OPTIMAL FORAGING AND RISK OF PREDATION

OPTIMAL FORAGING AND RISK OF PREDATION: EFFECTS ON BEHAVIOR AND SOCIAL STRUCTURE IN UNGULATES

JOHN G. KrE

United States Forest Service, Pacific Northwest Research Station, 1401 Gekeler Lane, La Grande, OR 97850

Optimal foraging theory predicts that animals will either attempt to maximize energy gained or minimize time spent to obtain a fixed amount of energy. A time-minimizing approach implies that an animal is attempting to maximize time spent in other behaviors such as reproduction or to minimize its exposure to temperature extremes, predators, or some other factor in the environment while foraging. Indeed, many ungulates must balance the need to obtain sufficient energy and other nutrients required for maintenance, growth, and reproduction while avoiding predation. Adopting social behavior that results in the formation of herds confers several advantages to the individual because of the difficulty a predator has in approaching large groups, or in capturing individuals in the confusion caused by a fleeing herd. Such behavior is often seen in ungulates occurring in open habitats where coursing predators are common. The problem becomes more acute, however, for ungulates living in closed habitats year-round, where predators commonly hunt by stealth, or for those sex and age classes such as females with young that exhibit solitary behavior. Such species or sex and age classes would be expected to exhibit a time-minimizing strategy at least seasonally. Use of linear-programming models of dietary choice have been successful in predicting classes of forages consumed by ungulates and other generalist herbivores and indicate that they often follow an energy-maximization strategy. Nonetheless, overwhelming eVidence indicates that ungulates modify their behavior in the presence of predators. I suggest that decisions about when and how to forage are being made at different scales, and these differences may account for observed discrepancies between models and empirical evidence. Finally, new analytical techniques such as stochastic dynamic programming may allow development of more realistic models of foraging behavior and may better incorporate observed behaviors in ungulates.

Key words: ungulates, foraging behavior, optimal foraging theory, optimization, linear programming, stochastic dynamic programming, predation risk

Thirty years ago, ecologists began to look at foraging behavior in animals and ask how such behaviors are influenced by natural selection (Emlen, 1966; MacArthur and Pianka, 1966). Optimality theory has allowed great strides in the understanding of behavioral problems by integrating methodologies from biology, ethology, environmental physiology, and economics (McFarland, 1977). The concept that animals make decisions about foraging behavior in a way that leads to long-term fitness has generated a large volume of often contradictory literature over the last 25 years and

Journal of Mammalogy, 80(4): 1114-1129. 1999 1114

has formed the basis of optimal foraging theory (Newman et al., 1995; Pyke, 1984; Pyke et al., 1977; Stephens and Krebs, 1986).

I review some early models of foraging behavior and discuss results obtained by searching for optimal solutions. I then compare those results with knowledge about how ungulates alter behaviors such as habitat selection and social organization in the presence of predators. I review empirical evidence from the literature regarding foraging behavior of four species of cervidsmoose (Alces alces), white-tailed deer

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November 1999 SPECIAL FEATURE-UNGULATE LIFE-HISTORY STRATEGIES 1115

(Odocoileus virginianus), reindeer and caribou (Rangifer tarandus), mule and blacktailed deer (Odocoileus hemionus, O. h. columbianus)-and two species of bovidsgreater kudu (Tragelaphus strepsiceros) and domestic cattle (Bos taurus). Finally, I suggest why early models of optimal foraging may be inadequate to portray behavioral decisions ungulates make under the risk of predation, and suggest that newer, more complex models may provide better insights to such behaviors.

MODELS OF OPTIMAL FORAGING BEHAVIOR

Schoener (1971) suggested that an optimization approach could be useful in describing behavioral decisions made by a foraging animal. He outlined the problem in three parts: choosing an objective function to be maximized or minimized, defining cost-benefit functions, and selecting a computational technique for finding the optimal solution. The four primary aspects of foraging behavior considered were optimal diets, optimal foraging space, optimal foraging period, and optimal foraging-group size (Schoener, 1971). In building an optimization model of foraging behavior, two assumptions are necessary. First, searching for, handling, and eating food items requires time and energy, and second, benefits to the animal must be positive. Schoener (1971) argued that net energy yield (the energy obtained from food minus the energy used to obtain it) was the appropriate currency. There also may be some loss in fitness resulting from foraging as a result of the lack of time to participate in other activities such as defending a territory, reproducing, thermoregulating, and avoiding predators.

Schoener (1971) considered two limiting cases to the general model. The first was those animals whose fitness was maximized when they minimized time spent gathering a given energy requirement. In this instance, net energy gained beyond the fixed requirement would not add to reproductive fitness. He called these animals time minimizers. He suggested that this special case

might best fit females with a relatively fixed reproductive output per season (fixed brood or litter size) and males in general. An important aspect of a time-minimizing strategy is that not only does additional time spent feeding not increase reproductive fitness but may actually reduce it.

The second case included animals in which fitness would be maximized when net energy gain is maximized for a given time spent feeding. These animals could increase reproductive fitness by continuing to feed (within limits, for example that resulting from satiation or rumen fill) as long as the benefits to the animal were positive. These animals were referred to as energy maximizers (Schoener, 1971). This special case might fit females with variable brood or litter sizes.

