Testing the Marginal Value Theorem Using Bumblebees and Delphinium Nelsonii Author(S): Donald A

Nordic Society Oikos

The Effect of Plant Density on Departure Decisions: Testing the Marginal Value Theorem Using Bumblebees and Delphinium Nelsonii Author(s): Donald A. Cibula and Michael Zimmerman Source: Oikos, Vol. 43, Fasc. 2 (Jul., 1984), pp. 154-158 Published by: Wiley on behalf of Nordic Society Oikos Stable URL: http://www.jstor.org/stable/3544763 . Accessed: 16/09/2014 11:12

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This content downloaded from 130.15.101.145 on Tue, 16 Sep 2014 11:12:47 AM All use subject to JSTOR Terms and Conditions OIKOS 43: 154-158.Copenhagen 1984

The effectof plantdensity on departuredecisions: testing the marginalvalue theoremusing bumblebees and Delphinium nelsonii

Donald A. Cibula and Michael Zimmerman

Cibula,D. A. and Zimmerman,M. 1984. The effectof plantdensity on departure decisions:testing the marginalvalue theoremusing bumblebees and Delphinium nelsonii.- Oikos 43: 154-158.

The discrete,stochastic analog of the marginalvalue theorempredicts that bumblebeesshould respond to increasesin interplantdistance by increasingthe percentageof open flowers visited per inflorescence. This prediction was tested using Bombusflavifrons workers foraging for nectar in naturallyoccurring populations of Delphiniumnelsonii. Results suggest that bumblebees respond as predictedto reduc- tionsin plantdensity. However, under experimental conditions, bees compensated forpotentially high flight costs by visiting neighboring plants with increased relative frequency,thus reducing actual flight expenses. This result suggests that bumblebees maynot assess flight costs directly, but rather, use plant density to estimatepotential foragingcosts. At times,this method of assessmentcould yield an overestimateof foragingcosts, resulting in sub-optimaldeparture decisions.

D. A. Cibula, Dept of Biology,Syracuse Univ., Syracuse, NY 13210, USA. M. Zim- merman(correspondence), Dept of Biology, Oberlin College, Oberlin,OH 44074, USA.

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Accepted 14 September 1983 ? OIKOS

