Opportunity-Cost Foraging Models for Stationary and

The University of Chicago

Opportunity-Cost Foraging Models for Stationary and Mobile Predators Author(s): Bruce Winterhalder Reviewed work(s): Source: The American Naturalist, Vol. 122, No. 1 (Jul., 1983), pp. 73-84 Published by: The University of Chicago Press for The American Society of Naturalists Stable URL: http://www.jstor.org/stable/2461007 . Accessed: 23/09/2012 16:57 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp

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Vol. 122, No. 1

The AmericanNaturalist

July1983

OPPORTUNITY-COST FORAGING MODELS FOR STATIONARY AND MOBILE PREDATORS BRUCE WINTERHALDER Departmentof Anthropologyand Ecology Curriculum,Universityof NorthCarolina, Chapel Hill, NorthCarolina 27514 SubmittedApril 1, 1982; Accepted January6, 1983

dietbreadth theorybyrelating HereI developan extensionofoptimalforaging through theconceptofopportunity activities decisionsto otherfitness-enhancing costs. Optimalforagingtheoryguides currentecologicalresearchon the feeding behaviorsof predators(reviewsin Orians 1971;Schoener1971;Charnovand Orians1973;Pykeet al. 1977;Krebs 1978;HassellandSouthwood1978;see also Kamiland Sargent1981).The analyticprocedureinvolves(1) choiceof a cur(2) whichis takento be a directproxyforfitness; rency,a measurableparameter constraints functions whichreflect construction ofa modelbased on cost-benefit appropriate to an adaptiveproblem;and (3) solutionforthe optimalbehavior or netrate (Schoener1971,p. 369). Timeand energy,expressedas an efficiency economic mostwidelyused(Smith1979),although parameter, are thecurrencies or linearprogramming and otherfoodcompomodelswhichconsidernutrients andWagner1978; behavioranalysis(Altmann nentsare beingappliedto foraging Belovsky1978; Westoby1978; Rapport1980; Keene 1981). The cost-benefit and Pianka1966; functions mayconsiderdietbreadth(Emlen1966;MacArthur Schoener1969a, 1969b; Rapport1971; Pulliam1975, 1981a, 1981b; Norberg habitats(Charnov 1977;Hughes1979;McNair1979);use ofpatchesor different 1976b;Charnovet al. 1976;Parkerand Stuart1976;Oaten1977;Morrison1978; Green 1980); foraging groupsize and use of space (Brown 1964;Horn 1968; Hamiltonand Watt1970;Covich 1976;Verner1977;Dill 1978;Caraco 1979a, time 1979b;Mitaniand Rodman1979;Oriansand Pearson1979);and foraging is treatedas one elementin a period(Schoener1974).Each of thesefunctions "decision" hierarchy (Charnovand Orians1973,pp. 9-10). thatorganHypothesesaboutadaptivebehaviorare based on theexpectation isms will have evolved the abilityto optimizetheirperformance of fitnessactivitiesrelativeto timeand energycosts (Cody 1974;cf. Lewontin enhancing 1979; MaynardSmith1978),and thatthe outcomeof such a processcan be ofsomeprewithsimplemodels(Levins1966).Limitedconfirmation investigated dictionshas been achievedin thelaboratory (Charnov1976a; Krebsand Cowie Am. Nat. 1983. Vol. 122, pp. 73-84. ? 1983 by The Universityof Chicago. 0003-0147/83/2201-0006$02.00. All rightsreserved.

