Figure 13.1. The giving-up densities of porcupines (Hystrix indica) in experimental food patches set in the Negev Desert, Israel. A high giving-up density suggests a high perceived cost of predation. Food patches began with 50 chickpeas mixed into 8 liters of sifted sand. The porcupine's perceived cost of predation increases with moonlight, and decreases with the amount of perennial shrub cover. The authors observed higher giving-up densities (shown as the mean numberofchickpeas left behind in a food patch) on moonlit nights (bright) than on nights with less than a quarter moon (dark). Giving-up densities were highest in a habitat without any perennial shrub cover (BARREN), lowest in a habitatwith ca. 12% shrub cover (VEG), and intermediate in the habitat immediately adjacent to the porcupine's burrow (< 5% shrub cover, WADI). (After Brown and Alkon 1990.)

a very high predation cost of foraging? Two factors probably contribute to this pattern: harassment from predators and the need for the porcupine to respond to this harassment. On moonlit nights or in open habitats, predators may easily spot porcupines. Furthermore, it may pay predators to deviate from their path and challenge encountered porcupines—an ill or otherwise incapacitated porcupine may be vulnerable. To deter the unwanted attentions of a predator, a healthy porcupine may be obliged to raise it quills and take up a defensive posture. In this way, predators represent more of a harassment cost than a mortality cost to the porcupines (fig. 13.1).

In Aberderes National Park, Kenya, the black rhinoceroses suffer harassment from spotted hyenas, and many exhibit missing tails from such encounters. However, we know of only one instance in which hyenas killed a black rhinoceros. In this case (reported by a ranger in 1998), a pack ofhy-enas set upon the rhino when it became mired in wet clay. Before killing the rhino, the hyenas dehorned it. These hyenas had probably never killed a rhino before. However, their experience harassing rhinos, and the rhinos' responses to this harassment, suggest that the hyenas had ample experience with rhinos and their defensive tactics. In response to hyena harassment, rhinos perceive a lower foraging cost ofpredation in the more open habitats of the forests and glades ofAberderes. In these habitats, they have more room to maneuver. Berger and Cunningham (1994) reported that dehorning of black rhinoceroses in Namibia to discourage poaching led to attacks by hyenas on mothers and their young. The speed ofthe hyenas' response suggests that the hyenas and rhinos had considerable behavioral experience with each other's tactics. A tension exists between rhinos and large carnivores even though the carnivores almost never kill rhinos. It is unlikely that any organism, regardless of taxon, is free from a foraging cost of predation.

Even top predators experience a foraging cost of predation. They probably have two sources of predation-like costs. First, top carnivores often inflict injury or death on one another in the form of direct interference. The claws and teeth that make predators dangerous to prey also make them dangerous to one another. Examples include dragonfly larvae attacking each other, the susceptibility of venomous snakes to conspecifics' venom, and the posturing and fighting within groups of mammalian carnivores. Great-horned owls may raid the nests of red-tailed hawks, and vice versa. Lions steal the captures of spotted hyenas, and spotted hyenas reciprocate by harassing or killing lone lionesses or their young. The presence of conspecifics or other predator taxa can increase the foraging costs of an individual predator.

Second, prey can injure carnivores. If oblivious to injury or pain, a mountain lion can probably kill a North American porcupine easily. However, a muzzle or paw full of quills may incapacitate and starve a lion. Sweitzer and Berger (1992) found that mountain lions increased their consumption of porcupines during an extreme winter with deep snow. J. Laundre (personal communication) found porcupine quills embedded in several dead mountain lions retrieved during a period oflow mule deer abundance. A predator faced with the risk of injury while capturing prey should add a cost of "predation" to its other hunting costs. A predator down on its luck (in a low energy state or with a high marginal value of energy) should be willing to broaden its diet to include higher-risk prey or to take on bolder hunting tactics that simultaneously increase the probabilities of success and injury.

More generally, one can think of the predation costs of foraging as the opportunity costs a forager pays while trying to avoid a catastrophic loss. This catastrophic loss can emerge from the risk of mortality or injury from predators, amensals, prey, competitors, combatants, and even accidents. The giving-up density of raccoons increases with height in a tree (Lic 2001), presumably as a consequence of the greater risk of falling from increasing heights.

The examples developed here show the importance and pervasiveness of the predation costs of foraging. The next step in our analysis considers how animals respond to these costs. Three classes of responses can affect the organism's ecology, the ecology of its predators, and the ecology of its own resources: time allocation, vigilance, and social behaviors. The next two sections explore some of the ecological consequences of time allocation and vigilance (chap. 10 deals with social foraging).

13.4 Ecological Consequences of Time Allocation

Animals should balance the conflicting demands of food and safety (see chap. 9). In terms of time allocation, this balancing can occur in the context of patch use (small-scale habitat heterogeneity in food availability and risk) or habitat selection (large-scale heterogeneity). Within a depletable food patch, a forager should stop foraging when

where H is the quitting harvest rate, C is the metabolic cost of foraging, P is the predation cost of foraging [as given in eq. (13.1)], and O is the missed opportunity of not spending the time at other fitness-enhancing activities (Brown 1988). Each of these terms can have units of energy per unit time, nutrients per unit time, or resource items per unit time, although for any given application of equation (13.2) we must express all four elements of the equation in the same units. Box 13.2 explains how giving-up densities can be used to estimate the costs of predation.

