Critical transitions are qualitative changes of state that occur when a stochastic dynamical system is forced through a critical point. Many critical transitions are preceded by characteristic fluctuations that may serve as model-independent early warning signals, implying that these events may be predictable in applications ranging from physics to biology. In nonbiological systems, the strength of such early warning signals has been shown partly to be determined by the speed at which the transition occurs. It is currently unknown whether biological systems, which are inherently high dimensional and typically display low signal-to-noise ratios, also exhibit this property, which would have important implications for how ecosystems are managed, particularly where the forces exerted on a system are anthropogenic. We examine whether the rate of forcing can alter the strength of early warning signals in (1) a model exhibiting a fold bifurcation where a state shift is driven by the harvesting of individuals, and (2) a model exhibiting a transcritical bifurcation where a state shift is driven by increased grazing pressure. These models predict that the rate of forcing can alter the detectability of early warning signals regardless of the underlying bifurcation the system exhibits, but that this result may be more pronounced in fold bifurcations. These findings have important implications for the management of biological populations, particularly harvested systems such as fisheries, and suggest that knowing the class of bifurcations a system will manifest may help discriminate between true-positive and false-positive signals.