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1976;Wernerand Hall 1979;Rapport1980;Sih 1980)and in fieldstudies(Belovsky1981;Cowie 1977;Davies 1977),including somebyanthropologists analyzinghunter-gatherer behavior(O'Connelland Hawkes 1981;Smith1981;Winterhalder1980,1981;Hames and Vickers1982;Hawkeset al. 1982). Modelsofdietbreadthbased on simpletime-energy currencies areusedextenresearch.One typeconsidersmobile,searching sivelyin optimalforaging predatorsin a "fine-grained" andPianka1966)environment. The solution (MacArthur to thisoptimality has been reached model,expressedas a set of hypotheses, independently severaltimes(Pykeet al. 1977,p. 141).The secondmodelapplies thosewhichsearchwithout to stationary cost.Schoener(1974,p. 4170) foragers, has suggested thatan organism ofthistypemaybe eithera timeminimizer or an fromthismodelare based on thetimeenergymaximizer. Hypothesesderiving I willcall thesethesearching distinction. and staminimizer, energy-maximizer tionarymodels,respectively. Here I presenta graphicalinterpretation offoraging whichcan be adaptedto each of these two models. It has severaladvantages:(1) It moreexplicitly recognizesthatthetimeand energycosts and benefits are accruingto foraging costsandbenefits. "opportunity" Thus,theycanbe assessedorhavevaluetothe on fitness-related activities other organism onlyinrelativeterms,bytheireffects thanforaging.(2) It expandsthe conceptsof timeminimization and energy maximization byshowingthattheseareendpointsofa moregeneralmeasure,the fitnessvalue to the organismof marginaltrade-offs betweentimeand energy. Given this operationalmeaning,these conceptsapplyto both searchingand fromthe stationary foragers. (3) In someinstancesitextendspredictions deriving searching and stationary diet-breadth models. DEFINITIONS

AND MODEL

Two initialconceptsare necessary.The opportunitycost ofan activity(A) is the value of some alternative foregonebecause resourcesare investedin (A) rather thanthealternative (Mishan1975).Thisconceptassumesthatresourcesare limited relativetopotential uses,andthatoneamongthesealternative uses can be identified as theappropriate substitute measure.It also assumesthatthepotential coursesofactionare to be evaluatedrelativeto one another.Theseassumptions are consistent withevolutionary ecologytheory.The secondconcept,marginal value,recognizesthatthecostofcontinuing toproduce,orthevalueofcontinuing to consume,a good is likelyto dependon the amountalreadyproducedor consumed.Thus,an economicdecisionto produceor consumeeach additional unitwillfocuson itsmarginal costor marginal value,respectively. Similarly, the value or cost of an activityoftenchangesas a function ofits duration.Here an economicdecisionto cease or continuea particular behaviorwillfocuson the valueofthenext,or marginal unitofthatbehavior.The marginal valuetheorem (Charnov1976b)is an exampleoftheusefulness ofthisconcept;marginal value willbe relatedto fitnessisoclineanalysisbelow. The basic modelis presentedgraphically in figures 1-4. It occupiesone quadrantofan x-y plane.Foragingactivities arerepresented intheright portion ofthe

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activitiesin theleftportion.The verticalaxis on the quadrant;all nonforaging foraging; theverticalaxis on rightshowsthenetacquisition(Ea) ofenergyduring activities, subjecttothe (Ee) innonforaging theleftshowstheenergyexpenditure axis to therightofthe thatEa = Ee fora givenperiod.The horizontal constraint line(Pc-Pc) showsthetimespentforaging (Tf); thatto theleftoftheline(PAtimeis activities Pc) showsthetimespentinnonforaging (Tf). Notethatforaging timefromleftto fromtherightaxis; nonforaging readfromrightto leftbeginning axisis subjectto theconstraint fromtheleftaxis. The horizontal right, beginning thatTf + Tnf= Tt,where T, representsan appropriateintervalforanalysis. This can be optimization approachshareswithothersthe assumptionthatforaging studiedoverfairlyshorttimeperiods(Katz 1974;Pykeet al. 1977,pp. 139-140). activities can Combinations oftime(Tf) and energy(Ee) used in nonforaging inthisquadrantbyisoclineswhichconnectpointsofequalfitness. be represented A pointon thisisoclinemap represents the weightedaverageof time-energy fora particular set of thesenonforaging activities.These isoclines expenditures analysis;isoclines curvesused in micro-economic are similarto theindifference studiesby Rapport(1971, 1980)and Covich have been used beforein foraging (see StonierandHague 1973), economicassumptions (1972,1974).Usingstandard thatthe scarcerof two the isoclinesare drawnconvexto the origin,implying morevaluable.Thus, the jointlyused resourcesis likelyto be the relatively marginalvalue of good or activity(A) increases,or whatamountsto thesame ofB grows. itsrelativerateofsubstitution for(B) decreases,as thequantity thing, willprobawithabundantnonforaging energy, An organism time,butinsufficient an additional unitofenergymorethanone oftime, blyvalue(intermsoffitness) and vice versa.Isoclinesmoredistantfromtheoriginhave highervalue. activiofnonforaging Timeand energyare bothnecessaryfortheperformance isoclinescannotcross Hence,thefitness ties,althoughnotin fixedproportions. forindifference eitheraxis (Ee or Tf). In Tilman's(1980)detailedterminology essential"resources. theseare "interactive maps,to whichthereaderis referred, rateof In figures1-4 a straight linefromtheorigin(0 to o) showstheminimum or basal metabolicrate) withsurvival(theresting compatible energyexpenditure rateof as a function physiological oftime.Another(0 to 1) showsthemaximum oftime.It activities also as a function possiblefornonforaging energyexpenditure willbe straight iffatigue does notoccurorcan be ignored.The actualenergy-time bythesetwoboundare constrained fitness combinations availableto a predator aries.

