behavioral ecology vol 8 no. 5: 551-559 foraging to...

Behavioral Ecology VoL 8 No. 5: 551-559

Foraging to balance conflicting demands:novel insights from grasshoppers underpredation risk

K. D. Rothley, Oswald J. Schmitx, and Jared L. CohonSchool of Forestry and Environmental Studies, Greeley Laboratory, 'Yale University,370 Prospect Street, New Haven, CT 06511, USA

Animal foraging may be influenced by multiple demands simultaneously (eg., nutrient gain and predator avoidance). Conven-tional approaches to understand the trade-ofii between these demands require cramming them in ffmilar currencies, which isimpractical in many field situations. We introduce a new method, called multiobjective programming, as a framework to explorehow animals balance conflicting demands. Multiobjective programming allows one to explore die influence of foraging demandsdirectly, without explicit assumptions about how they enter into fitness and without conversion to some common currency. Usingmultiobjective programming, we show that, as foraging demands change, animait may adaptivety adjust their behavior, even ifthe constraints on feasible behavior are unaffected (contrary to die predictions of the conventional models). Hence, we maysee a variable response in foraging that is consistent with adaptive behavior. We used an empirical test with herbivore grasshop-pers and predator spiders to evaluate die utility of multiobjective programming Our experiments show that grasshoppers areable to optimally balance die foraging objectives of energy intake and vigilance under changing levels of predation risk. Themultiobjective model is used both to evaluate die biological «ignifiranrf of the broad variation that was observed in die grass-hoppers' foraging behavior and to quantify explicitly die trade-off between energy intake and predator avoidance. Key words:adaptive behavior, Mdanopius ftmui i ubrwn, multiobjective optimization, optimal foraging, single-objective optimization, trade-offs, variability. fBthav Ecol 8:551-559 (1997)]

Alarge body of evidence persuasively demonstrates that an-. imal foraging behavior can be influenced by multiple,

conflicting demands or objectives (Cockbum, 1991; Mangeland dark, 1988; Mangel and Ludwig, 1992; McNamara andHouston, 1986; Stearns, 1993; Werner and Gilliam, 1984).These demands may arise from exogenous sources, such asdie presence of predators (Houston et aL, 1993; lima andDill, 1990; Ludwig and Rowe, 1990; Mangel and dark, 1986;McNamara and Houston, 1987, 1994; Sih, 1980; Werner andGilliam, 1984), or endogenous sources, such as physiologicaldemands for survival and reproduction (Cockbum, 1991;Ludwig and Rowe, 1990; McNamara and Houston, 1996).Each demand may also vary in its importance among differentenvironments. The challenge, dien, is to identify how animalsbalance conflicting demands under different environmentalconditions.

One powerful way to understand how nnimaii balance con-flicting demands or objectives is to represent foraging choicesin an optimization framework. In such a framework, the trade-off between foraging demands, such as energy gain and pred-ator avoidance (Ludwig and Rowe, 1990; Mangel and Clark,1986; McNamara and Houston, 1987), is formalized mathe-matically using a combination of terms representing die de-mands. The model is then solved to identify die optimalforaging strategy that balances die trade-off

Empirical tests of such trade-off optimization models havehad mixed IUCCCM, as behavioral shifts not anticipated by diemodels are often observed. Usually animals exhibited broadvariation in their performance when compared to die singlepredicted optimum strategy. This variation has been inter-preted as an inability of foragers to make exact optimalchoices. (Janetos and Cole, 1981; Schluter, 1981; Ward, 1992;

Received 16 December 1996; accepted 26 February 1997.

1045-2249/97/S5.00 O 1997 International Society for Behavioral Ecology

Zach and Smith, 1981), as an indication of limiting constraintsthat prevent animal« from foraging optimally in a particularenvironment (Sih and Gleeson, 1995), or as die result of lim-ited information (BouskHa and Blumstein, 1992). 'Variation indie single optimal strategy is predicted only if diere is achange in die limiting constraints or a change in die way inwhich die terms representing die demands are nuuhemati-cally combined.

But wim changes in die relative intensity of foraging de-mands, such as an increase in die number of predators, it isunlikely diat any single trade-off strategy will maximize fitness.Instead, animal* may adjust dieir trade-off strategy in responseto /-hanging environmental conditions, even if mere has beenno change in any potential limiting constraints. Hence, dievariation diat has been offered as evidence of suboptimal be-havior in a classic optimization trade-off context may actuallybe consistent widi adaptive (optimal) behavior (Schmitz et aL,1997b).

Our understanding of animal behavior through optimiza-tion approaches may greatly improve by explicitly ^ramininghow animalu achieve a trade-off between conflicting demands.Here we introduce a mediod, called multiobjective program-ming (Schmitz et aL, 1997b), to provide die framework forthis approach. Widi multiobjective programming, it becomespossible to consider die consequences of conflicting demandson behavior widiout having to make assumptions about howmey enter into fitness. The key new insight we offer here isdiat we should not always expect animals to seek a single op-timal strategy that achieves a specific trade-off balance appli-cable to all situations. Instead, we may observe a range ofstrategies corresponding to die different weightings diat ani-mals may place on objectives under changing environmentalconditions. By comparing actual feeding behavior to die strat-egies predicted by die multiobjective programming model, wecan let animal* tell us which demands are important to diemand how uiey choose to trade-off these demands This insight

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552 Behavioral Ecology VoL 8 No. 5

then can be used to design new experiments that quantify theexact fitness consequences of trade-off behavior (Real, 1987;Schmitz et al., 1997b).