Inherent in only one of these special cases is the concept that foraging is a dangerous activity in predator-rich environments. The time-minimizer model implies that there are costs associated with spending additional time foraging, and those costs can include a greater probability of being killed by a predator.

Optimal foraging theory has been criticized previously (Pierce and Ollason, 1987). For example, natural selection varies over time and current behaviors may reflect past conditions and not current pressures. This is the spandrel analogy of Gould and Lewontin (1979), in which seemingly decorative architectural features may have no functional purpose but are merely by-products of design dictated by structural constraints. Conversely, even such seemingly nonfunctional architectural features such as the spandrels of Basilica de San Marco in Venice (Gould and Lewontin, 1979), more properly referred to as pendentives, play an important if not so obvious role in preventing the outward displacement of the domes with accompanying catastrophic structural failure (Mark, 1996). Although formulating testable hypotheses regarding optimal foraging theory may be difficult (Pierce and Ollason, 1987; Stephens and Krebs, 1986),

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1116 JOURNAL OF MAMMALOGY Vol. 80, No.4

such attempts can provide valuable evolutionary insights (Stearns and Schmid-Hempel, 1987).

Herbivores, in general, and ruminants, in particular, are not good models for testing hypotheses about optimal foraging theory. Unlike carnivores, herbivores are faced with food that varies in quality and quantity. They often must balance intake of various nutrients, and nutrient content often dictates forage selectivity (Hobbs and Swift, 1985; Stephan and Krebs, 1986; Weckerly, 1994). Some herbivores also reduce feeding time and lower metabolic rates seasonally (Robbins, 1983). In ruminants, gross intake of energy is not as important to the animal as is intake of digestible energy. As a result, selection of individual food items, ingestion, digestion, and rumination occupy a greater proportion of time than does searching for forage. Finally, many plants produce anti-herbivory compounds that act to inhibit microorganisms in the rumino-reticulum and caecum, forcing the herbivore to choose between maximizing energy intake while keeping intake of toxic compounds low (Belovsky and Schmitz, 1994). Although it is mathematically impossible to maximize one objective function (energy) while minimizing another (toxic compounds), the latter can be treated as a constraint in an optimization model (Belovsky and Schmitz, 1994). Although modeling foraging behavior in ungulates and other herbivores presents unique problems, concepts of optimal foraging theory have been applied successfully to these species with resulting insights unobtainable by other approaches.

OPTIMAL FORAGING UNDER THE RISK OF

PREDATION

Perhaps the greatest criticism of optimal foraging theory as originally postulated is that natural selection may be acting largely on other behaviors such as predator avoidance. Behavioral ecologists have long recognized that animals use some form of decision process in choosing what to do at any

particularly time and risk of predation often plays an important role in that process (Abrams, 1991, 1993; Krebs, 1980; Mangel and Clark, 1986; McFarland, 1977; McNamara and Houston, 1987; Sinclair and Arcese, 1995). Indeed, even Schoener (1971) explicitly embodied the concept of predator avoidance behavior in his timeminimization model.

Lima and Dill (1990) outlined the following behavioral decisions made under the risk of predation: when to feed, where to feed, what to eat, and how to eat it. How risk of predation influences when an animal feeds can be seen in species that feed at night. Such species have been shown to reduce the amount of time spent feeding during periods of bright moonlight to reduce the risk of predation. This phenomenon has been shown in deermice (Peromyscus maniculatus-Clarke, 1983), old-field mice (P. polionotus-Wolfe and Summerlin, 1989), bannertail kangaroo rats (Dipodomys spectabilis-Lockard and Owings, 1974), and snowshoe hares (Lepus americanus-Gilbert and Boutin, 1991), among other species. The tendency to reduce activity on moonlit nights varied seasonally in Indian crested porcupines (Hystrix indica) suggesting that tradeoffs were being made differently depending on seasonal variability in nutritional status, requirements, and forage availability (Alkon and Saltz, 1988). Bowers (1988), Brown et al. (1988), and Price et al. (1984) reported that increased moonlight causes kangaroo rats (D. merriami) and other desert rodents to use areas with heavier cover, reducing their exposure to owls and other aerial predators but also causing them to feed at lower rates. During summer when the dominant predators were rattlesnakes (Crotalus cerastes), however, moonlight did not alter microhabitat use or foraging behavior in kangaroo rats (D. deserti and D. merriami). Unlike the risk from owls, the danger posed by rattlesnakes was greater under shrubs and during dark nights (Bouskila, 1995). Clearly, animals are capable of recognizing threats from different

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predators and adjusting their foraging behavior accordingly.

Where the most productive forage patches also are the most risky, animals must tradeoff those risks with benefits obtained by feeding in those habitats (Lima and Dill, 1990). Gray squirrels (Sciurus carolinensis) feed closer to cover in exchange for reduced feeding rates (Newman and Caraco, 1987). Mule and black-tailed deer avoid productive foraging areas away from hiding and escape cover (Reynolds, 1966; Taber and Dasmann, 1958), although response distances vary as functions of geographic location, habitat type, season, sex, age, and other factors. In contrast, African antelope avoid dense cover in which predators can hide (Underwood, 1982). Again, habitat structure and type of predator can influence specific behavioral responses in prey.

