  We consider a stochastic version of the basic predator-prey differential
equation model. The model, which contains a parameter \omega which represents
the number of individuals for one unit of prey -- If x denotes the quantity of
prey in the differential equation model x = 1 means that there are \omega
individuals in the discontinuous one -- is derived from the classical birth and
death process. It is shown by the mean of simulations and explained by a
mathematical analysis based on results in singular perturbation theory (the so
called theory of Canards) that qualitative properties of the model like
persistence or extinction are dramatically sensitive to \omega. For instance,
in our example, if \omega = 107 we have extinction and if \omega = 108 we have
persistence. This means that we must be very cautious when we use continuous
variables in place of jump processes in dynamic population modeling even when
we use stochastic differential equations in place of deterministic ones.
