31
 function also can be expected to oscillate (Rykiel and

 Kuenzel, 1973). Some oscillating models demonstrate

 persistence; others are unstable (Holling, 1973). Time

 delays longer than the natural periodicity of the system

 (in the equation dx/dt = rx, the natural period, or time

 constant, is 1/r) almost inevitably cause instability

 (Smith, 1974). On the other hand, simple changes in the

 governing equations, representing adjustments or

 modifications in the basic structure of the system, can

 stabilize the system (Smith, 1974).

 On the basis of mathematical analysis, Oster and

Takahashi (1974) predicted that, when intrinsic oscillating

factors (periodic forcing functions) are imposed on systems

with intrinsic oscillating factors (time delays), beat

frequencies may result. If, however, the frequency of the

intrinsic oscillation is close to the characteristic

frequency of the external oscillators than a phenomenon

known as entrainmentt" may occur, and the system will

respond to the external freauency only. This allows

biological oscillators to "latch on" to the environment

(Pavlidis, 1973). In the case of the Wood Stork, if

rainfall periodicity is operating on a 5 yr cycle and there

is a 4 to 5 yr delay between fledging and breeding, then a

synchronization of the intrinsic cycle and the extrinsic

cycle may occur.

 The present existence of the birds is evidence that

their population was maintained under natural conditions.