Stephens & Foraging - Behavior and Ecology - Chapter 9 docx

A growing area of research focuses on this fundamental trade-off.This chapter examines how danger from predators affects foraging behavior.Early theory assumed that fitness was highest wh

Foraging in the Face of Danger

Peter A Bednekoff

9.1 Prologue

A juvenile coho salmon holds its position in the flow of a brook To

conserve energy, it positions itself in the lee of a small rock

Distinc-tive blotches of color on its sides, called parr marks, provide effecDistinc-tive

camouflage As long as it holds its position, it is virtually impossible to

see The simple strategy of keeping still hides it from the prying eyes of

potential salmon-eaters Kingfishers and herons threaten from above,

and cutthroat trout, permanent residents of the stream, seldom reject a

meal of young salmon The threat posed by these and other predators

is ever present

The clear water flowing past the salmon presents a stream of food

items: midges struggle on the surface; mayfly nymphs drift in the

cur-rent But, here’s the rub: to capture a prey item, the salmon must dash

out from its station, potentially telegraphing its position to unwelcome

observers When the salmon feels safe, it will travel quite a distance to

intercept a food item, making a leisurely excursion to collect a drifting

midge as far as a meter away from its location

Detecting a predator changes the salmon’s behavior Depending on

the level of the perceived threat, the salmon has several options It may

flush to deep water or another safe location It may stop feeding

alto-gether, but hold its position It may continue feeding, but dramatically

Figure 9.1 Patch residence time increases with travel time between patches (as predicted), but blue jays stay in patches much longer than the optimal residence time Solid squares show observed residence times; open squares show the predicted optimal residence times (After Kamil et al 1993.)

reduce the distance it will travel to intercept food This series of graded sponses represents a sophisticated and often effective strategy to avoid preda-tors Sophisticated or not, all of these responses reduce the salmon’s feedingefficiency The salmon’s problem is far from unique; virtually all animals face

re-a trre-ade-off between re-acquiring resources re-and becoming re-a resource for re-another

9.2 Overview and Road Map

Resource acquisition is necessary for fitness, but it is not sufficient Food isgenerally good for the forager, but not if the forager is dead Danger affectsanimal decisions in many ways (see reviews in Lima and Dill 1990; Lima1998) Animals often face a trade-off between food acquisition and danger:the alternative that yields the highest rates of food intake is also the mostdangerous A growing area of research focuses on this fundamental trade-off.This chapter examines how danger from predators affects foraging behavior.Early theory assumed that fitness was highest when the net rate of foraginggain (i.e., net amount of energy acquired per unit time) was highest Earlyempirical tests consistently showed that foragers are sensitive to foraging gain(see Stephens and Krebs 1986) As predicted, many animals spend more timefeeding in each patch when patches are farther apart (Stephens and Krebs1986; Nonacs 2001) Animals often stay in patches longer, however, thanthe time that would maximize their overall rate of energy gain (Kamil et al.1993; Nonacs 2001; fig 9.1) Tests suggested that early rate-maximizingmodels were partly right: foragers are sensitive to their rate of energy gain,but often do not fully maximize it (see also Nonacs 2001) This observation

Distance from cover (m)

after hawk scare

before hawk scare

Figure 9.2 Black-capped chickadees are more likely to carry small food items to cover before eating

them when cover is close and after a simulated hawk attack (After Lima 1985a.)

suggested that some non-energetic costs must be important By pointing outthe importance of such costs, early tests of rate-maximizing models providedthe springboard for the study of foraging and danger

Black-capped chickadees often carry food items from a feeder to a bushbefore consuming them They are more likely to carry larger items and aremore likely to carry items if the feeder is closer to a bush (Lima 1985a; fig.9.2) Carrying an item to a bush decreases a chickadee’s rate of intake, butintake rate is decreased less with large items and close distances Steve Limahypothesized that chickadees carried food to cover in order to reduce theirexposure to predators He tested this hypothesis by flying a hawk model inthe area during some trials After having seen the hawk model, chickadeeswere more likely to carry food to safety (Lima 1985a; fig 9.2) Thus, animalsare willing to reduce their intake rate in order to reduce danger