Tradeoffs between choosing an optimal diet and reducing risk of predation also can influence what an animal eats (Lima and Dill, 1990). Lima and Valone (1986) reported that gray squirrels rejected small food items with a high ratio of energy gained per unit of handling time in preference to larger food items with a lower ratio that they could more easily carry back to cover patches for consumption. Squirrels appeared to be trading off decisions not only about what to eat but how to eat it in exchange for reducing predation risk. Desert heteromyid rodents also appear to be more selective for seed types in areas away from protective cover (Bowers, 1988). Williamson and Hirth (1985) reported that the dietary niche in white-tailed deer was broader, containing more browse species, when deer were closer to edges of clearcuts than when deer were foraging farther away from cover. Deer fed in the middle of clearcuts only when preferred forage species were present in abundance. Weixelman et al. (1998) also noted that distance from escape cover affected diet selection in Alaskan moose (A. a. gigas), with diet selectivity declining with increasing distance from cover. In instances such as these, predic-

tions about what optimal diet choices should be, when made in the absence of considerations regarding the risk of predation, can be different from empirical results (Lima and Dill, 1990).

Finally, risk of predation can affect decisions an animal makes about how to feed. Relationships between habitat structure (open versus closed habitats), social structure (group size), body size, type of predator, and anti-predator strategies in ungulates are beyond the scope of this review. Nevertheless, there is a positive relationship between body size in ungulates and both forage biomass and the fiber content of forage consumed (Estes, 1974; Geist, 1974; Jarman, 1974). Grasslands, tundra, and other open habitats usually contain abundant forage resources that are often high in fiber, at least seasonally. As a result, plainsdwelling ungulates in general are larger than those that occupy denser habitats such as shrublands and forests, although smallbodied plains dwellers are not uncommon (Estes, 1974). Furthermore, larger-bodied, plains-dwelling ungulates are more likely to adopt a stand-and-fight response to predator attack as opposed to the hiding response seen in smaller ungulates living in closed habitats (Eisenberg and McKay, 1974; Geist, 1974).

Ungulates living in open habitats form larger social groups than do those living in closed habitats (Estes, 1974; Jarman, 1974). Differences in size of social groups can vary as a function of habitat structure even within a single species. Hirth (1977) compared social structure between white-tailed deer from forested habitats in Michigan with those from savanna habitats in south Texas. Deer in south Texas showed a marked tendency to form larger groups when occupying more open habitats. The relationship between group size and habitat structure was believed to be related primarily to strategies of predator avoidance but also possibly as a mechanism to optimize foraging efficiency (Hirth, 1977). Molvar and Bowyer (1994) also reported that size

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of social groups in Alaskan moose was related positively to distance to cover. When moose ventured out in the open, they formed larger foraging groups. For a given group size, foraging efficiency, defined as the percentage of active time spent foraging, declined significantly with distance from cover (Molvar and Bowyer, 1994).

One advantage to living in large groups is that anyone individual can be less vigilant and can spend more time feeding because a predator is less likely to approach a larger group unnoticed. As a result, an individual can spend more feeding with little or no decrease in overall vigilance of the group (Lima, 1995; Lima and Dill, 1990). Other mechanisms also may play a role such as a reduction in individual risk of predation through encounter, dilution, and confusion effects (Roberts, 1996). Indeed, a combination of detection and dilution effects in elk (Cervus elaphus) can account for 69% of the variability in vigilance frequency (Dehn, 1990). Decreases in vigilance rates with increasing group size also may be functions of easier location and observation of other group members (Quenette, 1990).

The position of an animal within a group can affect its vigilance rate. Those at the periphery of a large group show greater levels of vigilance and a higher degree of variability in vigilance rates (Berger and Cunningham, 1988). As the group size grows, the ratio of the perimeter of the space occupied by the group and numbers of individuals in the group decreases, conferring greater advantages to larger groups. In instances where groups are relatively stable and made up of related family members, some individuals may forgo feeding altogether for some time to act as sentinels (Lima and Dill, 1990; Rasa, 1986).

Berger and Cunningham (1988) reviewed the relationship between body size and vigilance rates among female ungulates in South Dakota. They compared vigilance or searching rates in the following species, listed in order of decreasing body size-

bison (Bison bison), mule deer, bighorn sheep (Ovis canadensis), and pronghorn (Antilocapra americana). They observed that mean time spent searching for predators declined with increasing group size in all four species. After effects of group size were controlled, however, smaller-bodied ungulates were more vigilant than were larger-bodied species, presumably because smaller ungulates were more vulnerable to predation (Berger and Cunningham, 1988). They concluded that both group size and body size must be considered when evaluating foraging behavior.