We report here on field experiments that examined theclassic problem of foraging to balance energy gain for survivaland growth with the avoidance of predaton (lima, 1985; Lud-wig and Rowe, 1990; Mangel and Clark, 1986; McNamara andHouston, 1987). We placed old-field grasshoppers under dif-ferent levels of predation risk. Their foraging behavior wasrepresented with a multiobjective model that explicitly consid-ered the trade-off between nutrient gain and predation risk,parameterized with field data. A single-objective model wasalso created to farilitai^ the development and interpretationof the multiobjective model. We found that the grasshoppersaltered their diet choices in response to increased levels ofpredation risk. Multiobjective programming analysis revealedthat this change in behavior may reflect the grasshoppers'varying relative preference for nutrient gain and predatoravoidance, even though the animals were not constrained todo so under increased risk.

METHODS

StndySite

The study was conducted during 1994 through 1996 at the'Ale-Myers Research Forest in northeastern Connecticut, USA,near the town of Union. The research location is a 3240-hanortheastern hardwood ecosystem interspersed with oldfields. The old-field sites have a variety of grass and forb spe-des, the most abundant being Solidago rugosa, Solidago gra-minifolia, Erigeron annuus, Trifolium Ttpms, AsUrnovttangUae, Daucus canto, Phltum prattnst, and Poa praten-sis. Our focal spedes for this study, the herbivore grasshopperMdanophu fmurrubrum, is common in this system. The mostcommon arthropod predaton include wolf spiden (Lycosidat)and nursery web spiders (Pisuridat). A complete descriptionof the study site is presented in Schmitz et aL (1997a).

Model construction

Our foraging models predict how a generalist grasshopper,Mttanoplus ftmurrubrum, should select its diet under chang-ing levels of predation risk. M. femurrubrum grasshoppers mayconsume both grasses and forbs (Heifer, 1987; Vickery andKevan, 1967). Feeding trials with M. ftmurrubrum grasshop-pers indicated that several spedes of grasses and forbs presentin the old-field community were edible. We aggregate all ed-ible spedes of plants into two groups: grasses and forbs. Wedo this for two reasons. First, these two resource types arepatently distributed relative to each other in die field, whichhas an important bearing on grasshoppers' search behavior(discussed below). Second, the net nutritional content andthe cropping rates for grasshoppers of plants within thesegroups, as measured through feeding trials, are similar (Be-lovsky, 1986a,b; Schmitz et aL, 1997a). The model formulationcould be easily adjusted to treat each plant spedes individuallyby adding variables to represent each spedes. The solutiontechniques would remain unchanged.

The goal of this study was to determine whether grasshop-pers adaptively balance multiple, variable, conflicting de-mands. We used a multiobjective programming model to pre-dict the foraging strategies representing the adaptive balanceof multiple demands. For comparison, we also formulated asingle-objective model to predict how grasshoppers would for-age if they instead considered foraging demands individually.Both models are based on the linear programming technique

(Belovsky and Schmitz, 1991; Schmitz et aL, 1997b). We se-lected the linear programming approach because of its con-siderable success in helping to understand herbivore foragingbehavior (Belovsky and Schmitz, 1994). Multiobjective pro-gramming has. been applied to problems related to the man-agement of wildlife (e.g., Hof and Raphael, 1992; Mendoza,1988), but it has not been applied to animal foraging behaviorbefore the study of Schmitz et aL (1997b).

The first step in the formulation of both models is to iden-tify the physical and physiological constraints that limit dailyconsumption of grasses and forbs. As with many herbivorespecies (Belovsky and Schmitz, 1991,1994), grasshoppers arepotentially constrained by three important factors: digestivecapacity, daily feeding time, and minimum energy require-ments. These foraging constraints can be stated mathemati-cally as:

Vs + «f*f: (la)

(lb)

T,

where 4 is the energy content of the tth food (•' =• g for grass,» » f for forbs), E-ia the daily minimum energy intake, b, isthe wet mass/ dry mass ratio for the ith food, D is the digestivecapacity of the grasshopper (calculated as the product of theturnover rate and the crop volume), c, is die cropping timefor tile tth food, and T is the maximum time available forfeeding. The two dependent model variables are Xp the dailydry-mass grass consumption, and x,, the dairy dry-mass forbsconsumption. The form of the time constraint (Equation lc)assumes that grasshoppers in this field system exhibit a spatialnonsimultaneous search pattern for grasses and forbs {stnsuBelovsky et aL, 1989). The grasses and forbs are patchily dis-tributed relative to each other, so that grasshoppers cansearch only for one food type at a time. Together, these threeconstraints bound the set of feasible foraging strategies. Anexample of the feasible set of foraging strategies for the M.ftmurrubrum grasshoppers is provided in the next section,based on parameter values measured in our field system.