154 OIKOS 43:2 (1984)

This content downloaded from 130.15.101.145 on Tue, 16 Sep 2014 11:12:47 AM All use subject to JSTOR Terms and Conditions foragingin a naturallyoccurring population of Del- Introduction phiniumnelsonii whose density has been experimentally Many animals utilize resources that occur in discrete manipulated. clumpsor patches. An animal thatvisits many patches D. nelsonii is an ideal species for this test because duringa foragingbout mustcontinually decide whether resource presentationmeets all of the criteriaof the to remainin the presentpatch or move to another.One discrete, stochastic version of the marginal value of the questions optimal foragingtheory attempts to theorem.It is an herbaceousspecies bearingflowers on answer is: how long should a foragerremain in each a single verticalinflorescence. Thus, each plant or in- patchin orderto maximizeits rate of net energyintake florescencemay be consideredto be a single,discrete (RNEI)? patch.There is a negativecorrelation between height of Charnov (1976) addressed this question from a a floweron the raceme and standingcrop of nectar theoretical standpoint and developed the marginal (Pyke 1978b). Bees exhibitstereotypic behavior when value theoremto predictwhen an optimallyforaging foragingon thisspecies, commencing at bottomflowers animalshould leave a givenpatch and move to another. and movingup the verticalinflorescence (Pyke 1978b). The model assumesthat by feeding,a foragerdepresses Given these nectarpatterns and systematicbee move- the availabilityof food in a patch(Charnov et al. 1976), ments,it is possible forbees to estimatethe RNEI ex- thus lowering its RNEI below what it could have pected fromany floweron an inflorescence.It is thus achieved by an earlier move to anotherpatch. But, if expected that bees foragingfor nectar on D. nelsonii moves are made too soon too muchtime and energyare could use the departurerule predictedby the discrete, spenton interpatchtravel yielding a sub-optimalRNEI. stochasticanalog of the marginalvalue theorem.Such A numberof testsof the marginalvalue theoremhave behavior would be consistentwith previous studies been carriedout (Krebs et al. 1974, Cowie 1977, Pyke showingthat B. flavifronsworkers flying between (Pyke 1978a, 1982, Heinrich 1979, Hodges 1981, Zimmer- 1978c), as well as within(Pyke 1979), D. nelsoniiin- man 1981a, Best and Bierzychudek1982) and, in gen- florescencesare, in fact,foraging optimally. In addition, eral, resultsare consistentwith its predictions. Hodges (1981) and Zimmerman(1983) have shown The marginalvalue theorem,as formulatedby Char- that the departure decisions made by B. flavifrons nov (1976), is only applicable to a systemin whichan workersin responseto the standingcrops of nectaren- animal'sRNEI decreases deterministicallyand continu- counteredon D. nelsonii inflorescencesare consistent ously withtime spent foragingin a given patch (Pyke withpredictions from optimal foraging theory. 1978a). Pyke (1978a, 1981) modifiedthe model,making it applicable to a discrete,stochastic system such as animals foragingfor nectarin patches of flowers(e.g. Methods inflorescences).In this case, food occurs at fixed,discrete points (i.e. flowers)on an inflorescence,and the Fieldworkwas conductedduring June and July,1980, at amountof energyobtained at any flowermay be corre- Kebler Pass (elevation 3048 m a.s.l.), a montane lated with the amount of energyobtained at a previ- meadow in Gunnison National Forest, 11 km W of ously visitedflower (Pyke 1978a). The pertinentques- CrestedButte, Colorado. A 20 m2study plot was estab- tion is thus how many flowersper inflorescencean lished in a dense populationof D. nelsonii.All D. nel- optimallyforaging animal should visit,not how long it sonii plantswithin the plot were distinctivelymarked by should stay on each inflorescence. tyingcolored pieces of embroiderythread to theirstems The average RNEI for the habitat is a functionof and theirlocations were mapped. The numberof open timeand energycosts of interpatchmovement and thus flowerson each inflorescencewas countedevery other changesin thesecosts affect departure decisions (Cowie day. 1977). As costs of interpatchmovement increase, the B. flavifronsworkers were observed as theyforaged discrete, stochastic analog of the marginal value for nectar withinthe studyplot. As a bee flew from theorem predicts that an optimally foraginganimal plant to plant,the color codes of visitedplants and the should visit more flowersper patch because of three numberof flowersvisited were recorded. Using plant related variables. 1) As the distancesbetween flower maps and flowercensus data, foragingbouts were re- patchesin a givenhabitat increase, a foragermay travel created and the percentageof open flowersvisited per greaterdistances when movingbetween patches and, plant,flight distances, nearest neighbor status of visited thus,incur increased foraging costs (Waddington 1980). plants and interplantspacing distances were deter- 2) If otherfactors remain constant, an increasein these mined.Interplant distance was measuredas thedistance costs should resultin a decrease in the average RNEI between a plant and the nearestnonspecific individual forthe habitat.3) As thisrate is lowered,there will be havingat least one open, available flower.The nearest an increasein the numberof flowerswithin any patch at neighborstatus of a visitedplant indicates whether that which the expected RNEI exceeds the overall habitat plant was the closest or second, third,etc., closest rate. The purpose of our researchwas to test this de- neighborof the plantjust visited. parture prediction with Bombus flavifronsworkers The experimentwas divided into threephases. Dur-