For a given species, differences in habitat structure can effect rates of vigilance. For example, pronghorns increased their vigilance rates when in habitats characterized by taller vegetation and restricted visibility (Goldsmith, 1990). In this instance, increased vigilance was accomplished by both longer scanning bouts and increased frequency of scanning. Similar increases in vigilance rates were noted for a variety of African antelope occupying habitats with denser vegetation (Underwood, 1982).

In summary, ungulates living in open habitats tend to be larger than those occupying closed habitats. Open-habitat dwellers are exposed more frequently to coursing predators than to those predators that hunt by stealth. Ungulates in open habitats are more likely to form larger social groups, where they rely on vigilance to detect predators at a safe distance and react according-1y. As group size increases, individual vigilance rates decline with no decrease in overall group vigilance. As a result, with less individual responsibility for detecting predators and an anti-predator strategy of detecting coursing predators at a distance, large-bodied, open-plains dwelling ungulates in large herds would be expected to more often exhibit an energy-maximization strategy of foraging.

Conversely, smaller-bodied ungulates, those living in closed habitats, and those exposed to predators that hunt primarily by stalking and stealth show greater rates of

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vigilance. With such an anti-predator strategy, such species should follow a time-minimization foraging model. Further, if foraging behavior is relatively plastic within a species, changes in foraging strategies with differences in underlying mechanisms related to sex, age, reproductive status, and season would be expected. For example, a female might be part of a large herd foraging in open habitats during autumn and early winter where she might behave as an energy maximizer. During parturition, however, if she were to isolate herself and her neonate in habitats with denser cover, she might shift to a time-minimization strategy.

OPTIMAL FORAGING IN UNGULATES:

CASE STUDIES

Optimal foraging in moose.-Belovsky (1978) used linear-programming techniques to construct optimization models for testing two alternate foraging strategies in moose on Isle Royale, Michigan: energy maximization and time-minimization. The latter strategy was suggested as an alternative to lower the risk of predation by wolves (Canis lupus) or to lower exposure to adverse environmental conditions leading to thermal imbalance such as heat gain during summer.

Linear programming is one of many optimization modeling techniques (Starfield and Bleloch, 1986). This method consists of defining an objective function to be either maximized or minimized, subject to a series of constraints. The objective function is a combination of two or more variables, and the constraints are linear combinations of those variables, which must be less than, equal to, or greater than some constant. One model developed and tested for moose consisted of an objective function of maximizing energy intake while the other minimized the time spent feeding (Belovsky, 1978). Variables in the model were three forage classes-aquatic plants, leaves of deciduous shrubs, and forbs; hence, the model was one of dietary choice.

One constraint was the daily energy re-

quirement of an individual animal, which had to be greater than or equal to the metabolic demands for maintenance in the simplest case (Belovsky, 1978). The minimum daily intake of sodium, a required nutrient known to be in short supply in forages on Isle Royale, was a second constraint. A third constraint was the digestive capacity of moose, which was a function of the size of the rumen. Finally, and perhaps most importantly, the amount of time available for feeding was the last constraint. This constraint was based, in part, on the need to spend time ruminating, but also on the need for a moose to limit activities to times and habitats that allowed thermoregulation (Belovsky, 1978). This constraint differed when moose were feeding in terrestrial versus aquatic habitats because of the high thermal conductivity of water.

Linear-programming models with twovariable objective functions can be solved graphically, whereas those with three or more functions can be solved using a simplex algorithm (Starfield and Bleloch, 1986). Alternatively, models for moose with three variables (consumption of aquatic plants, leaves, and forbs) can be solved pairwise (Belvosky, 1978). Conclusions drawn for the solutions of the two models were that a time-minimization diet differed significantly from the observed diet of moose on Isle Royale but the energy-maximization diet did not (Belovsky, 1978).

That moose on Isle Royale should follow an energy-maximizing strategy, which does not allow the consideration of risk of predation in making foraging decisions, is curious because of foraging patterns are known to be influenced by such risk as previously discussed (Edwards, 1983; Molvar and Bowyer, 1994; Weixelman et al., 1998). Furthermore, female moose with young on Isle Royale have been shown to choose small islands free of wolves because of increased survival of young, even though forage conditions were poorer than on mainland sites (Edwards, 1983; Stephens and Peterson, 1984). Even if female moose are

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following an energy-maximizing strategy within a site, predator avoidance may play a role in site selection.

Optimal foraging in greater kudu.Owen-Smith (1994) studied foraging behavior in hand-reared, free-ranging greater kudu and interpreted results in the context of optimal foraging theory. During the dry season, kudus expanded their dietary niche to include plant species not eaten during the wet season (Owen-Smith, 1994). The total time spent active and the percent of active time spent feeding also both increased during the dry season. Digestive capacity increased to allow a greater daily intake of lower quality forages. Kudus appeared to be neither energy-maximizers nor time-minimizers but seemed to be meeting their energy requirements with least overall cost (Owen-Smith, 1994). Classical linear-programming models of their behavior failed to account for variations between days and between foraging sessions in parameters assumed to be constraining forage intake (Owen-Smith, 1993). Owen-Smith (1993) further suggested that the energy maximizer-time minimizer dichotomy failed to take into account fitness consequences of alternate foraging decisions.