The next step in the construction of both the single objec-tive and the multiple objective foraging models is to identifythe potential foraging objectives. Previous work with grasshop-pers (Belovsky, 1986b) indicates that in the absence of pre-dation risk, grasshoppers attempt to ma^imm- their daily en-ergy intake. This foraging goal is an appropriate surrogate forfitness, as nutritional status has effects on development, fe-cundity, and mortality (Bernays and Simpson, 1990). Becauseof the direct fitness benefits derived from predator avoidance,we assume that grasshopper feeding may also be influencedby vigilance. These two foraging demands can be stated math-ematically at

max Z,(x) - «fxf + etx,,

max Z,(x) = T - (e,xf +

(2a)

(2b)

where Z, is the energy consumed per day, Z, is the daily timeavailable for vigilant behavior, and the other parameters aredefined as above for Equations l a - l c Because T is a constant,Equation 2b could be replaced with an equivalent statement:

min Z,(x) (3)

where thii equation represents the more familiar objective tominimize the time spent feeding (Schoener, 1971). The twobehavioral objectives, Z, and Z* conflict as time spent feedingreduces the time available for vigilance.



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Rothley et al • Adaptive foraging 553

pTSflnftcrTialkMi

Parameter values for die constraint equations (Equations la-ic) and die objective equations (Equations 2a and 2b), wereobtained by field studies and from die literature. For our fieldstudies, we used grasshoppers of varying sizes to allow for testsof die sensitivity of die models' predictions to grasshopperbody size.

Tfu tiwu constraintCropping time, <Land c,, was assumed to vary with body sizeand forage type. Therefore, we ran feeding trials with grass-hoppers to measure cropping times for grasses and forbs in-dependently. In each feeding trial, a single grasshopper wasstarved overnight, measured in length, and placed in a 1-1glass jar. A fresh plant sample was traced on a piece of graphpaper and then placed in die jar widi die grasshopper. If diegrasshopper fed, we timed die length of die foraging bout Aforaging bout was defined as a continuous interval of foodintake. A bout was considered completed when SO s hadelapsed with no food intake. Foraging bouts ranged from SOi to 52 min. The plant sample was dien retrieved and retracedon die graph paper. We determined die area of plant materialconsumed by comparing die two tracings.

We calibrated die area of die tracings to a dry mass mea-sure. For each plant species, plant samples were traced ongraph paper, dried at 60*C for 48 h, and then weighed toobtain an estimate of die dry mass per unit area. We usedthese plant data to convert the area of plant material con-sumed in die feeding trials to dry-mass values. A ratio of dielength of die feeding bout versus dry-mass consumed duringdie bout was dien calculated for each feeding trial. We useda nonlinear regression to fit die allometric function:

W" (A) (Xs) (4)

where W is die cropping time, X is die length of die grass-hopper, and A and B are constants to obtain an equation re-lating body length to cropping time for both grasses andforbs.

We calculated die maximum time available for feedingbased on estimates of daily activity time. Activity time is as-sumed to represent maximum daily feeding time because ac-tivity time appears to be limited by die diermal environment(Belovsky and Slade, 1986). A SO-m transect across die fieldwas traversed every SO min over a 12.5-h period. While movingacross die transect, each M. ftmurrubrum grasshopper ob-

served to jump out of die way was recorded. An estimate ofdie percentage of each SO-min period that die grasshopperscould be considered active was calculated as (Belovsky andSlade, 1986):

* - 5 '••• 25, (5)

where fa is die percentage of SO-min period, t, diat grasshop-pers can be active, n, is die number of grasshoppers observedduring t, and N is the highest number of grasshoppers ob-served during any SO-min period. An estimate of the dailymaximum time available for feeding (in min/day) was calcu-lated as

(6)

While this is only a rough method for estimating die max-imum available daily feeding time, it has been calibrated withdetailed time budget measures for a host of species (Belovskyand Slade, 1986). Moreover, die results were comparable tothose from a companion study designed to estimate feedingtime in enclosed terrariums (Schmitz et al., 1997a). The max-imum daily feeding time estimated in our field system wasmuch lower than .die feeding time realized for grasshoppersin a prairie environment (Belovsky and Slade, 1986). We dis-cuss later die sensitivity of our results to thii estimate.

Dtgestxvt constraintGrasshoppers' crop volumes vary significandy with body size.Therefore, we collected 50 grasshoppers from die field, mea-sured their length, and removed and weighed dieir crops (in-cluding contents) on an electronic balance. To estimate max-imum crop volume, only die data from die heaviest 15% ofdie crops for each body length were retained. A nonlinearregression similar in form to Equation 4, where W is die wet-mass crop weight, X is die length of die grasshopper, and Aand B are constants, was used to obtain an equation relatingbody length to crop volume.

The wet mass/dry mass ratios for grasses and forbs, \ andbr, and die crop turnover rates of grasshoppers were obtainedfrom die literature (Belovsky, 1986b). These values were as-sumed to be reasonable estimates for die true values of ourstudy system.