To begin this chapter, I examine why foraging gain and danger are erally linked, and I build a life history framework for modeling foraging anddanger I discuss how danger may change with the internal state of the ani-mal, time, and group size These topics lead to inquiries on how animals assessdanger and whether they should overestimate danger I close with my view

gen-of the prospects gen-of the field Within each section, I outline some principles,often with the help of simple models, and illustrate those principles with asampling of examples

9.3 Why Does Increased Foraging Lead to Greater Danger?

Animals often face alternatives that differ in both foraging gain and danger.Obviously, foragers should avoid options that combine poor feeding with

great danger and choose options that offer good feeding with little danger.Most often, however, animals face difficult choices in which the options forbetter feeding also entail greater danger Such difficult choices are ubiquitousfor several reasons, and wherever one or more of these reasons applies, organ-isms face a trade-off between feeding and danger After sketching out variousroutes to a trade-off, I return to a general conceptual approach because themany routes to a trade-off converge on the same basic consequences.

Time Spent Exposed

Guppies feed day and night when no predators are around, but only duringthe day if predators are around (Fraser et al 2004) In response to indications

of danger, many animals restrict their feeding time (Lima 1998, see especiallytable II) An animal that feeds part of the time can restrict its feeding to thesafest period, but it must extend its feeding time into more dangerous periods

in order to feed for longer For example, small birds must extend their feedingtime into the twilight periods around dusk and dawn, when they are less able

to detect attacks in the low light and deep shadows (see Lima 1988a, 1988c;Krams 2000) For bats that feed on insects, darkness is safer, but emergingbefore nightfall may allow greater feeding ( Jones and Rydell 1994) Feeding

at night is also safer for minnows (Greenwood and Metcalfe 1998) and juvenilesalmon (Metcalfe et al 1999) In order to increase feeding, however, thesefish have to feed during the more dangerous daylight period

Habitat Choice

While actively foraging, animals often choose between habitats that differ indanger and productivity For example, aquatic snails feeding on algae face atrade-off because more algae grows on the sunny side of rocks, but the tops

of rocks are also more exposed to fish predators (Levri 1998) The basic ecology

of exposure leads to the trade-off: exposure to sunlight allows more synthesis, but exposure often leaves foragers more vulnerable to predators.Similarly, sunfish can find more zooplankton to eat in the open-water por-tions of lakes because these areas produce more phytoplankton, which supportthe zooplankton The open areas, however, provide no refuge from attack,whereas the weedy littoral zone provides refuge, but less food (Werner andHall 1988) Animals switch between these two kinds of areas during growthbecause both foraging gain and danger change as they grow (Werner and Gil-liam 1984)

photo-In other cases, the attack strategy of the predator and the escape strategy

of the prey combine to create the trade-off In boreal forests, the swooping

attacks of pygmy owls make the outer, lower branches of trees particularlydangerous (Kullberg 1995), and small birds avoid these branches unless com-petition or hunger forces them there (e.g., Krams 1996; Kullberg 1998b).Within a foraging group, individuals on the leading edge will first encounternew sources of both food and danger (Bumann et al 1997) Animals oftenmove to edge positions when hungry (Romey 1995) and to central positionswhen alarmed (Krause 1993) Habitat choice may involve another layer ofcompromise when foragers face conflicting pressures from different kinds ofpredators For example, grasshoppers can reduce bird predation by stayinglow on a blade of grass, but they can minimize predation by lizards and smallmammals by positioning themselves high on grass stems When both kinds ofpredators are around, grasshoppers choose intermediate positions (Pitt 1999).

As these examples emphasize, animals choose between habitats on small as well

as large spatial scales, and both kinds of choices have ecological consequences

Movement

Creatures great and small move less when predators are around (Lima 1998,table II) A forager actively searching for food can cover a greater area bymoving faster By covering a greater area, it is likely to encounter more feedingopportunities, and may also encounter more predators (Werner and Anholt1993) Besides simply crossing paths with more predators, moving foragersincrease the likelihood of an attack Anaesthetized tadpoles are less likely to bekilled by aquatic invertebrate predators (Skelly 1994), and tadpoles generallymove less when danger is greater (Anholt et al 2000) When movement is inshort bursts, as in degus, greater movement may involve both faster speedswhile moving and shorter pauses between bursts (Vasquez et al 2002) I willconsider movement in further detail below after developing a general model