Optimal foraging in white-tailed deer.Schmitz (1991) modeled foraging behavior in white-tailed deer during winter in Canada to test if these herbivores followed an energy-maximization strategy, or one where they were behaving as time minimizers to reduce their exposure to cold temperatures. In winter, white-tailed deer in cold climates must balance the need to rest in stands of dense conifers thereby conserving body heat with the need to forage in open habitats were forage is more abundant but where it is colder (Schmitz, 1991). During early winter, Schmitz (1991) observed foraging behavior of deer that closely matched that predicted by an energy-maximization strategy but significantly different than that of a time-minimizing strategy. In late winter, however, predicted time budgets of the two strategies were indistinguishable, and

the observed behavior matched either one equally well (Schmitz, 1991). In late winter, deer actually decreased the total time in activity and the proportion of active time spent foraging because of increasing temperatures. He hypothesized that this was in response to the risk of overheating while still in winter pelage in the warmer environment (Schmitz, 1991). Schmitz (1990) also concluded that when white-tailed deer were being supplementally fed during winter, they were still behaving as energy-maximizers.

Optimal foraging in reindeer and caribou.-Ferguson et ai. (1988) studied a herd of caribou on Pic Island in Lake Superior, Ontario. Although most populations of caribou had gone extinct on the surrounding mainland, they persisted in small numbers on the island. Three hypotheses were tested: that forage availability was greater on the island, that caribou on the island did not develop infections of meningeal worm (Parelaphostrongylus tenuis) because ofthe scarcity of white-tailed deer (the usual host for this parasite), and that caribou persisted because of the infrequent island visits by wolves and black bears (Ursus americanus). The first hypothesis was rejected because the island had a lower abundance of preferred shrubs and forbs. The second also was rejected because, although no protostrongylic larvae were found in caribou feces on Pic Island, neither were any observed in feces from either caribou or deer on the nearby mainland peninSUla (Ferguson et al., 1988).

When the caribou visited the mainland, they selected forbs that allowed a large bite size (Ferguson et aI., 1988). On Pic Island, however, forage was too scarce to allow for such selectivity and caribou spent longer intervals feeding. Ferguson et al. (1988) concluded that when on the mainland, caribou were selecting for forbs that provided a high mass per bite to minimize the time they were unable to watch for predators. Conversely, because predators were scarce on Pic Island, caribou were able to persist

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there because although forage was less abundant, the animals could spend more time searching for and consuming forages. They concluded that caribou were acting as time-minimizers (Ferguson et al., 1988).

Skogland (1991) also argued that energy maximization alone may not account for behavior of foragers that are vulnerable to predators. He argued that when foraging in open habitats, herbivores have three options: restrict themselves to habitats with a low risk of predation, form groups, or spend less time in some activities to increase time available for predator detection and avoidance (Skogland, 1991). Wild reindeer in Norway used all three options. During parturition, females generally sought high-elevation sites where forage conditions were poor but the risk of predation also was low (Skogland, 1991). Comparison of a well-fed herd of reindeer in good condition and one in poorer condition before the start of hunting season and the risk posed by humans showed that reindeer in the poor-condition herd spent more time feeding than those in good condition. Moreover, reindeer in the poor-condition herd reduced the time that they spent feeding after hunting started (Skogland, 1991; Skogland and Gr!1lvan, 1988). The good-condition animals also formed larger groups and were more vigilant after hunting started. Skogland (1991) concluded that the reindeer in the good-condition herd were behaving as time minimizers, but those in the herd under nutrient stress were acting like nutrient maximizers.

Optimal foraging in mule deer, blacktailed deer, and domestic cattle.-Belovsky and Schmitz (1994) reported results of a linear-programming model to predict consumption of grasses and browse by mule deer during late winter and early spring. A time-minimizing strategy predicted a diet composed exclusively of grasses. An energy-maximization strategy predicted a diet of 72% browse, which closely approximated observed diets that averaged 76% browse (Belovsky and Schmitz, 1994).

Between 1983 and 1993, my colleagues and I conducted a series of studies on the interactions between migratory mule deer and black-tailed deer and grazing by domestic cattle. Our study sites were located on a montane summer range in the central Sierra Nevada of California and on a foothill winter range in northern California used by black-tailed deer from late autumn through spring. From the summer-range research, we previously reported effects of cattle grazing on hiding cover (Loft et aI., 1987), habitat use (Loft et aI., 1991), and home range sizes (Loft et aI., 1993) in mule deer. How deer foraging behavior changed under different cattle stocking rates and details of the study area and methods are available elsewhere (Kie et al., 1991). Preliminary results from the winter-range research on black-tailed deer also have also been reported (Kie, 1996; Kie and Boroski, 1995).

