  The critical properties of a simple prey-predator model are revisited. For
some values of the control parameters, the model exhibits a line of directed
percolation like transitions to a single absorbing state. For other values of
the control parameters one finds a second line of continuous transitions toward
infinite number of absorbing states, and the corresponding steady-state
exponents are mean-field like. The critical behavior of the special point T
(bicritical point), where the two transition lines meet, belongs to a different
universality class. The use of dynamical Monte-Carlo method shows that a
particular strategy for preparing the initial state should be devised to
correctly describe the physics of the system near the second transition line.
Relationships with a forest fire model with immunization are also discussed.