OIKOS 43:2 (1984) 155

This content downloaded from 130.15.101.145 on Tue, 16 Sep 2014 11:12:47 AM All use subject to JSTOR Terms and Conditions ing phase I, foragingbouts were observedunder natur- decreasesmonotonically with plant size ( = 0.430;0 x2 ally occurringplant densities.During phase II, density = 22.61; P < 0.005; N = 145). Departurefrom of D. nelsonii was reduced by randomlybagging (with monotonicityis not significant(X2 = 2.26; 3 df; P > nylonnetting) a fractionof the population.Because the 0.10; N = 145). Themean size of visited plants (Tab. 1) nettingprevented bees fromvisiting flowers, bagged differssignificantly among phases (k-samplevan der plantswere consideredto have no available flowersand Waerdentest; W = 6.62; 2 df;0.05 > P > 0.025; N = were not censused duringthis phase. Foraging bouts 148) so plantsize was treated as a covariateand analysis were observed under thisexperimentally reduced den- ofcovariance was usedto determinewhether the mean sity.All plantswere thenunbagged and again, foraging percentageof open flowersvisited per plantdiffered bouts were observed (phase III). amongphases. Variance due to size classwas removed priorto determiningvariance due to interplantdistance (themain effect). The mean percentageof open flowersvisited per Results plantdiffers significantly among phases (Tab. 2). As Bagging plants reduced densityby 51.8% relative to predicted,during phase II, whenplant density was de- phase I and 42.7% relativeto phase III. The mean in- creasedand interplantdistances were significantly interplantdistances (Tab. 1) differsignificantly among creased,bees visited a greaterpercentage of open flow- phases (k-samplevan der Waerdentest (Marascuilo and ers per plant relativeto both controls(Student- McSweeney 1977); W = 6.36; 2 df; P = 0.042; N = Newman-Keulstest; P < 0.05). The twocontrols did 395). Mean interplantdistance for phase II is signific- notdiffer significantly from one another(Tab. 1). antlygreater than that for phase I, but is not signific- The departuredecision prediction assumes a positive antly greater than the mean for phase III (Tab. 1). relationshipbetween interplant distance and bumblebee Contraryto the design of the experiment,unbagging flightdistances. During phase II thisassumption was not plants did not quite restore plant spacing to their met.Mean flightdistances for phase II were,in fact, originalvalues. Flower mortalityover the course of the significantlyshorter than the means for both phases I studyreduced plant densityand resultedin non-signif- and III (Tab. 1), implyingthat bees flewto nearby icantdifferences in interplantdistances between phases plantswith greater relative frequency during phase II. A II and III. k-samplevan der Waerden test shows that the means of The percentageof open flowersthat bees visitedper the frequencydistributions of the nearestneighbor plantis not independentof plantsize (i.e. thenumber of statusof visitedplants (Tab. 1) differsignificantly open flowerson a plant) (X2= 24.87; 4 df; P < 0.005; N amongphases (W = 8.63; 2 df;0.025 > P > 0.01; N = = 145). A testfor trend shows thatbees visitedhigher 122). A posterioritests indicate that the mean nearest percentagesof flowerson small plants than on larger neighborstatus of visited plants for phase II is signific- plants.The percentageof open flowersvisited per plant antlysmaller than those for both phase I and III. The mean interplantdistance for phase II was, however, substantiallygreater (30.8%) thanthat for phase III, Tab. 1. Meansand sample sizes for variables measured at Ke- and mayhave been largeenough to triggerthe same Pass. bler responseby bees. Phase

I II III Discussion Interplantdistance (m) 0.110' 0.157W 0.120db Bumblebees,as predicted,adjusted their departure de- N = 170 N= 82 N= 143 cisionsduring the experimentalperiod in whichplant Plantdensity (no. plantsm2) 8.50 4.10 7.15 Flightdistance (m) 0.468W 0.322b 0.768a Tab. 2. Resultsof analysisof covarianceused to testnull N = 65 N= 39 N= 21 hypothesisthat the means forpercent of open flowersvisited per plant do not differamong phases. Plant size (numberof Nearestneighbor status 7.67' 3.03b 7.55a open flowerson visitedplants) was used as a covariate. N= 63 N= 39 N= 20 Size (no. openflowers/ Source of variation df SS MS F P visitedplant) 3.78 3.51 3.33 N= 60 N= 45 N= 24 Covariate: Percentflowers visited 42.80a 54.67b 45.65a Plant size ...... 1 0.724 0.724 18.98 0.001 N = 60 N= 45 N= 24 Maineffect: Phase ...... 2 0.369 0.185 4.84 0.009 Explained...... 2 1.093 0.364 9.55 0.001 a. Differentsuperscripts indicate values that differ between Residual...... 125 4.770 0.038 phasesat P < 0.05. TOTAL ...... 128 5.863 0.046 b.