BOX 13.2 Giving-up Densities

Joel S. Brown

When a goose is grazing, it does not eat entire grass plants. A part of each leaf is torn away, and a part is left behind. Nor does a browsing moose eat all the twigs and leaves from each bush. Foragers at depletable patches do not consume all of the contents. We call the amount of food that a forager leaves behind the "giving-up density," or GUD.

Even humans exhibit GUDs. An "empty" drink can or bottle is not actually empty—there are dregs left that could be had with enough dexterity, patience, and perseverance. The same goes for eating pieces of chicken. Some do indeed eat all—meat, cartilage, marrow, and bone. But generally, most humans leave some of the chicken uneaten at the end of a meal. This remainder is also a GUD.

What do GUDs tell us about the forager, its environment, and its opportunities and hazards? The marginal value theorem conceptually anticipates GUDs. In most food patches, the forager's harvest rate declines as the food is depleted, and there is a positive relationship between the patch's current prey density and the forager's harvest rate. Since the GUD is simply the current prey density when a forager quits the patch, the GUD provides a surrogate for the forager's quitting harvest rate. The predictions of the marginal value theorem can be recast in terms of GUDs. A forager should have a higher quitting harvest rate (higher GUD) in a rich than in a poor environment; and a forager should have a higher quitting harvest rate (higher GUD) as travel time among patches declines.

Two studies, one with bees (Whitham 1977) and one with tiger beetles (Wilson 1976), empirically anticipated GUDs. Whitham asked why honeybees left dregs of nectar behind in flowers. He suggested that bees maybe unable to access all of the flower's nectar, or that it might not be worth the effort. This latter interpretation sees the flower as a depletable food patch, and sees the dregs as a GUD reflecting the costs and benefits of harvesting the flower. Wilson examined the consumption of insect prey by tiger beetles as influenced by the tiger beetles' habitat of origin. Tiger beetles from habitats rich in prey consumed a much smaller proportion of the offered prey than tiger beetles from habitats poor in prey. He suggested that partial prey consumption may be analogous to the use of patches where the tiger beetles' harvest rate declines as the prey is consumed. The GUD of the tiger beetles corresponded to the beetle's habitat quality as predicted.

How thoroughly should a forager use a food patch when there may be predation risk, activity-specific metabolic costs, and numerous alternative activities to consider, or when the patch itself may become depleted as a consequence of the forager's activities? We will start by defining some terms. Let predation risk, $ (units of per time), be the forager's instantaneous rate of being preyed upon while engaged in some risky activity. Let the reward from foraging, f (items or joules per unit time), be the instantaneous or expected harvest rate of resources while foraging under predation risk. Let a forager have a number of alternative foraging choices that vary in risk, $, and rewardf With depletable food patches, we assume that patch harvest rate, f, declines as resources are harvested. The effect of predation risk on the cost of foraging depends on how risk and resources combine to determine fitness. Let F(e) be survivor's fitness. It gives fitness in the absence of predation (expressed as a finite growth rate). Assume that F increases with net energy gain, e. Let p be the probability of surviving predation over a finite time interval. This probability is influenced by the cumulative exposure of the individual to risky situations. As more time is allocated to risky situations, p declines; as more time is allocated to safer situations, p increases.

Consider four fitness formulations. Each of these formulations shares a time constraint such that the time devoted to all activities must sum to the total time available:

The first model considers an organism attempting to maximize the probability ofsurviving over some time interval with the requirement ofmain-taining a certain energy state, k. This model can be appropriate for animals surviving through ajuvenile or larval stage to adulthood, or for animals that must survive through a nonbreeding season. The second model considers an organism that attempts to maximize its state while maintaining a threshold level of survivorship, k. Given that survivorship is really a component of fitness, rather than a constraint, this model seems less applicable. This safety constraint can provide an approximation for fitness maximization when the modeler wants the objective function to merely be net energy gain. The third model closely fits classic predator-prey models in which fitness is the difference between population growth in the absence ofpredation and the predation rate. This model applies where there is either a rapid conversion of energy gain into offspring or where there is communal raising of young or full compensation by the surviving partner so that the death of a parent or helper does not jeopardize the current state and investment in offspring. The fourth model, in which an organism's fitness is its survivor's fitness (or net reproductive value in dynamic programming models; see Houston et al. 1993) multiplied by the probability of achieving that fitness, is probably most applicable to food-safety trade-offs. In this case, a forager must survive over some finite time period before realizing its fitness potential.

The optimal patch use strategy (Brown 1992) shows that in all cases, a food patch should be left when the benefits of the reward rate, H, no longer exceed the sum of metabolic, C, predation, P, and missed opportunity, O, costs of foraging: H = C + P + O. In the following equations (one for each fitness formulation), the term on the left-hand side is H, and the terms on the right-hand side are C, P, and O, respectively:

UP $p , $t d F/de d F/de u p $ Model 3 : f = c +--—--+

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