its predator or parasite.

Type
Articles
Information
The Canadian Entomologist , Volume 92 , Issue 8 , August 1960 , pp. 582 - 594
Copyright
Copyright © Entomological Society of Canada 1960

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Nicholson, A. J. 1933. The balance of animal populations. Journ. Anim. Ecol. 2: 132–78.CrossRefGoogle Scholar
Nicholson, A. J., and Bailey, V. A.. 1935. Proc. Zool. Soc. London, 1935, pp. 551–98.CrossRefGoogle Scholar
Thompson, W. R. 1922. Théorie de l'action des parasites entomophages. Les formules mathématiques du parasitisme cyclique. C.R. Acad. Sci., Paris 174: 1201–4.Google Scholar
Thompson, W. R. 1929. On the part played by parasites in the control of insects living in protected situations. Bull. Ent. Research 20: 457–462.CrossRefGoogle Scholar
Thompson, W. R. 1947. La croissance et la reproduction des êtres vivants. Laval Théologique et Philosophique III: 195–221.CrossRefGoogle Scholar
Varley, G. C. 1958. Meaning of Density - dependence and related terms in population dynamics. Nature 181: 1778–1781.CrossRefGoogle Scholar
Volterra, V. 1926. Variazioni e fluttuazioni del numero d'individui in specie animali conviventi. Mem. Acad. Lincei. (6) 2: 31–113.Google Scholar
Volterra, V. 1927. Variazioni e fluttuazioni del numero d'individui in specie animali conviventi. R. Comitato Talassografico Italiano Memoria 131.Google Scholar
Volterra, V., et D'ancona, Umberto. 1935. Les associations biologiques au point de vue mathématique. Actualités Scientifiques et Industrielles. Paris. No. 243.Google Scholar