A fitness isoclinemapis a sufficient (see Levins1966)whichcan be parameter Becausetimeandenergy to an organism's adaptivecircumstances. quitesensitive are interactive, essentialresources,an organism limitedin one maybe limitedto distinctions somedegreein theother.Nonetheless, thismodeloffers operational timeto the strictly whichpass continuously fromthe strictly energy-limited is unitof energygainedby foraging limitedcases. If thefitness froma marginal then greaterthanthatattachedto an additionalunitoftimefreedfromforaging, (fig. theorganism is energylimited.The isoclineswilltendtowardthehorizontal is timeis thelarger,theorganism unitofnonforaging 1). Ifthegainto a marginal timelimited andrepresented bya fitness mapwhichis morenearlyvertical(fig.2).

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Ee

E

Density FIG. 1.-Opportunity-cost modelfora stationary forager whichis energy limited. resourcedisappears of highranking preyis greaterin A thanin B. The highestranking symbolsare used in thisand entirely fromthe environment of foragerC. The following subsequent figures: Tf,timespentforaging in an interval timespentin nonforaging T.; T,tf, chosenforanalysis;Ea, netenergyacquiredwhile activities in T.; T., totaltimeofinterval activities; foraging; Ee, energyexpendedin nonforaging Al. . . fn,isoclinesof increasing survivablerate of energyexpenditure in nonforaging fitness;c, line showingminimum expenditure activities as a function oftime;~,Slineshowing maximum possiblerateofenergy by the in nonforaging activities as a function of time;*, optimaldietbreadthas specified relevantmodel;PC-PC, partition betweenTnand Tf,theformer readleftto rightand the latterrightto left.

Formally,ifthefitnessisoclineis givenby a function if,thentherelativerateof tof substitution at somepointx is givenbythenegativeoftheslopeofthetangent is energylimited, forvalues> 1 itis timelimited. atx; forvalues< 1 theorganism An organismcan behaveas one or the otherdependingon its locationon the seasonality, life fitnessmap.The formoftheisoclinescan be adjustedto reflect cycle,or otheradaptivecircumstances. in figures1 and 2 is thatfora stationary The foragingmodel represented procedure (Schoener1969a, predator. Theoptimaldietis derivedbythefollowing line seg1969b,1971,pp. 369-370):Arrangepotentialpreytypesas end-to-end timeforitem mentsofslopee1/h1(netenergygainperunitofpursuit andhandling time,that i) fromthelargestto smallestvalue,beginning attheorigin(forforaging to thenumberof to theright).Set thelengthofeach e~Ihssegmentproportional intherelevanttimeperiod.The projection thatpreytypewhichare encountered ofa segmente~Ihsontothehorizontal axis represents thetimedevotedto typei; theprojection ontotheverticalaxis showsthenetenergygainfromi. The optimal forager takesall ofthehighest ranking preywhichpass by,addingpreyinorderof

OPPORTUNITY-COST

FORAGING MODELS

R~~~~~~~~~~~~~~f

77

IPc IC

A f2 Ee

Ea

a

Tnf

|

Tf

FIG. 2-General opportunity-cost model for a stationaryforagerwhich is time limited. Resource conditionsthe same as in fig. 1.

