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Notes on the Volterra Equations

Published online by Cambridge University Press:  31 May 2012

W. R. Thompson
W. R. Thompson
Affiliation:
Ottawa, Ontario
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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

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References

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