ABSTRACTThis paper investigates stability conditions of an empirical predator-prey system using a model that includes a single delay term,τ, in description of the predator dynamics. We derive theoretical conditions onτ, in terms of other model parameters, and determine how changes in these conditions define different stability regimes of the system. We derive optimal model parameters by fitting model to empirical data, using unconstrained optimization. The optimization results are combined with those from the theoretical analysis, to make inference about the empirical system stability.Our results show that Hopf bifurcation occurs in the predatory-prey system whenτexceeds a theoretically derived valueτ* > 0. This value represents the critical time for prey availability in advance of the optimal predator growth period. Set into an ecological context, our findings provide mathematical evidence for validity of the match-mismatch hypothesis, for this particular species.