[bfmaxd Fde Jb

The optimal level of vigilance behaves (mostly) as one would expect. Vigilance increases with the prey's encounter rate with predators, its survivor's fitness (yet another form of the asset protection principle; Clark 1994), and predator lethality. Vigilance declines with net feeding rate and with the marginal value of energy. Optimal vigilance exhibits a hump-shaped pattern when plotted against the value of vigilance. If vigilance reduces predation risk effectively, the forager needs very little vigilance. If vigilance has little effect on predation risk, then there is no point in being vigilant.

In this formulation, vigilance reduces feeding rate according to f (u) = (1 — u)fmax, specifying the cost of vigilance in units of reduced feeding rate. Herefmax gives the forager's feeding rate in the absence of vigilance, so that fmax = f (0). The rate at which feeding rates decline with vigilance sets the exchange rate between food and vigilance (cf. Gilliam and Fraser's [1987] tenacity index).

Vigilance and Trophic Cascades

Vigilance, like the cost of predation, sets off a behavioral cascade that influences both the forager's prey and its predator (Kotler and Holt 1989). In a typical trophic cascade, a predator inflicts mortality on a forager species, and the reduced forager population inflicts less mortality on its prey. Hence, the presence of a third trophic level (the predator) raises the standing crop of the first trophic level (the forager's prey; Hairston et al. 1960). At the extreme, trophic cascades can lead to the paradox of enrichment (Rosenzweig 1971). Imagine a system with three trophic levels characterized by exploitative competition only. Increasing the productivity of the plants (via precipitation, nitrogen, temperature, etc.) will paradoxically cause no increase in the number of herbivores, because the predators increase in numbers so as to just

Figure 13.2. The effect of plant productivity on the abundance of plants, herbivores, and predators. The model assumes that herbivores and predators compete only through exploitative competition. Below a threshold productivity level, the abundance of plants cannot support any herbivores. As productivity increases, so does the plant abundance. Above a threshold level of productivity, the system can support herbivores. In this region of productivity, the abundance of plants remains constant with productivity, while the abundance of herbivores increases with productivity. Above a second threshold in productivity, enlarged herbivore populations can now support a predator population. Above this productivity threshold, the abundances of both plants and predators increase with productivity, while the abundance of herbivores remains constant with productivity (see Oksanen and Oksanen 1999).

Figure 13.2. The effect of plant productivity on the abundance of plants, herbivores, and predators. The model assumes that herbivores and predators compete only through exploitative competition. Below a threshold productivity level, the abundance of plants cannot support any herbivores. As productivity increases, so does the plant abundance. Above a threshold level of productivity, the system can support herbivores. In this region of productivity, the abundance of plants remains constant with productivity, while the abundance of herbivores increases with productivity. Above a second threshold in productivity, enlarged herbivore populations can now support a predator population. Above this productivity threshold, the abundances of both plants and predators increase with productivity, while the abundance of herbivores remains constant with productivity (see Oksanen and Oksanen 1999).

match the increased productivity of the herbivores. The extra productivity goes straight up the food chain, through the prey and to the predators. The increased productivity of the plants causes an increase in plant biomass, no change in herbivore abundance, and an increase in the number of predators (fig. 13.2; see Oksanen and Oksanen 1999).

A similar phenomenon happens when predators frighten prey into increased vigilance. The predator's presence reduces the herbivore's feeding rate on plants. With fear in the system, we need to distinguish between mortality-driven (N-driven) and fear-driven (|-driven) population interactions. Obviously these are endpoints of a continuum, but the distinction is useful. Holt (1977) anticipates this distinction in his "r/a" measure of apparent competition ability. The term r is the prey's intrinsic growth rate; it measures how fast the prey population can grow in the face of predation (N-driven component). The term a is the predator's rate of encountering the prey; it measures the predator's ability to catch the prey (|-driven component). A prey species with a higher r/a has an advantage over other prey species in terms of persisting in the face of a common predator.

In an N-driven system, predators have little effect on the behavior ofprey. The predator influences the dynamics and abundance ofits prey through direct mortality. Classic predator-prey models (Rosenzweig and MacArthur 1963) fall into this category. Current interpretations of the lynx-hare cycle and weasel-vole cycle fall into the category of N-driven predator-prey systems. Despite some behavioral responses, the populations of hares (Krebs et al. 1995) and voles (Hanski et al. 2001) rise and fall with the tide of lynx and weasels, respectively, as these highly effective predators inflict high and often unsustainable mortality on their prey.