of foraging in the face of danger

Detection Behavior

Most animals perform behaviors that increase their chances of detecting andescaping from predators The best studied of these behaviors are pauses dur-ing foraging to scan the environment for potential danger (see Bednekoff andLima 1998a; Treves 2000) Animals can raise their rate of food consumption

by scanning less frequently, but at the cost of detecting attacks less effectively(e.g., Wahungu et al 2001) Investigators have often operationally definedvigilance as raising the head above horizontal While this operational defini-tion works well for birds and mammals, animals with different body formsand lifestyles may require other operational definitions For example, lizards

basking with their eyes shut and one or more limbs raised off the substratumseem to be showing little antipredator behavior (Downes and Hoefer 2004).Overall, the varied postures and attention required for foraging probablyaffect predator detection in many organisms For example, guppies react lessquickly to predators when foraging than when not foraging, and even lessquickly when foraging nose down (Krause and Godin 1996).

Depletion and Density Dependence

For a burrowing animal such as a marmot, safety comes from fleeing back tothe burrow (Holmes 1984; Blumstein 1998) Marmots feed near their bur-rows, and so deplete food in the area (Del Moral 1984) Due to this depletion,

a marmot can feed at a higher rate, but at greater danger, by venturing fartherfrom the burrow Thus, reactions to initial differences in danger produce dif-ferences in foraging Many lizards also feed from a safe central place (Cooper2000) Such lizards can find more prey farther out, but at a cost The actions

of a lizard also produce a gradient of food and danger for its potential prey.The grasshoppers the lizard preys on can find a richer, less depleted foodsupply near the lizard’s perch, but obviously, feeding near the lizard increasesthe possibility of attack (Chase 1998) Thus, a spatial trade-off at one trophiclevel may have cascading effects on other trophic levels

In a manner similar to food depletion, density dependence can produce atrade-off when potential prey congregate By congregating, prey decrease oneanother’s feeding rates through competition and also decrease one another’sdanger through safety-in-numbers advantages When avoiding predatoryperch, 92% of small crucian carp concentrate in the safer shallows, compoun-ding the differences in food availability between shallows and open waters(Paszkowski et al 1996) In theory, the outcome depends on the balance ofcompetitive and safety-in-numbers effects and on how free predators are tochoose habitats, but we may often expect habitats to be made either safe butpoor or rich but dangerous by these mechanisms (Hugie and Dill 1994; Moody

et al 1996; Sih 1998)

9.4 Modeling Foraging under Danger of Predation

Foraging for a Fixed Time

Bluehead chubs alter their foraging in response to changes in energetic returnsand danger from green sunfish The best explanation for their behavior com-bines food and danger in a life history context (Skalski and Gilliam 2002) Tobuild models of foraging under danger of predation, we start from the first

principle of foraging theory—that food is good We assume that higher aging success leads to greater reproductive success in the future To includedanger, we need a second principle—that death is bad for fitness Early re-search was uncertain on how to incorporate danger into foraging models (seebox 1.1), perhaps because it is not obvious how to combine the benefits offoraging and the costs of predation Because the costs and benefits are indifferent units, we need to translate both foraging gain and danger into somemeasure of fitness A life history perspective is essential, and it leads to a simplesolution that exists precisely because the costs and benefits of foraging underdanger of predation are linked.

for-Decisions made under danger of predation are life history problems cause, if predation occurs, the forager’s life is history In a life history, the

be-basic currency to maximize is expected reproductive value, b + SV, where

b is current reproduction, S is survival to the following breeding season, and

V is the expected reproductive value for an animal that does survive to the

next breeding season (see Stearns 1992) I concentrate here on foraging and

fitness during a period without current reproduction (b= 0), so the measure

of fitness is SV, the future benefits multiplied by the odds of surviving to

realize them I expect increased foraging to decrease survival to the time ofreproduction, but to increase future reproduction if the animal does survive.Death lowers expected future fitness to zero Therefore, the cost of beingkilled is the reproductive success a forager could have had if it had survived.This linkage means that when we ask how much risk a forager should accept