IWblelParameter value* for a 26.1-m

Parameter

Cropping timeGrassesForbs

Bulk ratioGrate*Forbf

Energy contentGrassesForbs

Crop volumeCrop turnover rateDigestive capacityTime available for feedingEnergy requirements

m grasshopper

Variable Value

<i<f

*

DTE

10.9312.05

1.642.67

7.049.76

0.054.09Oi l4.400.15

Units

h/g-dry

g-wet/g-dry

kj/g-dry

g-wet/ turnoverturnovers/dayg-wet/dayh/daykj/day

Source

Field experiment

Belovsky (1986b)

Belovsky (1986b)

Field experimentBekmky (1986b)

Field experimentBelovsky (1986b)



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a.

Feasible foraging strategies

AB Digestive constraintCD Energy constraintEF Time constraint

Nondominated diets

•mass grass consumption [g-dry/day]

b.Feasible objective combinations

Nondominatedstrategies

0.000 0.100 0.200 0.300 0.400 0.500 0.600

Energy intake [KJ/day]

0.700 0.800 0.900

Figure 1Example of the graphical representation of the feasible set of foraging strategies for a 26.1-mm grasshopper, (a) Feasible strategies graphedwith respect to the grasshoppers' potential resources: grass (xj and forbs (i,). Point A indicates the energy-maximizing diet of 100% grass.Point C indicates the vigilance-maximizing diet of 100% forbs. The arrow indicates the shift from an energy maximizing diet of 100% grassto a mixed diet (gnuse* and forbs) as the grasshoppers' perceived level of predation risk increases. The darkened border running from Athrough B to C Indicates the feeding strategies corresponding to the nondominated set. (b) Feasible strategies graphed with respect to theforaging objectives: energy intake (Z,) and vigilance (2^). Point A indicates die energy-maximizing strategy, corresponding to a diet of 100%grass in panel a. Point C indicates the vigilance maximizing strategy, corresponding to a diet of 100% forbs in panel a. The nondominatedset is denoted by the darkened border running from A through B to C The arrow indicates a shift from a strategy that favors energy intaketoward a strategy that increasingly favors vigilance as the grasshoppers' perceived level of predation risk increases.



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Rowley et aL • Adaptive foraging 555

IWUeZDiets and objective values for the labeled pointa of the feaafiile actfor • Z&l-mm grasshopper

100% T

Point

ABCDEF

3

. J I J V

Diet (g-ary/aay;

x,, gran x* forbs

0.130.000.000.020.400.00

0.000.080.020.000.000.37

Objective values

Z\, energy(kj/day)

0.900.760.150.15InfeastbleInfeaiible

Zf, vigilance(h/day)

3.013.464^14.17InfeaiibleInfeaiible

IJ

I£

Energy constraintThe energy content for grasses and forbs, ^ and a,, and theenergetic requirements of the grasshoppers were obtainedfrom the literature (Belovsky, 1986b). These values were as-sumed to be reasonable estimates for die true values of ourstudy system. Energy requirements are expected to vary withbody size, but this parameter did not change the qualitativepredictions of the models and so was not explicitly measured.

The parameter values based on the average body lengthgrasshopper used in our experiments (x — 26.1 ± 0.61 mm,n •* 42) are summarized in Table 1.

Model predictions

SingU-obftctiv* linear programming modelThe range of feasible foraging strategies, defined by die con-straints (Equations la-lc) , can be represented graphically byplotting die foraging constraints as lines on a two-dimensionalgraph using die decision variables, Xj and x,, as die axes (Fig-ure la). The graph shown was constructed using die param-eter values for an average-length grasshopper (x •» 26.1 ±0.61 mm, n - 42). While die exact solution varies, the qual-itative shape is similar for all grasshopper body lengths widiindie range studied. The shaded region (including die line seg-ments bounding die shaded region) indicates the set of fea-sible feeding choices. Based on this figure, a grasshopper dietmay consist of grass only (Figure la, tine AD), forbs only (Fig-ure la, tine BQ, or any intermediate combination (Figure la,all other points in die feasible set). Note that die time con-straint (Equation lc; Figure la, tine EF) does not intersect diedigestive constraint (Equation lb) as it does in most previouslinear programming model solutions (Belovsky and Schmitz,1994). Thus, die time constraint will not determine die opti-mum; Le. diere is a surplus of time available to feed.

A single-objective linear program representing die grass-hoppers' foraging choice to balance die trade-off of die po-tential foraging objectives of maximizing energy intake andma-rimiTHng vigilance (Equations 2a and 2b) was solved usingLINDO (UNDO Systems, Inc., 1995). The energy-maximizingsolution is a diet of 100% grass (Figure la, point A). Thevigilance-maximizing solution is a diet of 100% forbs (Figurela, point C). It is noteworthy that this model never predictsthat die optimal strategy is a mixed diet (both grasses andforbs). These results, as well as die objective values, Z, and Z*,for these diets are summarized in Table 2. Note that all diets"above" line AB, die digestive constraint, (e.g., Figure la,points E and F) are infeasible.

Our predictions for die single objective model are that inthe absence of predation risk, grasshoppers should select adiet composed entirety of grass (Figure 2a). As predation riskincreases, die grasshoppers may switch to a diet composedentirely of forbs (Figure 2a). Because die time constraint does

Oft

1

b.

1

0.00

twotfUm

C.