In a | -driven system, the predators do not appear to control their prey's population through mortality. A casual examination may even suggest that the predators have little or no effect on prey mortality. However, the predators may strongly influence prey behavior, population dynamics, and population sizes by inducing increased vigilance in the prey. In both N- and |-driven predator-prey interactions, the predator reduces the prey's per capita population growth. In N-driven systems, this occurs via direct mortality (the prey feed the predator). In | -driven systems, this occurs more subtly via reduced prey fecundity (forgone opportunities to convert resources into offspring) or indirect increases in prey mortality from other sources (increased likelihood of starvation, exposure, or death by other predators and pathogens).

Zebras and lions on the Serengeti and the Indian crested porcupine and its suite of Negev "predators" probably represent |-driven predator-prey interactions. Fox squirrels (Sciurus niger) and gray squirrels (S. carolinensis) may represent a | -driven predator-prey interaction in which fear underlies the mechanism of coexistence. In the midwestern United States, fox squirrels occupy wood margins and gray squirrels occupy the interiors of many of the same woodlots and forests (Brown and Yeager 1945; Nixon et al. 1968; Brown and Batzli 1984). It seems that gray squirrels are better at interference and exploitative competition, but are more sensitive to predators, than fox squirrels (Stapanian and Smith 1984; Lanham 1999; Steele and Wiegl 1992). This trade-off forms a mechanism of coexistence in which the fox squirrels occupy the riskier habitats and gray squirrels the safer habitats.

Two observations suggest that the coexistence of these squirrels is a Prather than an N-driven process. First, it is unlikely that the squirrels actually provide the prey needed to support the predators that promote the squirrel species' coexistence. For instance, in Illinois, abundant populations of voles, white-footed mice, chipmunks, and cottontail rabbits support the hawks, owls, foxes, and coyotes that generate the riskier and safer habitats. Hence, the level of predation risk results from apparent competition (Holt 1977; Holt and Lawton 1994) in which voles and rabbits indirectly interact with the squirrels via their common predator. Second, this diverse and sometimes abundant population ofpredators kills very few squirrels. Red-tailed hawks, for example, have difficulty catching fox squirrels and gray squirrels (Temple 1987), and the predators' diets contain relatively few squirrels. In a bizarre twist of community ecology, predators that the squirrels do not support and predators that mostly frighten rather than kill the squirrels dictate many aspects of the squirrels' foraging behavior (Brown et al. 1992; Bowers et al. 1993; Brown and Morgan 1995) and promote their coexistence.

Vigilance and Predator Facilitation

Vigilance can produce predator facilitation and promote the coexistence of predators (Sih et al. 1998). Imagine a forager facing two predators in which u1 provides effective vigilance against predator 1 and u2 provides effective vigilance against predator 2. We can extend the vigilance model to recognize two sources of predation risk:

The forager must now choose its optimal level of vigilance in response to its encounter rates, mi, with each ofthe predators. The optimal level ofvigilance for each predator still satisfies equation (13.4) for u*. But now the presence of the first predator not only influences U1*, it also influences U2*. Increasing the abundance of predator 1 causes an increase in m1 that increases u1. This increase in U1 lowers the average feeding rate of the forager, which decreases its state, F, and increases its marginal value of energy, dF/d e (if there are diminishing returns to survivor's fitness from net energy gain). Either fitness effect will reduce u2 and make the forager more vulnerable to predator 2. As in the case ofowls, snakes, and gerbils, the presence ofpredator 1 can make it easier for predator 2 to catch the prey. Predator-specific vigilance strategies promote coexistence among predator species if paying attention to one sort of predator causes the forager to be less attentive to another predator species (Sih 1998; Sih et al. 1998).

13.6 Fear and Population Dynamics

Foragers can pay the cost of predation either by directly feeding their predators (in N-driven systems) or by changing their behavior and thereby reducing their fecundity (in |l-driven systems). Here we examine how one can incorporate fear into predator-prey dynamics and how |l-driven systems determine the shape of predator and prey isoclines (Holt 1983; Abrams 1982, 1984;Holt et al. 1994; Holt and Lawton 1994).

We start with a typical model with three trophic levels:

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