Predator Switching

In the North Pacific Ocean, populations of seals, sea lions, and sea otters have sequentially collapsed over the last several decades (Springer et al. 2003). Scientists initially thought that physical changes in the ocean or competition with fisheries were to blame, but it now appears that killer whales are responsible. Killer whales usually consume great whales (such as sperm whales and bowhead whales), but great whale numbers were significantly decreased after World War II by human whaling. With their primary food source reduced, killer whales "switched" to consuming seals. When their consumption reduced the availability of these prey, killer whales then switched to sea lions and finally to sea otters. The result is the sequential collapse in pinniped and other populations observed by scientists (Springer et al. 2003).

Formally, we say that a predator "switches" if its relative attack rate on one of two prey species increases faster than the relative abundance of that species (Murdoch and Oaten 1975). The multi-prey functional response defined in section 11.3 provides a null model against which switching responses can be measured; if N/ is the number consumed of prey type i, then this model implies that N{/N2 = («1/^2) N1/N2, so that the relative frequency of prey in the diet faithfully reflects (up to a constant) relative prey abundances.

Ecologists have traditionally believed that predator switching stabilizes both predator and prey populations and permits the coexistence ofspecies that otherwise might exhibit competitive exclusion (Roughgarden and Feldman 1975). In the prologue, we discuss how lynx switch to consuming red squirrels when snowshoe hare numbers are low, a behavior that may allow snowshoe hare populations to recover more easily (at which point lynx switch back to consuming hares) and may also sustain the lynx during troughs of low hare numbers. However, as the collapsing pinniped populations in the killer whale example show, predator switching may not always lead to system stability.

Van Baalen et al. (2001) created a top-down model that illustrates how predator switching can have both stabilizing and destabilizing effects. They modeled a special case ofpredator switching in which the preferred prey type occurred in one patch and an alternative prey type occurred in a second patch. They further assumed that the alternative prey type existed at a fixed density, and that predators knew the optimal preferred prey density at which to switch between patches and could do so instantaneously and without cost. They found that the predator and preferred prey did not equilibrate to a fixed point, but instead formed a limit cycle. Predator switching did not produce a stable equilibrium because switching predators alternated between the preferred and alternative prey patches as the density of the preferred prey changed. This behavior destabilized population dynamics because switching released the preferred prey when their numbers were low, and this reproductive response permitted the prey to increase. The predator then switched back to the preferred prey, whose population was still growing, and continued to grow because there was a lag in the growth response of the predator population as a whole. The instability emerges from the interplay of individual behavioral responses and the time-lagged responses that are always inherent in the responses of populations to changes in the environment.

Van Baalen et al. (i001) also examined other cases in which predators were "nonoptimal" foragers. In this context, "nonoptimal" means only that the foraging behavior deviated from the expectations of the idealized model. For instance, predators may switch between patches gradually. Van Baalen and colleagues modeled this behavior by altering the proportion oftime the predators spent foraging in the alternative prey patch. This gave the predators a sigmoid functional response, and a stable population equilibrium arose. When the switching threshold was replaced with a sigmoidal curve, predator switching acted to stabilize the populations. Thus, time dependence in prey switching made the system more stable. One possible reason for such time dependence is that the predator does not adjust to changes in prey numbers instantaneously, but instead has a learning curve that takes time. If gradual switching reflects the need for learning, these results suggest that slow learning may lead to more stable dynamics. However, iflearning is so slow that predators in effect move randomly between patches, the system again becomes unstable, and predators and prey go extinct. The reason is that predators that switch between patches randomly do not necessarily leave the preferred prey patch when prey numbers are low, and they can drive the preferred prey to extinction.

This result illustrates the importance of considering complementary models of a given problem. Kimbrell and Holt (i004, i005) have explored an individual-based computer model based on the mathematical model of van Baalen et al. (i001). Kimbrell and Holt's model took a "bottom-up" approach. Predators moved on a grid consisting of two patches and chose which of the two patches to exploit. When all predators foraged optimally, or when predators switched gradually between patches, Kimbrell and Holt's model agreed with van Baalen et al.'s results. However, when predators randomly switched between patches, Kimbrell and Holt found that populations of predator and prey could sometimes persist. This difference in results arises from the spatially explicit and stochastic nature of the bottom-up approach. The van Baalen et al. model assumed mean-field dynamics and thus assumed that all predators in the preferred prey patch consumed prey with a fixed probability. The Kimbrell and Holt model, however, explicitly modeled space in each patch and assumed that predators moved stochastically within each patch. Thus, at low predator numbers, the stochastic movement of predators left small

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