• spfckr twoqtidtn

Figure XA graphical representation of the predicted and observed diets forthe grasshoppers, (a) Predictions of the single-objective foragingmodel. In the absence of predators, the grasshoppers are predictedto choose a diet of 100% grass. As the level of predatkm riskincreases, the grasshopper! are predicted to switch to a diet of100% forbs (0% grass.) (b) Predictions of the multiobjecthre model.Grasshoppers foraging in the absence of predadon are predicted tohave the diet that is most highly composed of grass. As the level ofpredadon risk increases, the amount of grass in the grasshoppers'diet is predicted to decrease, (c) Observed diets of thegrasshoppers. Error bars indicate Set.

not intersect the feasible region, both the energy-maximizingand vigilance-maximizing solutions lie on the single-diet axes.Even if die time available for feeding were decreased by 50%,the time constraint would still not intersect the feasible re-gion. In a companion study designed to estimate feeding timeunder predation risk in enclosed terrariums (see Schmitz etaL, 1997a), the maximum observed reduction in time spentfeeding was only 18%. Thus, observed time budget changesin the time available for feeding grasshoppers under preda-tion risk do not change die predictions of the single objectivemodel.

MuiHobjtctiv* linear programming modelFor a multiobjective model, the grasshoppers' foraging objec-tives are not treated as stria alternatives, but instead as theendpoino of a continuum. Foragers are not restricted toswitching between single-objective diets; instead, it is assumedthat foragers use some intermediate weighted combination ofthe objectives. Further, foragers' relative preferences for the



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Table 3

Treatment code

ControlZero spidersOne spiderTwo spiders

s

No. ofgrasshoppers

0333

No. ofspiders

0012

Table 4Obwrred diets

Treatment

Zero spidersOne spiderI wo ipiden

Diet

*r&

0.070.040.02

(g-dry/day)

nss Xff forbs

0.030.050.01

Objective values

(kj/day)

0.790.770.24

Z*vigilance(h/day)

3.273.364.06

objectives may change under different environmental condi-tions. Multiobjective linear programming analysis is used toidentify this continuum of feeding strategies that representadaptive trade-offs between the objectives.

The objective equations, Equations 2a and 2b, are used tocalculate the feasible combinations of objective levels that cor-respond to the feasible foraging strategies. For example, Table2 gives the diet (x. and Xf combination) and the correspond-ing objective function values (Z, and Z, combination) for dielabeled points on Figure la. The feasible set of objective vahiecombinations can be plotted on a graph using the objectives,Z, and Zj, as the axes (Figure lb). Note the relationship be-tween Figures la and lb. Point A on Figure la indicates thefeeding strategy that yields the combination of objectives val-ues shown by point A in Figure lb.

It is with this representation that we gain new insight re-garding the optimal compromise solutions and can examinethe tradeoffs in different fitness components, measured indifferent currencies, in the same analysis. We can quicklyidentify borders AB and BC (darkened on Figure lb) as diecontinuum of intermediate strategies representing die adap-tive compromise solutions to the energy intake-risk avoidancetrade-off. The foraging strategies corresponding to these so-lutions are indicated by the darkened borders on Figure la.These solutions are said to be nondominated: for each dietwithin < this set, there is no other feasible diet that increasesthe amount of one objective (e.g., increased vigilant behavior)without giving a lower level of the other objective (reducedenergy intake) (Schmitz et aL, 1997b). Animals that feedadaptiveh/ would be expected to choose diets only from thiscontinuum. This analysis also yields an explicit quantificationof the trade-off between die objectives. For foraging strategiesalong the AB border, the trade-off between time available forvigilance and energy intake is 3.2 h/kj. For foraging strategiesalong die BC border, the trade-off is 1.2 hAJ-

We use this set of adaptive trade-off strategies as die basisfor our predictions. In die absence of perceived predationrisk, grasshoppers will eat die diet that yields die highest levelof energy. Again, this corresponds to a diet toward 100% grass(Figure la, point A). However, as die level of perceived pre-dation risk increases, grasshoppers use a diet that increasinglyfavors die vigilance maTimiTing objective. This changing rel-ative preference for die objectives corresponds to a shift alongdie set of adaptive trade-off solutions toward die vigilance-maximizing solution (indicated by die arrow on Figure lb.)In terms of feeding strategy, diis shift translates to an increasein die percentage of die diet composed of forbs (indicated byarrow in Figure la). For our experiments, grasshoppers in theabsence of predators should exhibit die highest daily intakeof grass. As predation risk increases, grasshoppers should ex-hibit a decline in die amount of grass in dieir diet (Figure2b). Note that in tile multiobjective framework, we cannotpredict diat die grasshoppers will consume die energy-maxi-mizing diet (100% grass) in die absence of predators. Thiswould require die assumption that in die absence of preda-tors, grasshoppers forego all vigilant behavior in favor of feed-

ing. Instead, we make a more modest assumption that grass-hoppers will have their lowest preference for vigilance in dieabsence of predators.