decreasingeilhi untilit achieves a diet breadthwhichsatisfiesits energyrequirements. The vertical axis at this diet breadth representsthe total net energy acquisition (Ea); the horizontalaxis the total timedevoted to foraging(Tf). One importantassumptionof this model mustbe mentioned.Search costs are not charged against the foragingof this predatorbecause other activities are assumed to occur in intervalsbetweenpursuitand handlingofprey.In thepresent analysis I have retained this assumption,but consider as well activities (Tf) whichof expedience or necessityare incompatiblewithforaging.Avoidingexposure to predatorsor to hazardous weatherare possible examples. It is unlikely thatall fitness-related activitiescould be performedsimultaneouslywithforaging at all times. The rightand leftportionsof the model are linkedin the followingway: Each diet breadthis associated witha certaingain of energy(Ea) and an investmentof time (7T). These can be plottedas a foragingconstraintline on the fitnessmap. The optimaldiet is the point where this line touches the highestpossible fitness isocline. This linkage establishes the opportunitycosts (time) and benefits(energy)offoragingby evaluatingthemrelativeto alternativeuses oftimeand energy in performing otherfitness-enhancing activities.Such an approach is necessary because timeand energyor otherproxycurrenciesused in foragingstudiesneed not be related to fitnessin a strictlylinear fashion. In the context of natural selection,an additionaljoule (or minute)may notbe as valuable (or costly)as the last. The combinationof foragingconstraintsand fitnessisoclines is analogous to manyanalyses of consumerchoice in micro-economics(see Covich 1972).

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The stationaryforagingmodel itselfdoes not give a unique solution to the question of optimal diet breadthbecause it does not specifyhow the organism evaluates timeand energy.Schoener's (1971) algorithmspecifiesassignmentof an "energyrequirement,"but as notedabove thisis relativeto adaptivecontextand to opportunitycost. To determinediet breadth it is necessary to know if the foragingorganismneeds to save foragingtime more than gain energy,or the reverse. The time-minimizer and energy-maximizer concepts do this. The combination of the stationarymodel with a fitnessmap gives explicitmeaningto the all feasiblecombinationsofmarginaltimeand energy generalcase by representing valuation. Resultsfor StationaryOpportunity-Cost Foragers Figure 1 depicts the general case for an energy-limited stationaryforager.I show threeforagingconstraintcurves whichdifferin the abundance of thehigher rankedprey. Density of the highestrankedtype decreases fromA to B; in C it disappears entirely. As the environmentbecomes richer(witheilhi constantforeveryitem)energy intakegrowsas does timespentforaging.If no new and highlyrankedpreyappear in the environment, and no highlyrankedpreydisappearfromit,dietbreadthwill not change (compare A and B). This result can be explained as follows: The greatestfitnessis obtainedby includingall preytypesup to and includingthe last typewhichhas a slope (readingrightto left)steeperthanthe nexthighestfitness isocline. Designate this item edblhdb, where dbl = diet boundary.So long as the fitnesscurves are straightand roughlyparallel, as will be the case for a strong energymaximizer,the diet boundaryitem (edblhdb) will be the same eilhi fora range of resource abundances and constraintlines. If a highrankingpreytype is added to or eliminatedfromthe organism's environment,diet breadthwill increase or decrease by one item,respectively(compare B and C). If eilhi increases forone or more highlyrankeditems,thentimespentforagingdecreases, energy intakeincreases,but slightly,and again dietbreadthremainsthe same. Statedas a hypothesis,the optimal stationaryforagertakes all resource types up to and includingthe last eilhi with a value greaterthan the marginalfitnessvalue in activitiesof energywithrespectto time.Of course, iftheefficiency nonforaging of pursuingand handlingan itemoutside of the diet shouldbecome greaterthanedb/ hdb, it will enterthe optimaldietbreadth.These observationscan be combinedto generatethefollowingprediction:Whetheror notan itemis includedin thedietof a stationaryforagertendingstronglyto time-minimization or energy-maximization strategiesdepends only on its eilhi, and is independentof the abundance or pursuitand handlingefficienciesof itemsof higherrank. Figure 2 depicts a stationaryforagerwhich is time limited, hence a time minimizer,facingthe same foragingconstraintcurves as givenin figure1. As the abundance of highrankingresources increases, thispredatorshould increase its remain foragingtimeand its energyintake.Its dietbreadthand foragingefficiency the same (compare curves B and A). The effectsof changes in the pursuit efficiencyfor highranked items are determinedas in the previous case. If high

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ranking preydisappearfromtheenvironment, foraging timemayincrease(compare B and C). Higherpursuitefficiencies willdecreaseforaging time,increase energyintakeand foragingefficiency. Diet breadthwill remainthe same, or possiblyincrease,ifone or moreitemspreviously just outsideofthedietattains an eilhi > edblhdb. Resultsfor Searching Opportunity-Cost Foragers

