  We analyze general two-species stochastic models, of the kind generally used
for the study of population dynamics. We show that the conditions for the
stochastic (microscopic) model to display approximate sustained oscillatory
behavior are governed by the parameters of the corresponding deterministic
(macroscopic) model. We provide a quantitative criterion for the quality of the
stochastic oscillation, using a dimensionless parameter that depends only on
the deterministic model. When this parameter is small, the oscillations are
clear, and the frequencies of the stochastic and deterministic oscillations are
close, for all stochastic models compatible with the same deterministic one. On
the other hand, when it is large, the oscillations cannot be distinguished from
a noise.