to produce one additional offspring, we need to know how many offspring itwould produce otherwise For example, a forager that would otherwise ex-pect to produce one offspring might risk a lot to produce a second, while aforager that would otherwise expect to produce three offspring should riskless to produce a fourth, and a forager that would otherwise expect to produce

a dozen should risk little to produce a thirteenth This linkage of costs andbenefits sets up an automatic state dependence: the potential losses from beingkilled increase with previous foraging success, so the relative value of furtherforaging is likely to be lower (see Clark 1994) Even if the fitness gains offoraging are constant, the costs should increase, since the expected reproduc-tive value increases, and that entire value would be lost in death In line withthis logic, juvenile coho salmon are more cautious when they are larger, be-cause larger individuals expect greater reproduction if they survive to breed(Reinhardt and Healey 1999)

Now I will repeat these arguments mathematically For a nonreproducinganimal, fitness equals the future value of foraging discounted by the probabil-

ity of surviving from now until then, W(u) = S(u)V(u), where u is a measure of foraging effort, W is fitness, S is survival, and V is future reproductive value.

Fitness, survival, and future reproductive value are all functions of foraging

effort u In general, we expect survival to decrease and future reproductive value

to increase with foraging effort More specifically, we expect survival to

decre-ase exponentially with mortality, S(u) = exp[−M(u)], where M(u) is mortality Mortality rate, M(u), and future reproductive value, V(u), could take var-

ious mathematical forms For simplicity, I define foraging effort as a fraction

of the maximum possible effort, so that u varies from zero to one and does not have units This allows mortality, M(u), and future reproduction, V(u),

to be given as simple functions of foraging effort

Mortality is a function of the amount of time spent exposed to attack,the attack rate per unit time, and the probability of dying when attacked(see Lima and Dill 1990) Greater overall foraging effort could affect any of

these components For now I use a descriptive equation for mortality, M(u)

= ku z , where k is a constant and the exponent z gives the overall shape of the trade-off Later we will examine two specific cases to see what k and z might mean biologically, but for now I will simply label k as the mortality constant and z as the mortality exponent The general principle is that mortality should increase with foraging effort at a linear or accelerating rate; that is, M(u)=

ku z with z ≥ 1 If foragers exercise their safest options first, we expect

an accelerating function because additional food comes from increasingly

dangerous options A mathematically convenient value for the exponent, z=

2, matches observed changes in behavior well enough (Werner and Anholt1993), but other values are not ruled out, so I also examine a linear relationship

(z = 1) as well as more sharply accelerating ones (z = 3 and z = 4) For all

values, survival declines as foraging effort increases, but the contours of the

decline depend on the exponent of the mortality function, z (fig 9.3) As we

Figure 9.3 Survival declines with foraging effort The swiftness of the decline varies with z, the exponent

shall see near the end of this chapter, the value of this exponent determineswhether foragers should over- or underestimate danger.

For the relationship between foraging effort and future reproductive value,

we will use V(u) =κu.Inthisequation,theconstantκ translatesforagingeffort into future offspring, and u is foraging effort We expect future reproductive

value to increase with total foraging effort Studies have shown that greaterforaging success leads to greater fitness in adult crab spiders (Morse andStephens 1996), water striders (Blanckenhorn 1991), and water pipits (Frey-Roos et al 1995) Particularly for any organisms that are able to grow, reducedforaging in the presence of predators can lead to considerable long-term losses

of potential reproduction (Martin and Lopez 1999; see also Lima 1998, tableIII)

A linear relationship between foraging and future reproductive value is ful for its simplicity Other relationships may occur in nature, and the relation-ship may differ between the sexes even within a species (Merilaita and Jor-malainen 2000) I use a linear relationship here because it allows simple modelswith clear conclusions, even though these models may somewhat understatethe effects of danger The results of more complex models, in which futurefitness is a decelerating function of foraging gain, strongly support the con-clusions I reach using this simpler linear relationship

use-To complete the modeling framework, assume that foraging effort must

be greater than some required effort, R This requirement, R, is the required

rate of feeding divided by the maximum rate of feeding and so is a proportionwithout units A forager starves if its foraging effort is less than the require-ment, and avoids starvation as long as its foraging effort is greater than the

requirement A forager gains some amount of fitness, V(R), by just meeting

the requirement, but increases its future reproductive value by foraging at arate higher than the requirement

Assembling the pieces described above, we get the overall equation for

fitness: W(u) = S(u)V(u) = [exp(−ku z )][κu] We can find the optimal foraging effort, u∗, if we differentiate W(u), set the derivative to zero, and solve for u.