The stationary foragermodelitselfdoes notgeneratea uniquesolutionto the questionof diet breadthwithoutspecification of the marginalfitnessvalue of variousnonforaging timeand energycombinations. In contrast,the modelfor searching predators specifiesa uniqueoptimaldietbreadth, basedon a maximum netrateof intake.It does not,however,indicatehowlongtheorganism should forageat thisratenorhowmuchenergyit shouldharvest.Predictions aboutthe latterare possibleusingan opportunity cost approach. The fundamental theorem is based on theMacArthur and Pianka(1966)graphical modelformobilepredatorsin a fine-grained environment (as modified by MacArthur 1972,pp. 61-62;Pianka1978,pp. 263-266;see Schoener1971,p. 308). Severalalgebraicmodelsgiveessentially thesame results(Charnovand Orians 1973;Pykeet al. 1977).In thiscase activesearchhas two interrelated conseas partoftheoptimizaquences:(a) searching costsare chargedto thepredator tionproblem;and (b) foraging occursexclusiveofotheractivities. by definition Thatis, foraging takestheorganism away(intimeand space)fromsafety, mates, and offspring. The opportunity cost is moredirectherethanin the stationary betweena declining foragercase. The optimaldietis determined by a trade-off searchcost, and an increasing pursuitand handlingcost,per unitof preycaptured,as less andless valuablepreyare addedto thediet.In MacArthur's (1972, the "an animalshouldelecttopursuean itemifandonlyif,during p. 62)phrasing, timethepursuit wouldtake,itcouldnotexpectbothtolocateandtocatcha better item.'' Each dietbreadthinthismodelestablishes a rateofintakewhichwillappearas a straight lineinthefitness foraging constraint map(figs.3, 4). Figure3 depictsan thatis energylimited.As theabundanceofhighranking organism preyincreases, dietbreadthdecreasesand thenetacquisition ratewhileforaging improves.The constraint linewillpivotclockwise(compareA and B). For thisisocline foraging In thericher map,energyintakeincreases,andforaging timeis reducedslightly. and at the narrower environment dietbreadththisorganism foragessomewhat less butharvestsconsiderably moreenergy.An increasein pursuitcostswould In also narrowthedietbreadth, butwitha decreaseinoverallforaging efficiency. thisinstancetheforaging constraint linewouldpivotcounterclockwise. Figure4 achieves As thehabitatbecomesricher,thisorganism depictsa timeminimizer. thehighest fitness timedevotedtoforaging bysimultaneously decreasing and,for thefitnessmap depicted,increasing Werethefitness its energyintakeslightly. curvesmoreverticaland linear,foraging timeand energyintakewouldshrink untiltheorganism gathersonlyenoughenergyto meetitsminimal (Tnf)expenditurerate,butthatamountwouldstillincreaseas dietbreadthshrinks.


80

PA

/3

FIG. 3.-Opportunity-cost modelfora searchingenergy-limited forager.The foraging constraint curveis based on theMacArthur and Pianka(1966)model.The densityofhigh ranking preyis greater forB thanforA.