Research on summer range was conducted in a high-mountain basin in the Sierra Nevada where habitat types included meadow-riparian, aspen, montane shrub, conifer, and sagebrush (Loft et al., 1991). On summer range, female mule deer spent 32% of the time feeding, 8% of the time traveling, and 60% of the time resting (Kie et al., 1991). These herbivores spent more time feeding with increasing rates of cattle stocking, averaging 24, 31, and 44% of the time feeding with no, moderate, and heavy cattle stocking rates, respectively (P < 0.01; Fig. 1). In contrast, time spent resting declined from 67% in the absence of cattle to 60% with moderate stocking and 50% with heavy stocking. Time spent traveling by deer did not differ between stocking rates (P > 0.10) but increased from 6% in early summer to 11 % in late summer when averaged for both years (P < 0.05; Fig. 1). Time spent traveling increased from a summer-long average of 4% during 1984 to 12% in 1985, a year in which rainfall was below average (P < O.OI-Kie et al., 1991).

In the two pastures grazed by cattle in

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~ 20 w c..

1984

~ RESTING

Il!I!I!I!I!!I TRAVELING

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EARLY LATE EARLY LATE EARLY LATE

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FIG. i.-Percent time spent feeding, traveling, and resting by mule deer on summer range in California as a function of year, season (early summer was from 6 July to 10 August, late summer was from 11 August to 17 September), and cattle stocking rate (Kie et al., 1991).

1984, deer spent more time feeding during late summer than during early summer (P < 0.05; Fig. 1). Conversely, in 1985 (the dry year), deer in the two pastures grazed by cattle spent less time feeding in late summer (P < 0.05). The differences in time spent feeding by deer between early and late summer were accompanied by inverse changes in time spent resting (Fig. 1). Average duration of a feeding bout by deer did not differ among rates of cattle stocking (P > 0.10). Increases in percent time spent feeding by deer with heavy cattle grazing were a result of deer adding more feeding bouts per day rather than an increase in the duration of each bout. Number of feeding bouts initiated by deer during each 6-h quarter of the day varied as a function of cattle-stocking rate (Kie et al., 1991). In the absence of cattle, most feeding bouts were initiated at dawn and dusk. More feeding bouts were added during the day under moderate grazing and during both day and night under heavy grazing. Deer initiated more feeding bouts during night with increasing number of days to the nearest full moon. Total time spent feeding by deer, however, was not affected by number of days to the nearest full moon. Deer decreased the proportion of but not the total

time spent feeding each 24-h period during nights with bright moonlight (Kie et aI., 1991).

Overall, cattle spent 45% of their time feeding, 6% traveling, and 50% resting (Kie et al., 1991). Unlike time spent feeding by deer, no significant differences were noted in percentage of time feeding by cattle with respect to stocking rate (P > 0.10). Cattle were equally likely to initiate feeding bouts during anyone-quarter of the day or night, and began more feeding bouts at night during periods of bright moonlight (Kie et al., 1991).

Mule deer on summer range attempted to meet the high nutrient demands of lactation (Carl and Robbins, 1988; Hanley, 1984) while minimizing their exposure to predators and ensuring the survival of their offspring. Competition for herbaceous forage with cattle resulted in deer spending more time fee/ling summer-long in 1984, and in early summer during 1985. Only in late summer during the drier year in 1985 did deer respond to cattle grazing by decreasing the time they spent feeding. In addition, changes in the timing of feeding bouts by deer also may have affected their susceptibility to predation. In the absence of cattle grazing, most deer feeding bouts were ini-

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tiated at dawn and dusk. Fewer bouts were begun during the middle of the day because of the potential added energetic costs of thermoregulation (Beier and McCullough, 1990; Parker and Robbins, 1984; Schmitz, 1991), and at night because of increased chances of predation. Mountain lions (Felis concolor) are more active at night (Seidensticker et al., 1973), are efficient predators on adult mule deer, and are abundant in the Sierra Nevada. With moderate rates of cattle stocking, deer added feeding bouts during the day but not at night. Only with heavy cattle stocking did deer initiate more feeding bouts at night. During nights with bright moonlight, deer fed less and shifted feeding activities to other times of the day.

Data from summer range indicated that: 1) female mule deer acted as time-minimizers when forage conditions were good, spending as little time as possible obtaining sufficient energy to meet their requirements, thereby minimizing their risk of predation, and 2) female mule deer acted as energy-maximizers when forage conditions were poor, feeding only as the benefits outweighed the energetic costs (Kie et aI., 1991). Although we have previously suggested that the latter strategy occurred during late summer 1985 as result of below average rainfall and poor forage conditions (Kie et aI., 1991), reductions in time spent feeding may have resulted from two additional factors. In one study, reductions in access to free water resulted in reductions in dry matter intake in white-tailed deer (Lautier et al., 1988). The dry conditions in late summer 1985 likely reduced abundance of surface water, but other sources were available in the study area, and deer still had access to free water albeit at fewer sources. Indeed, increases in time spent traveling by deer in 1985 and during late summer in both years may have been a result of decreased availability of free water. Poor forage conditions in late 1985 also may have resulted in increased mortality of young deer, and reductions in time spent feeding by females without young because

of lower energy requirements. Although females likely shifted to an energy-maximizing strategy in late summer 1985, changes in foraging behavior may have resulted from other factors, and I cannot rule out that deer may still have been acting as timeminimizers.

The foraging strategy of cattle was uncertain, but it was not likely one of timeminimization. There were no efficient predators on adult cattle, and these large-bodied, open-habitat ungulates did not exhibit a foraging strategy influenced by fear of predation.