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This content downloaded from 130.15.101.145 on Tue, 16 Sep 2014 11:12:47 AM All use subject to JSTOR Terms and Conditions densitywas significantlyreduced, and visitedincreased thoughnot predictedby the marginalvalue theorem, percentagesof blossomsbefore leaving individual flow- appears to increase foragingefficiency, but it is not eringstalks. This resultis in contrastto that foundby withoutcost. Because standingcrops of nectaron adja- Zimmerman(1981a) who also worked withB. flavi- centD. nelsoniiplants are positivelycorrelated (Pleas- frons workersas well as B. bifariusworkers. Zimmer- ants and Zimmerman1979, Zimmerman1981b), visits man (1981a) compared the mean percentageof open to nearby neighborsafter encountering a low reward flowersthat bees visitedper plantfor two plantpopula- inflorescencemay yield additional below-average re- tions differingsignificantly in density.These popula- wards. Thus, the higher flightcosts associated with tions are 8 km apart and differby 300 m in elevation. longermoves are oftenwell worthpaying. In any case, Contraryto prediction,the mean percentageof open as pointedout by Zimmerman(1981a), the behavioral flowersvisited per plant did not differsignificantly be- flexibilitydemonstrated by animalsstrongly implies that tweenthe two sites (Zimmerman1981a). The cause of those optimalforaging models predictinga shiftin any the differencebetween these two studiesis not entirely one particularbehavior in response to environmental clear. Uncontrolleddifferences between Zimmerman's conditions are too simplistic to accurately predict study sites may have had confoundinginfluences on foragingbehavior. foragingbehavior. Secondly, the mode of resource It should be pointedout thatrates of nectarproduc- presentationon Polemoniumfoliosissimum differs sub- tion and/orvolumes of standingcrop may have varied stantiallyfrom that on D. nelsonii, possibly affecting among experimentalphases. Such a change, however, bees' abilitiesto predictfuture rewards on a plant.Un- should not have had a significanteffect on bumblebee like D. nelsonii, resource presentationon P. foliosis- departuredecisions. Ollason (1980) has presentedthe simum is non-orderly;flowers appear to be scattered mathematicalverification demonstrating that departure randomlyover the plants' outer surfaces.Additionally, decisionsare actuallyindependent of the overallhabitat it is unknownwhether the correlationin nectarvolumes average reward value while Cibula and Zimmerman between adjacent blossoms on a D. nelsonii raceme (unpubl.) have confirmedthat under experimental con- (Pyke 1978b) also occurs on P. foliosissimum.These ditions bumblebees on D. nelsonii (as well as on D. factorsmay lead to differentdeparture rules for the two barbeyiand Aconitumcolumbianum) forage in a man- plant species. ner consistentwith Ollason's predictions. Althoughthe predictionof the analog of the marginal The behavioral responses observed in the present value theoremwas met duringthe experimentalphase studyalso have some relevanceto the mannerin which of the currentstudy, examination of anotheraspect of bees assess the costs of foraging.All optimal foraging bumblebee behavior suggeststhat this result may, in models assume that animals are constantlycomparing fact, be paradoxical. The predictionthat bees would theirenergetic expenditures with their energetic gains visitmore flowersper inflorescenceunder low density and makingmovement decisions based on the ratio of conditionsstemmed directly from the assumptionthat thesetwo values. The currentwork raises the possibility under such conditionsinter-inflorescence flight costs thatanother method exists. Bees maynot estimate flight would be increasedrelative to highdensity conditions. costs directly,but ratheruse an assessmentof plant Larger movementcosts should resultin foragersbeing spacingdistances as an indexof potentialforaging costs. less inclinedto leave patches(Cowie 1977, Zimmerman Bumblebee foragingduring phase II is consistentwith 1981a). Despite the fact that plant spacing distances this hypothesis.Upon enteringan area of low plant were greaterduring the experimentalphase of the pre- density,bees, in an attemptto decrease theirforaging sent study, bees flew significantlyshorter distances costs,increase theirfrequency of moves to near neigh- duringthis phase than duringcontrol periods. If re- bors and visitmore flowers per inflorescencebefore de- duced flightdistances indicate lowered inter-inflores- parting.It is possible forbees to overcompensate,how- cence flightcosts (Waddington 1980), the discrete, ever, and this is what appears to have happened in stochasticanalog of the marginalvalue theoremactually phase II. Duringthis period bees increasedtheir utiliza- predictsthat the numberof blossoms visitedper stalk tion of nearest neighborsto such an extentthat their should have been lowest during the experimental absolute flight distances were actually significantly period. Therefore, because of decreased flightdis- shorterthan duringeither control period. The number tances,this result implies that bees are not foragingin a of blossoms visitedper inflorescenceduring this time mannerconsistent with the marginalvalue theorem. period,however, was consistentwith that expected had The shorteningof flightdistances in response to a bees' flightdistances been greaterthan in the control decrease in plant densityis due to the increased fre- phases. If departuredecisions are based on a visualper- quencywith which bumblebees began to move between ception of the environmentinstead of on the actual near neighbors.Bees made the same response to low flightcosts incurred, overcompensation can thuslead to densitystands of P. foliosissimum(Zimmerman 198 la). sub-optimalforaging. The resultsof the presentstudy In both cases it appears that changes in plant density suggestthat if bees are basing departuredecisions on triggereda behavioralresponse that decreased the cost directlyestimated costs, they are not foragingin keep- of inter-inflorescencemovement. This behavior, al- ing withpredictions of the marginalvalue theorem.If,