We find that

so long as u∗≥ R.

The foraging effort that maximizes fitness (i.e., is optimal) decreases as the

danger constant k increases As the mortality exponent z increases, optimal foraging effort decreases less sharply with increases in k (fig 9.4) Modelers

sometimes assume that animals maximize survival during the nonbreedingseason (see McNamara and Houston 1982, 1986; Houston and McNamara

Figure 9.4 Optimal foraging effort declines with the expected number of attacks by predators The

swift-ness of the decline varies with z, the exponent of the curve relating foraging effort to mortality.

1999) This assumption is justified whenever the requirement is greater than

the feeding rate that would otherwise be optimal, R > 1/(√z

kz) Thus, a life

history approach can converge on models that assume survival maximizationeven when future reproductive value increases linearly with foraging effort

In order to examine our model further, we need to look more closely

at the relationship between mortality and foraging effort, m(u) = ku z tality depends on the encounter rate with predators, time spent exposed topredators, and the probability of being killed per encounter The relationshipbetween mortality and foraging effort includes effects on any of these threecomponents I consider two situations here

Mor-First, consider tadpoles encountering predatory dragonfly larvae Tadpolesmove while foraging, while dragonfly larvae sit and wait for prey If a tadpolemoves faster, it encounters both more food and more predators In this case,

the exponent, z, reflects changes in metabolic cost per distance moved and the constant, k, combines the relative encounter rate with predators and the

probability of being killed in an encounter This logic applies to any foragermoving at different speeds with relatively immobile food and predators

Second, consider birds hunted by Accipiter hawks, which move a great

deal while hunting Because the hawks seek them out, greater foraging effortwill not cause foragers to encounter more predators, but it may make themmore likely to be killed when they do encounter a predator In this case, the

constant k includes a constant attack rate, α, and the exponent, z, reflects

how foraging effort increases the probability of being killed in an attack Thislogic applies when predators move rapidly and foragers are relatively im-mobile

The interpretation of the mortality function, m(u) = ku z, depends on thebiology of the predators and prey I use the second scenario to gain some in-sight into models that maximize survival Here an animal is exposed for a

period T at an attack rate α Thus, αT is the number of attacks the animal

can expect while foraging The optimal feeding rate will approach the quirement with only a modest number of attacks at a moderate level of re-

re-quirement, particularly if the mortality exponent z is small (see fig 9.4), and

will approach any level of requirement if the expected number of attacks islarge enough Danger can cause animals to behave as if they are foraging tomeet a set requirement

Gathering Resources with No Time Limit

So far, we have considered foraging for a fixed time We can modify ourframework to address the classic problem of gaining a fixed amount of re-sources from foraging within a potentially unlimited amount of time (Gilliam1982; see also Werner and Gilliam 1984; Stephens and Krebs 1986; Houston

et al 1993) Here a fixed amount of reproduction, V, occurs whenever ficient resources, K, are accumulated Thus, the reproductive value is fixed, but the time to reach it depends on gain, so W(u) = exp[−M(u)T(u)]V, and

suf-T(u) = K/u − R In this function, fitness will be maximized when M(u)/ (u − R) is minimized, which is another rendering of Gilliam’s M/g rule (see box 1.1) Using our equation for mortality, M(u) = ku z, we differentiate andsolve for the optimal foraging effort,

The mortality exponent, z, is the key parameter; u∗= 2R if z = 2, but u∗=

4R/3 if z= 4 In contrast to our previous results, here the optimal foragingeffort decreases when mortality is a more sharply accelerating function of

foraging effort (fig 9.5) If the requirement, R, is large, foraging at the maximum rate (u∗= 1) may be the best option available to foragers Notice

also that the optimal effort does not depend on the constant, k, but only

on the exponent z This means that the shape of the trade-off is the key,

while the exact level of danger is irrelevant Animals in environments withdifferent absolute levels of danger would have the same optimal behavior aslong as their trade-offs between foraging and mortality followed the samebasic function

Figure 9.5 For growing animals, optimal foraging effort increases with the amount of energy required to

stay alive, R, and decreases as the mortality function becomes more sharply accelerating.