Research on effects of cattle grazing on foraging behavior in black-tailed deer during autumn, winter, and spring was conducted on oak (Quercus) savanna foothills in northern California (Kie, 1996; Kie and Boroski, 1995). Herbaceous understory species consisted of annual grasses and forbs. These species germinated with rains in October and November after migratory black-tailed deer arrived on the winter range (Kie and Boroski, 1995). During the cool autumn and winter, these plants provided limited amounts of high-quality forage for both cattle and deer. With warming weather in February and March, rates of plant growth increased and herbaceous forage was both abundant and nutritious. As annual plants began to mature in April and May, herbaceous forage quality declined and became less digestible (Kie and Boroski, 1995).

On winter range, black-tailed deer spent an average of 47% of their time feeding, 14% traveling, and 40% resting (Kie, 1996). The time spent feeding by deer was affected by cumulative animal-months of cattle grazing, but the effect depended on the grazing period, and to a lesser extent, the pasture. From 15 November to 14 January, each animal-month reduced the time spent feeding by deer by 0.59%, 0.46%, and 0.48% in the three pastures (Table 1). These effects were much less pronounced in all pastures after 15 January (Table 1).

Between 15 November and 14 January,

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TABLE I.-Estimated effects of cumulative animal-months of grazing by cattle in three 259-ha pastures on percentage of time feeding by female black-tailed deer on winter range. For example, each additional animal-month of grazing in pasture 1 from 15 November to 14 January reduced the time spent feeding by deer by 0.59%. There were significant (P < 0.05) effects of pasture, animalmonths of grazing, animal-months X period, and animal-months X pasture interactions (Kie, 1996).

Effects of cattle grazing (animal-months)

Pasture 15 November-14 January 15 January-14 March 15 March-IS May

2 3

-0.59% -0.46% -0.48%

deer appeared to act as energy-maximizers. The limited amount of available herbaceous forage was further reduced by cattle grazing, and I had previously argued that deer fed less with increasing cattle stocking because the energetic cost of feeding was greater than the benefit derived from extra time spent feeding (Kie, 1996). Growth of annual herbaceous plants increased with the onset of warmer weather, interspecific competition for forage did not appear to be occurring between deer and cattle, and as a result no significant changes in foraging behavior by deer were observed after midJanuary.

Examination of additional data provided an alternative explanation, however, to the reductions in time spent feeding by deer from 15 November to 14 January. In grazed pastures, deer exhibited a slight but nonsignificant increase in the consumption of forbs (J. G. Kie, in litt.). Fecal nitrogen in deer, an indicator of crude protein intake, actually increased during December and January as function of increasing animalmonths of cattle grazing (Kie and Boroski, 1995). Finally, fecal diarninopimelic acid did not differ as a function of cattle animalmonths, suggesting that digestible energy intake remained constant even though less time was spent feeding by deer (Kie and Boroski, 1995). Although deer survival was fairly high during the winter range study (70% probability of survival for 36 months after original date of capture using a staggered-entry Kaplan-Meier technique-Pollock et al., 1989), mountain lions killed

-0.08% 0.05% 0.03%

-0.07% 0.06% 0.04%

three of 50 radio-collared deer on the winter range or at the start of spring migration, coyotes killed one on winter range, and nine other deer died from undetermined causes (Kie and Boroski, 1995). It may be that black-tailed deer on winter range, much like mule deer on summer range, were making tradeoffs between foraging behavior and risk of predation, and following a timeminimization strategy.

DISCUSSION

Much debate has occurred about optimal foraging theory, and the role that appropriate models play in predicting behavioral responses (Belovsky, 1986, 1990, 1994; Hobbs, 1990; Owen-Smith, 1993, 1994, 1996). Use of linear programming to model foraging behavior has been criticized for being biologically unrealistic, for relying on circular arguments, and curiously, for being too successful given statistical realities (Owen-Smith, 1993, 1996). For example, circularity can arise if constraints such as the maximum time available for feeding is estimated from observed average values when those variables may not be constraining at such levels (Owen-Smith, 1996). Furthermore, assumptions required under linear programming have been criticized for bearing no relationship to processes known affect digestion in generalist herbivores (Hobbs, 1990). Those criticisms, however, have been convincingly rebutted (Belovsky, 1990).

Linear-programming models of dietary choice by forage class have been applied,

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however, to >33 species of generalist herbivores and in most instances, they have indicated herbivores usually follow an energy-maximizing strategy (Belovsky, 1986; Belovsky and Schmitz, 1994). Even species known to be very sensitive to risk of predation such as snowshoe hares (Lepus american us-Gilbert and Boutin, 1991) may appear to be energy-maximizers under such models (Belovsky, 1984a). Clearly, such models have withstood repeated tests (Belovsky, 1994). Belovsky (1984b), however, acknowledged that foragers in general might mix the two strategies, maximizing nutrients during some seasons and behave as time-minimizers during others such as mating season. The pertinent question is why do linear-programming models of dietary choice work so well, especially in light of what is known about predatoravoidance strategies in ungulates and other mammals?