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This content downloaded from 130.15.101.145 on Tue, 16 Sep 2014 11:12:47 AM All use subject to JSTOR Terms and Conditions on the otherhand, bees estimateforaging costs indi- Krebs,J. R., Ryan,J. C. and Charnov,E. L. 1974. Huntingby rectlyvia plantdensity, foraging models need to be re- expectationor optimalforaging? A studyof patch use by formulatedto incorporatethis behavior. Clearly, chickadees.- Anim. Behav. 22: 953-964. tests Marascuilo, L. A. and McSweeney, M. 1977. Nonparametric need to be designedthat are capableof distinguishing and distribution-freemethods for the social sciences. - betweenthese two methods of decision-makingif the Wadsworth,Belmont, CA. efficiencyof bumblebeeforaging and the utilityof Ollason, J. G. 1980. Learningto forage- optimally?- Theor. optimal models Pop. Biol. 18: 44-56. foraging are to be evaluated. Pleasants,J. M. and Zimmerman,M. 1979. Patchinessin the dispersionof nectarresources: Evidence forhot and cold spots. - Oecologia (Berl.) 41: 283-288. Pyke,G. H. 1978a. Optimal foragingin hummingbirds:Test- Acknowledgements- We are indebtedto A. Frucht,R. Gross ingthe marginalvalue theorem.- Am. Zool. 18: 739-752. and J. Pleasantsfor making needed improvementsin an earlier - 1978b. Optimal foragingin bumblebees and coevolution draftof this manuscript.This study was supportedby NSF withtheir plants. - Oecologia (Berl.) 36: 281-293. grantsDEB 80-04280 and DEB 81-01800 and by a grantfrom - 1978c. Optimal foraging: Movement patterns of the Societyof Sigma Xi. We appreciatetheir support. bumblebees between inflorescences.- Theor. Pop. Biol. 13: 72-98. - 1979. Optimalforaging in bumblebees:Rule of movement betweenflowers within inflorescences. - Anim.Behav. 27: 1167-1181. - 1981. Optimal foragingin nectar feeding animals and References coevolution with their plants. In: Kamil, A. C. and Sargent,T. D. (eds), Foraging Behavior. Garland Press, Best, L. S. and Bierzychudek,P. 1982. Pollinatorforaging on New York. foxglove(Digitalis purpurea): A test of a new model. - - 1982. Foragingin bumblebees: Rule of departurefrom an Evolution 36: 70-79. inflorescence.- Can. J. Zool. 60: 417-428. Charnov, E. L. 1976. Optimal foraging:The marginalvalue Waddington,K. D. 1980. Flightpatterns of foragingbees rela- theorem.- Theor. Pop. Biol. 9: 129-136. tive to densityof artificialflowers and distributionof nec- - , Orians,G. H. and Hyatt,K. 1976. Ecological implications tar. - Oecologia (Berl.) 44: 199-204. of resourcedepression. - Am. Nat. 110: 247-259. Zimmerman,M. 1981a. Optimal foraging,plant densityand Cowie, R. J. 1977. Optimal foragingin great tits (Parus the marginal value theorem. - Oecologia (Berl.) 49: major). - Nature,Lond. 268: 137-139. 148-153. Heinrich,B. 1979. Resource heterogeneityand patternsof - 1981b. Patchinessin the dispersionof nectar resources: movementin foragingbumblebees. - Oecologia (Berl.) Probable causes. - Oecologia (Berl.) 49: 154-157. 140: 235-245. - 1983. Plant reproductionand optimal foraging:Experi- Hodges, C. M. 1981. Optimal foragingin bumblebees: Hunt- mental nectar manipulationsin Delphinium nelsonii. - ing by expectation.- Anim. Behav. 29: 1166-1171. Oikos 41: 57-63.

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