W

~~~\\f nf~~~~~~~~~~~~~~~~~

Tnf

Ee

PAA

fS

5

Tf Ea

FIG. 4-Opportunity cost model fora searchingforagerwhich is time limited.Resource conditionsas in fig.3.

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time approachallowsone to predicttheoptimalforaging The opportunity-cost thesearch predator.Factorsaffecting and optimalenergyintakefora searching fitness themarginal forand thepursuitand handlingof prey,or thoseaffecting in themodelanditspredictions can be incorporated valuationsoftheorganism, line,or thefitnessisocline constraint theireffectson theforaging by examining towardan For thoseorganismswhichdo nottendstrongly map,respectively. of an however,actualpredictions strategy, or time-minimizer energy-maximizer timeor energyintakerequirea fairlydetailed increaseor decreasein foraging behavior of the fitnessmap. This suggeststhatreliableforaging understanding of the organism'snonforaging dependon a detailedunderstanding predictions and theirfitnessconsequences. activitiesand constraints DISCUSSION

to theidea of opportunity The advantageof thepresentmodelis itsattention are evaluatedrelativeto thetimeand energy costs. Foragingcosts and benefits suchas avoidinghazards,orengagactivities requiredforother,fitness-enhancing is recognizedthatall or social activities.Whileit generally ingin reproductive costs (e.g., Pianka 1978,p. 260), this proxycurrenciesmeasureopportunity awarenessdoes not commonlyfindits way explicitlyintomodels.Time and partlybecause theycan be measuredeasilyin currencies, energyare preferred oftheseunitsare relativemeasuresas far quantities absoluteunits.Butmarginal costapproachgets Theopportunity as naturalselectionandfitness areconcerned. withforagvariesdirectly thatfitness assumption aroundthesometimes incorrect or netrateofenergyintake(see Pykeet al. 1977;Krebsand Cowie ingefficiency 1976,p. 99). conceptsprovidea limitedopportuandenergy-maximizer The time-minimizer They can be generalizedby fitnessisoclines nitycost evaluationof foraging. of timeand energy.In effectsof all combinations whichshowtheevolutionary can be appliedboth distinction energy-maximizer thissense,thetime-minimizer, simple,theapproach graphically to stationary and to mobileforagers. Although behaviorthancan be allows somewhatmoresubtlepredictions aboutforaging a environment obtainedfromexistingmodels.For instance,in an impoverished searchingforagermay behave as an energymaximizer.As the environment efficiency becomesricherthepredator'sdietbreadthcontractsand its foraging lineintoa portionofthefitness constraint itsoptimalforaging increases,shifting gains.Addiachievesthehighestfitness strategy mapwhereina time-minimizer seasonalor to reflect isoclinescan be manipulated theformofthefitness tionally, space weatherthefitness seasonsofinclement changes.In nonbreeding life-cycle avoidingexposure;in a will reflectthe survivalpriorities of a timeminimizer on proviis highly dependent breedingseasonoffavorableweather,whenfitness of an priorities thereproductive thefitnessset mayreflect sioningof offspring, statedabove are onlybasic energymaximizerfeedingyoung.The predictions of or theinterior at themargins ones; especiallytheydo notexplorepossibilities thefitnessmap. It shouldbe evidentthata currencybesides fitnesscan be adaptedto this

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behaviorof the foraging investigating approach.For instance,anthropologists forenergy-time utility, orpreference, energy-time can substitute hunter-gatherers fitness. of extendor refinepredictions approachcan sometimes The opportunity-cost models.The extensionsapplymainlyto the stationary the simplercost-benefit valuationof time aboutmarginal foragercase. Here one musthave information ordietbreadthchanges.The opportuandenergyinordertopredictdietbreadth, or energymaximizers modelindicatesthatorganisms thatare strongly nity-cost of willrespondto changingabundancesor pursuitefficiencies timeminimizers andtheenergyintake,butin thetimespentforaging preybyaltering highranking applymainlyto the generaltheirdietbreadthwillremainthesame.Refinements modelprovidesa unique foragermodel.Here the simplecost-benefit searching marginal bytheorganism's unaffected optimaldietbreadthprediction, valuations approachwillshowinadditionhowlong oftimeandenergy.An opportunity-cost the organismshouldforageat the optimumrateand how muchenergyit will attempt to harvest,a majoradvantage.Because themodelspecifiesan optimal itmayprovidea relativeto otheractivities, in someinterval, duration offoraging and temporal behavior betweenforaging basis forexaminingthe relationship resourcepartitioning (see Schoener1974). SUMMARY

A simplegraphicaltechniqueis presented.It relatestwo existingforaging used as proxies valuationsofthetimeand energycurrencies modelsto marginal theseproxycurrencies forfitness. Foranthropologists itis also capableofrelating toimportant ofthemodelsareresponsive Thepredictions toutility orpreference. ecologyresearch:costs in behavioral theoreticalassumptionsof evolutionary costs, oftenevaluatedat the margin.The approach are opportunity trade-offs behaviorof offersa flexibleand potentially subtlemethodof analyzingforaging hypothofsomeexisting bothstationary andmobileforagers. It leadstoextension aboutmobile, hypotheses eses aboutstationary existing and itrefines predators, predators. searching ACKNOWLEDGMENTS

I thankA. P. Covich,S. K. DeGraff,P. Gardner,M. J. Kellum,N. Pearson, H. R. Pulliam,T. W. Schoener,E. A. Smith,and thereviewersforcomments, were and encouragement. Fundsforpage chargesand forillustrations criticism, ofNorthCarolina,ChapelHill. providedby theOfficeoftheDean, University LITERATURE CITED

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