Linear-programming models function best as models of dietary choice between forage classes. These models are less successful at predicting intake of individual plant species (Belovsky, 1981). Where linear-programming models predict a mix of forage classes in the diets as in mule deer (Belovsky and Schmitz, 1994), such predictions may rest on requirements of multiple nutrients rather than a strategy of energymaximization. Where both energy-maximization and time-minimization strategies correctly predict consumption of a single forage class as in elk (Belovsky and Schmitz, 1994), no conclusions can be drawn.

In addition to not scaling down to the level of plant species very well, linear-programming models do not seem to scale up well either. Energy-maximization strategies ignore the overwhelming evidence that ungulates modify almost all aspects of their behavior, including decisions about foraging as a function of risk of predation. Laca and Demment (1996) have argued convincingly that classical energy-maximization models can predict dietary choices during

grazing but not the timing and duration of such bouts. I agree and suggest that given success of linear-programming models for dietary choice in so many ungulates, that they may indeed be appropriate for modeling behavior while grazing, but that ungulates are making decisions about foraging behavior at different scales. For example, mule deer appear to be acting as time-minimizers at a broad scale, and considering risk of predation in determining when to forage, how long to forage, and how to organize socially while foraging. After those decisions are made, ungulates then may attempt to maximize energy intake, balance needs for other nutrients such as a sodium requirement in moose (Belovsky, 1978), and minimize consumption of toxic compounds (Belovsky and Schmitz, 1994).

In addition to not considering risk of predation or need to reproduce, energy-maximizing, linear-programming models do not allow behavioral decisions to change as a function of the internal state of the animal (Krebs and Kalcelnik, 1991; Laca and Demment, 1996). For example, an animal in poor condition may choose a foraging strategy more risky than one that is wellfed (Skogland, 1991). Finally, these models are deterministic when in reality, processes such as rates of food encounter and probability of being killed by a predator are stochastic (Krebs and Kalcelnik, 1991). Models incorporating stochastic dynamic programming consider the consequences of short-term behavioral decisions into longterm animal fitness (Krebs and Kalcelnik, 1991; Laca and Demment, 1996; Mangel and Clark, 1986; Newman et al., 1995). Such models have the capability to more realistically portray decisions animals make under the threat of predation, but they can be complex and difficult to parameterize. For example, although ungulates may be more vulnerable to predation while foraging than while resting, the quantitative, functional response of predation risk to additional time spent foraging is largely unknown. Further, such relationships may be

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1126 JOURNAL OF MAMMALOGY Vol. 80. No.4

nonlinear, and their estimation problematical at best.

What is needed are empirical tests of hypotheses to accompany development of new models of foraging behavior (McFarland, 1977). Use of hypothetico-deductive approaches and additional manipulative studies will be necessary to fully understand foraging behavior in ungulates. For example, Skogland (1989, 1991) suggested that patterns of sexual segregation among cervids, in which adult males and adult females exhibit some degree of spatial separation during periods of the year other than rut, can be viewed as a compromise between optimal foraging and predator avoidance. We have shown that risk of predation on female white-tailed deer with young influences patterns of sexual segregation in white-tailed deer (Kie and Bowyer, 1999). Incorporating more explicit models of optimal foraging into such analyses may strengthen our understanding of the processes involved.

Newborn ungulates can be broadly classified as either hiders or followers (Lent, 1974), although the differences can be indistinct even within a single species such as bison (Green and Rothstein, 1993), blacktailed deer (Bowyer et aI., 1998) or moose (Bowyer et aI., 1999). Carl and Robbins (1988) suggested that for ungulates with follower-type neonates, high energetic costs associated with reproduction are born largely by the young, but that for those with hider-type neonates, the costs are born by the female. Females with true, hider-type neonates behave much like central-place foragers, returning periodically to nurse their offspring. Central-place foragers have been shown to exhibit unique foraging behavior patterns associated with repeated visits to a central location, and one would expect related differences to appear between species with hider-type neonates and those with follower-type young.

Finally, some mule deer in southern California exhibit migratory behavior while others in the same area adopt a year-round,

resident strategy (Nicholson et al., 1997). Migratory females were at greater risk of predation than were resident females, and during years with low winter snowfall, suffered greater rates of mortality. Mortality rates of migratory females were lower during years of heavier snowfall, and precipitation and snow cover that varied annually was likely responsible for maintenance of migratory and non-migratory strategies within a single population. Again, incorporation of explicit models of optimal foraging behavior into such analyses may shed light on underlying processes involved.

ACKNOWLEDGMENTS

This review paper was presented as part of a special symposium on "Life-history Strategies of Ungulates: An Evolutionary Perspective", held during the 1998 annual meeting of the American Society of Mammalogists at Virginia Tech, Blacksburg, Virginia. I thank R. T. Bowyer, my co-chair of that symposium, for conceiving of the idea and inviting speakers. I thank G. Batzli and R. Powell for valuable discussions, and J. Berger, R. T. Bowyer, G. L. Kirkland, Jr., and an anonymous reviewer for providing comments on the manuscript.

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