9.5 Danger May Depend on State

Big fish may be better able to escape than small fish, and predators may attacklarge clams more often than small clams Body size often influences danger,but most models of growth ignore this possibility We would like to know

if danger depends on attributes of the individual that we label as state Many

studies demonstrate that antipredator behavior depends on state (see Lima1998; Clark and Mangel 2000), but that is not the same as demonstrating thatdanger depends directly on state because we expect antipredator behavior todepend on state whenever future reproductive value depends on state (Clark1994; see section 9.4) Fatter voles might venture out less on moonlit nightsfor a variety of reasons In order to say that they experience a higher risk, wemust directly compare fat and skinny voles

Examining the direct relationship between danger and state is difficult for

a combination of theoretical and empirical reasons In theory, the time course

of behavior depends on whether the effects of behavior and state combine byaddition or multiplication when we calculate mortality rate (Houston et al.1993) Empirically, this suggests that we should compare several quantitiesthat are difficult to measure I will illustrate this problem with the example offat reserves of small birds in winter Theoreticians originally developed theseideas for birds weighing 20 g or less, but the same principles apply to anyother animal for which starvation is a realistic threat

In winter, small birds do not grow, but they do need large energetic serves to survive the long, cold nights, plus any other periods of deprivation.Feeding more has value because it reduces the probability of starvation Even

re-in very harsh conditions, however, reserve levels are far lower than thereserves carried by long-distance migrants, suggesting that wintering birdscould carry more reserves than they do From this framework has grownthe study of optimal energetic reserves for foragers that could die of eitherpredation or starvation This area has expanded rapidly (see chap 7) and nowpossesses an impressive body of theory (Lima 1986; McNamara and Houston1990; Bednekoff and Houston 1994a, 1994b; Brodin 2000; Pravosudov andLucas 2000, 2001b) as well as a large collection of novel results that generallysupport the theory (e.g., Gosler et al 1995; Bautista and Lane 2001; Thomas2000; Olsson et al 2000; Cuthill et al 2000; see also Cuthill and Houston1997).

Whether birds pay extra costs when carrying more fat reserves is animportant, unsolved puzzle (see Witter and Cuthill 1993) Without such mass-dependent costs, the only cost of reserves is the foraging needed to acquirethem (see box 7.3) If carrying reserves reduces the risk of starvation, then wewould expect small birds to pay the acquisition costs for large reserves early inwinter, unless carrying those reserves also imposes a cost (Houston et al 1997).Some animals do fatten up for winter, but small birds seem to match theirforaging to their daily demands and therefore end up foraging more intenselywhen days are short and cold and food is less abundant In theory, this patternmakes sense with mass-dependent costs, but not without them (see Lima 1986;Houston et al 1997) Mass-dependent costs in models make it uneconomical

to forage in summer and fall and carry the reserves until needed in winter.These costs cause foragers to behave as if they are meeting a requirement over

a fairly short time horizon (see Bednekoff and Houston 1994b)

Excess body mass might be costly in several ways Extra mass might impairforaging performance, particularly while hovering or hanging from smalltwigs (Barbosa et al 2000; Barluenga et al 2003), or it might lead to increasedenergy expenditure (see Witter and Cuthill 1993; Cuthill and Houston 1997).These costs tax the value of reserves, but should not cause small birds torefuse “free” food when they encounter it If possessing larger reserves leads

to greater danger, however, this could make even free food too expensive toeat Birds at feeders generally eat far less than they could, and willow tits mayemploy hypothermia at night even when ad libitum food is available to themduring the day (Reinertsen and Haftorn 1983; see also Pravosudov and Lucas2000) These observations strongly hint that mass-dependent predation mayhelp explain the fat reserves of small birds

Logic and hints are a great start, but in science, we require evidence todecide the issue Unfortunately, we do not have the required evidence, and

we are unlikely to get direct evidence from the field It is difficult enough toobserve any acts of predation; to also know the relative masses of the victims