We conducted a field experiment widi adult M. fnmtrrubrumgrasshoppers and hunting wolf spiders (Lycosidtu) to evaluatedie predictions of die single-objective and multiobjective mod-els. Populations of grasshoppers and spiders were stocked intostandard aluminum experimental cages placed in an old field(see Schmitz et aL, 1997a). The cages were 1 m tall and en-closed a basal area of 0.25 m1. The cages were placed overnatural vegetation in randomized block experimental design;seven blocks, four cages per block. The plant species distri-bution in die field was highly heterogeneous such that grassesand forbs were present in all cages. We randomly assigned 4experimental treatments to the 28 cages (Table 3). Thesetreatments were designed to establish a broad range of pre-dation risk ranging from predator-free foraging to intensepredation risk: A control treatment, with no grasshoppers orspiders, was used to determine die plant abundance in dieabsence of herbivory.

Grasshoppers and spiders were introduced to die cages dur-ing a single morning. The cages were then left undisturbedfor 10 days. After this time, all grasshoppers in die cages werecounted (to determine die remaining population size in eachcage), removed, and stored in 70% ethyl alcohol, and all ed-ible (green) vegetation was dipped, sorted, and dried at 60°Cfor 48 h.

RESULTS

Analysis of variance indicated that die treatments had a sig-nificant effect (£<.O5) on die final dry mass of die grass. Bycalculating die difference between die final dry mass of dieplants in the cages containing grasshoppers and die final drymass of die plants in the control cages within each block, weestimated the total consumption by the grasshoppers in eachcage. This consumption estimate was then divided by thenumber of grasshoppers per cage and the time duration ofthe experiment to calculate the daily per capita consumption(Figure 2c). There was a significant difference (/K.05) in theper capita consumption between the treatments.

We used the daily per capita grass and forbs consumptionestimates to evaluate die performance of die foraging models.First, comparing the qualitative trends in die predicted andobserved grass consumption (Figure 2a—c), die observed for-aging patterns are clearly more «imilar to die predictions ofdie multiobjective model. The single-objective model predict-ed that in Ae absoaao of risk, the grasshoppers should con-sume a 100% grass diet, and as predation risk increased, diegrasshoppers should switch to a 100% forb diet. But in allcages, the grasshoppers were consuming a mixed (grass andforbs) diet The total remaining grass in die zero-spider



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Rothley et al • Adaptive foraging 557

a.

S

Feasible foraging strategies

Digestive constraintEnergy constraint

Nondominated strategies

0.05 0.1Daily dry-mass grass consumption [g-dry/day]

0.15

b.Feasible objective combinations

i1oa8

>

4.40 -I4.20 -4.00 -3.80 -3.60 -3.40 -3.20 -

J.UU T

0.00

c —P ^ ^ t w o spiders

D ^ ^ ^ ^ ^ _

1 It 1

0.20 0.40

Energy intake

— Nondominated strategies

0.60

[KJ/day]

B[^one spider^ ^ ^ z e r o spiders

1 ^Ts¥ 1

0.80 A 1.00

Figure 3Graphical comparison of the observed grasshopper diets (for the zero-spider, one-spider, and two-tpider treatments) and the predicted set offeasible and optimal strategies, (a) Observed diets graphed with respect to the potential food resources. No observed diet is dose to any ofthe predictions of the tingle-objective model [100% grass (point A) or 100% forbs (point B)]. Instead, the zero-spider and one-spider dietsappear to rail dose to the nondominated strategies predicted by the muldobjective modeL In this representation, the two-spider diet appearssuboptimaL (b) Observed diets graphed with respect to the foraging objectives. In this representation, all observed diets fall dose to thenondominated strategies as predicted by the muldobjective modeL This graph also allows the biological interpretation of die results. In theabsence of predators, the grasshoppers chose a strategy that most heavily favored energy intake. When a single spider was present, thegrasshoppers chose a strategy that more heavily favored vigilance. When two spiders were present, the grasshoppers chose a strategy thatmost heavily favored vigilance.

^ 1 ) , one-spider (p = .OS, removal of a single outlier dueto spatial variability in grass abundance), and two-spider (p ».04, removal of a single outlier due to spatial variability ingrass abundance) cages was significantly lower than the totalremaining grass in the control cages (Student's t test forpaired data, one tailed) .When compared to the total remain-

ing forbs in the control cages, the total remaining forbs inthe zero-spider (p " .08, removal of a single outlier due tospatial variability in forb abundance), one-spider (p » .08),and two-spider (p " .13, removal of a single outlier due tospatial variability in forb abundance) cages was significantlylower (Student's ttest for paired data, one tailed). The mui-



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558 Behavioral Ecology Vol. 8 Mo. 5

tiobjective model predicted a decrease in the percentage ofthe diet composed of grass with increasing predation risk. Thetrends in daily consumption of grass by the grasshoppersmatch this prediction.

