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response of the Wood Stork population to changes in water

patterns and fish production,



 Modeling Theory of Oscillating Systems

 For many animal populations a change in population

number such as that exhibited by Wood Storks within the

past 15 yrs is part of a long-term cycle. There are many

known animal cycles in nature, and in many cases a cycle in

one species can be related to that in another. Predator

population cycles can be dependent on prey cycles. Prey

cycles can be dependent on predator cycles or on the cycles

of alternate prey species (Bulmer, 1975). Although it

seems reasonable to think that the ultimate cause of a

series of linked species cycles would be an oscillating

climatic factor, in a number of well-known cases,

particularly the 10 (9.6) yr animal cycles of the Canadian

northwest, climatic influences, though sought, have not

been demonstrated (Bulmer, 1974).

 Systems showing population cycles generally have been

studied as systems with intrinsic oscillating capabilities.

Any simple two compartment population model may oscillate.

The classic two compartment prey-predator model of Lotka

(1925) and Volterra (1926) is a well known example of model

structure that will oscillate without oscillating input.

 A model with a time delay such as that imposed by

delayed breeding is almost certain to oscillate (Smith,

1974), and a model subjected to an oscillating forcing