Second, comparing the quantitative predictions of the sin-gle-objective and multiobjective models to the observed diets,the observed diets are dearly more similar to the predictionsof the multiobjective modeL We plotted the average per capitaconsumption of grass and forbs for each treatment (Table 4)using the protocol described above (figure 5a, feasible regionenlarged for clarity). The objective equations. Equations 2aand 2b, were used to transform the diet values into the cur-rencies of die objectives (Table 4). These objective-level valueswere then plotted in relation to the nondominated set of ob-jective combinations (Figure Sb). Looking first at Figure 3a,the average diets are all part of me set of feasible diet com-binations. No observed diet is dose to any of die predictionsof die single objective model [100% grass (Figure 5a, pointA) or 100% forbs (Figure 5a, point B)]. Tn«tM<4 the zero-spider and one-spider diets appear to fall dose to die non-dominated strategies predicted by die muldobjecdve modeLBut die average two-spider diet is not obviously dose to anypart of die nondominated set. This discrepancy could be ex-plained as die stochastic result of die large variability in forbabundance or as deterministic suboptimal behavior. There isno obvious way to determine whether either of diese inter-pretations is correct, nor can we ascribe biological significanceto any of diese results.

However, die plot of observed diets graphed widi respectto die objective values (Figure 3b) yields considerable newinsight. The grasshoppers feeding in die absence of predatorschose die diet that most favors die maximization of energyrelative to die odier treatments. The grasshoppers in die one-spider cages chose a diet that provides an intermediate bal-ance of vigilance and energy intake relative to die other treat-ments. The grasshoppers in die cages with die highest pre-dation risk chose an average diet that most heavily favors vig-ilance over energy intake. Viewed in diis representation, diegrasshoppers appear to be trading off between energy andvigilance. The proximity of die predicted diets to die non-dominated set suggests tiiat die grasshoppers are performingdiis trade-off optimally. The discrepancy between die two-spi-der cage diets and die predicted optimal diets (die nondom-inated set as represented in Figure 3a) is not so nearly exag-gerated in diis representation (compare die two-spider dietpoints in Figure 3a and b.) In other words, diis apparentlysuboptimal behavior has minimal consequences with respectto die attainment of die behavioral objectives. The averagediets for all treatments may then be consistent widi optimalforaging. These experimental results suggest tiiat both energyintake and predation risk are operational factors affectinggrasshoppers' foraging and diat grasshoppers are balancingdiese conflicting demands.

DISCUSSION

Our experiments suggest diat animals have die ability to op-timally balance multiple foraging influences. As die relativeimportance of diese influences changes, animah are able toadjust dieir foraging strategy, consistent widi die predictionsof an optimization framework. Hence, variation in foragingstrategy may be consistent widi optimal behavior.

The problem of optimal trade-offs between multiple, con-flicting objectives has been explored previously through mod-eling efforts in behavioral and evolutionary ecology. The stan-dard approach has been to combine mathematical terms diatrepresent die individual fitness components or objectives(e.g., energy intake, time devoted to feeding) into a single

fitness equation to approximate a single decision-making goal(objective). While we do not question diat tiiere may indeedbe a single function of die individual fitness objectives diataccurately captures an animal's foraging objective, there areseveral difficulties widi diis approach. First, die form of dieobjective function must be assumed. Specifically, it must bededded a priori whedier terms should be combined linearlyor nonlinearfy and whedier scalar multipliers (weights) arerequired to appropriately combine die terms. This may beextremely difficult given die multitude and complexity of po-tential inputs. Second, all fitness components must be con-verted into a common currency before mey can be madie-maticaDy combined. Again, diis may be difficult given diecomplexity of fitness.

Multiobjective programming analysis can simplify die mod-el formulation of trade-off behavior and die interpretation ofempirical data. The trade-off between objectives can be quan-tified widiout die conversion of die objectives into some com-mon currency. There is no need to assume animals' relativepreferences for die objectives a priori because tiiere is noneed to create a fitness function. Multiobjective programminganalysis predicts die range of foraging strategies diat repre-sent die optimal compromise between multiple, variable for-aging demands. Empirical information **̂ " be compared todiese predictions to determine animal«' preferences for diedemands under different foraging environments. The trade-off between die objectives can be explicitly quantified. Finally,by representing die objectives in their inherent currency, wecan interpret behavioral strategies according to dieir biologi-cal significance.

In our experiments, we did not test for variations in forag-ing strategies between males and females. Considerable evi-dence demonstrates diat males and females may have signifi-cantly different foraging strategies (e.g., Qutton-Brock et aL,1982). Because of die extreme sexual dimorphism exhibitedby die M. ftmurrubrum grasshoppers in our study, (x^ •= 22.3± 0.50 mm, n =» 19; x, - 29.2 ± 0.47 mm, n = 23), it maybe expected diat males and females may have different pref-erences for die foraging objectives. A companion studyshowed diat males and females may indeed have a differentialsusceptibility to predation as a result of die difference in bodysize (Schmitz et aL, 1997a). It would be interesting to repeatdiese experiments in a manner such diat die variations inforaging strategy between die sexes could be investigated.

We thank A. Beckerman, K. Johnson, S. Koenig, M. Mangel, D. Skelly,and two anonymous reviewer* for extremely helpful suggestion! andcomments. Financial support was provided by Sigma Xi and Weyer-haeuser fellowships to K.D.R. and by National Science Foundationgrant DEB-9508604 to O.J.S.

REFERENCES

Belovsky GE, 1986a. Generalist herbivore foraging and its role in com-petitive interactions. Am Zool 26:51-69.

Belovsky GE, 1986b. Optimal foraging and community structure: Im-plications for a guild of generalist grassland herbivores. Oecologia70J5-62.

Belovsky GE, Ritchie ME, Moorehead J, 1989. Foraging in complexenvironments: when prey availability varies over space and time.Theor Popul Biol 36:144-160.

Belovsky GE, Schmitz OJ, 1991. Mammalian herbivore optimal for-aging and the role of plant defenses. In: Plant defenses againstmammalian herbivores (Palo KT, Robbins CT, eds). Boca Raton.Florida: CRC Press; 1-27.

Belovsky GE, Schmitz OJ, 1994. Plant defenses and optimal foragingby mammaHan hCTDivOieS. J Mamma) 75: 816-832.

Belovsky GE, Slade JB, 1986. Tune budgets of grassland herbivores:body size similarities. Oecologia 7O.5S-62.



ownloaded from


Rothley et aL • Adaptive foraging 559

Bernays EA, Simpson SJ, 1990. Nutrition. In: Biology of graohoppen(Chapman RF, Joern A, eds). New Tforfc John Wiley and Son*; 105-128.

Bouskila A, Bhimstein DTf 1992. Rules of thumb for predadon hazard.MMmwii prediction* from a dynamic model. Am Nat 139:161-176.

Chitton-Brock TH, Guinnesi FE, Albon SD, 1982. Red deer behaviorand ecology of two sexes. Chicago: University of Chicago Press.

Cockbum A, 1991. An introduction to evolutionary ecology. London:Blackwe 11 Scientific

Heifer JR. 1987. How to know the grasshoppers, crickets, cockroachesand their allies. New Ybrfc Dover Publications.

Hof JG, n«ph«»i MG, 1992. Some mathematical programming ap-proaches for optimizing timber age-dan distribudons to meet mul-dspedes wildlife population objectives. Can J Forest Res 23:828-834.

Houston AI, McNamara JM, Hutchinson JMC, 1993. General resultsconcerning the trade-off between gaining energy and avoiding pre-dation. Phil Trans R Soc Lond B 341375-397.

Janetos A. Cole B, 1981. Imperfectly optimal animals. Behav Ecol So-ciobiol 9-.203-210.

Lima ST . 1985. Maximizing feeding efficiency and tpipitniTing timeexposed to predators: a trade-off in die black-capped chickadee.Oecologia 6&60-67.

Lima SL. Dill LM, 1990. Behavioral decisions made under die risk ofpredation: a review and prospectus. Can J Zool 68:619-640.

Ludwig D, Rowe L, 1990. Life history strategies for energy gain andpredator avoidance under time constraints. Am Nat 135:686-707.

Mangel M, dark CW, 1986. Toward a unified foraging theory. Ecology67:1127-1138.

Mangel M. Clark CW, 1988. Dynamic modeling in behavioral ecology.Princeton, New Jersey: Princeton University Press.

Mangel M, Ludwig D, 1992. Definition and evaluation of die fitnessof behavioral and developmental programs. Annu Rev Ecol Syst 23:507-536.

McNamara JM, Houston AI, 1986. The common currency for behav-ioral decisions. Am Nat 127:358-378.

McNamara JM, Houston AI, 1987. Starvation and predation as factorslimiting population size. Ecology 68:1515-1519.

McNamara JM, Houston AI, 1994. The effect of a change in foragingoptions on intake rate and predation rate. Am Nat 144.-978-1000.

McNamara JM, Houston AL 1996. State-dependent life histories. Na-ture 380-.215-221.

Mendoza GA, 1988. A muhiobjective programming framework for in-tegrating timber and wildlife management. Environ Manage 12:163-171.

Real L, 1987. Objective benefit verses subjective perception in dietheory of risk sensitive foraging. Am Nat 130J99—411.

Schhiter D, 1981. Does die theory of optimal diets apply in complexenvironments? Am Nat 118:139-147.

Schmitz OJ, Beckerman AP, O'Brien KM. 1997a. BehavionQy inducedtrophk i-^nAe*- die effect of predation risk on food web interac-tions. Ecology (in press).

Schmitz OJ, Cohon JL, Rothley KD, Beckerman AP, 1997b. Reconcil-ing variability and optimal behavior using multiple criteria in op-timization models. Evol Ecol (in press).

Schoener TW, 1971. Theory of feeding strategies. Annu Rev Ecol Syst£369-403.

Sih A, 1980. Optimal behavior can foragers balance two conflictingdemands? Science 210: 1041-1043.

Sih A, Gleeson SK, 1995. A limits-oriented approach to evolutionaryecology. Trends Evol Ecol 10-.378-381.

Steams SC, 1993. The evolution of life histories. Oxford: Oxford Uni-versity Press.

Vickery VR, Kevan DEMcE, 1967. Records of the orthopteroid insectsof Ontario. Proc Entomol Soc Ont 97:13-68.

Ward D, 1992. The role of sadsfidng in foraging theory. Oiko» 63:312-317.

Werner EE, GiUiam J, 1984. The ontogenetic niche and species inter-actions in size-structured populations. Annu Rev Ecol Syst 15:393-425.

Zach R, Smith JNM, 1981. Optimal foraging in wild birds? In: For-aging behavior: ecological, ethologies! and psychological approach-es (Kami! AC, Sargeant TD, eds). New York: Garland STPM; 95-113.



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