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Hummingbirds’ concentration preferences and the energetics of nectar feeding : predictions, tests and… Roberts, William Mark 1992

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HUMMINGBIRDS' CONCENTRATION PREFERENCESAND THE ENERGETICS OF NECTAR FEEDING:PREDICTIONS, TESTS, AND IMPLICATIONSFOR OPTIMAL FORAGING THEORY AND POLLINATION BIOLOGYbyWILLIAM MARK ROBERTSB.Sc., The University of British Columbia, 1987A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF ZOOLOGYWe accept this thesis as conformingTHE UNIVERSITY OF BRITISH COLUMBIAApril 1992© William Mark Roberts, 1992In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.Department of ^ZOOLOGYThe University of British ColumbiaVancouver, CanadaDate ^27 APRIL 1992DE-6 (2/88)iiABSTRACTAn important issue in pollination biology and foragingtheory is that average nectar sugar concentrations inhummingbird-pollinated plants are less than half those preferredby birds in published choice tests. One current explanation forthis discrepancy is that low concentrations maximize birds'energy intake rates. Previous workers have suggested that birdsmay prefer low concentrations at the nectar pool volumescharacteristic of the flowers they visit, which are much lowerthan volumes used in all previous choice tests. I used threeapproaches to study this issue. I modelled hummingbird visits toflowers on three temporal scales: tongue loading, the lickingcycle, and entire visits to flowers. The nectar concentrationthat maximizes energy intake rate increases with the temporalscale of integration, so that optimal nectar concentration forthe licking cycle is higher than predicted by models thatintegrate over only the loading phase of single licks. Sincebirds must position, insert, and withdraw their bills in additionto licking nectar, the optimum at the scale of flower visits iseven higher. This "overhead time cost" of handling flowermorphology, for most non-traplining hummingbirds under mostnatural conditions, is as great or greater than the cost ofhandling nectar. My modelling suggests that for these birds, thepotential variation in the fine-scale factors that determinenectar intake rate during licking has little effect on flowerhandling time, and therefore is unlikely to determine optimalnectar concentration or the profitability of visiting flowers.iiiTo test the models' validity, I measured fine-scale parameters ofhummingbird licking with a photodetector array that monitoredmovement of the tongue and nectar pool meniscus. The resultsallowed me to reject previous hypotheses about the details oflicking, but they supported the qualitative model prediction thatoptimal nectar concentration is low at the time scale of licking.To determine whether hummingbirds prefer concentrations thatmaximize energy intake rates over the licking cycle, over feedervisits or over foraging bouts, I tested concentration preferencesat low nectar pool volume with a computer-controlled fooddelivery and activity-monitoring system. Birds preferred thehighest concentration provided, which maximized energy intakerates over foraging bouts but not over finer time scales. Thelow nectar sugar concentrations characteristic of flowerspollinated by hummingbirds are not accounted for by birds'preferences nor by the energetics of nectar extraction.ivTABLE OF CONTENTSABSTRACT  ^iiTABLE OF CONTENTS ^  ivLIST OF TABLES  viLIST OF FIGURES ^  viiACKNOWLEDGEMENTS  viiiPREFACE  ^1INTRODUCTION  ^2CHAPTER 1. THE PROBLEM OF TEMPORAL SCALE IN OPTIMIZATION:THREE CONTRASTING VIEWS OF HUMMINGBIRD VISITS TOFLOWERS  ^7The fluid mechanics of nectar intake  ^8Intake rate over the loading phase of licking  ^10Energy intake rate over the licking cycle  ^15Energy intake rate over a feeding visit  ^23Limitations of the models  ^27Nectar intake parameters in nature and the laboratory  ^28Nectar volume in nature  ^31Implications for field manipulations  ^33Implications at fine temporal scales: intake rate andoptimal concentration  ^33Implications at coarser temporal scales  ^36CHAPTER 2. LICKING BEHAVIOUR AND THE ENERGETICS OF THELICKING CYCLE  ^42Materials and methods  ^43Results  ^47Conclusions  ^51VCHAPTER 3. HUMMINGBIRDS' CONCENTRATION PREFERENCES AT LOWVOLUME AND THE ENERGETICS OF FEEDING VISITS ANDFORAGING BOUTS  ^57Materials and methods  ^57Results  ^61Conclusions  ^64DISCUSSION  ^68Implications for optimal foraging theory  ^69Implications for pollination biology  ^71BIBLIOGRAPHY ^  81APPENDIX 1. GLOSSARY OF TERMS USED IN CHAPTER 1  ^95APPENDIX 2. SAMPLE SIZES IN FIGURES 11 AND 12  ^96viLIST OF TABLESTable^ Page1. Nectar uptake parameters for hummingbirds ^292. Analysis of variance of energy intake rates duringlicking with concentration at five nectar poolvolumes ^513. Bill lengths and body weights of experimental birds ^584. Analysis of variance of energy intake rates forfeeding visits and foraging bouts ^625. Sample sizes in volume and energy intake rate graphs ^96viiLIST OF FIGURESFigure^ Page1. A hierarchy of temporal scales of hummingbirdforaging ^82. Intake rates during tongue loading as a function ofsucrose concentration ^123. Energy intake rates during the licking cycle ^164. Contour plots of the number of licks required to emptya nectar pool as a function of concentration ^205. Energy intake rate during the licking cycle for 3nectar pool volumes under constant volume andconstant frequency licking ^226. Handling times and intake rates during a feeding visitfor 4 nectar pool volumes at 4 durations ofhandling time overhead under constant volumelicking ^247. Handling times and intake rates during a feeding visitfor 4 nectar pool volumes at 4 durations ofhandling time overhead under constant frequencylicking ^258. Recession of the fluid meniscus within single visits ^489. Variation in licking behaviour within single visits ^4910. Variation in parameters of licking behaviour withconcentration ^5011. Volume intake rates for feeding visits of 4 rufoushummingbirds at five concentrations ^6212. Energy intake rates for feeding visits and forforaging bouts, and concentrationpreferences ^6313. Generalized representation of two food typescorresponding to dilute and concentrated nectar....^66viiiACKNOWLEDGEMENTSI wish to thank several people for their help and support:Lee Gass gave advice and suggestions on all aspects of myresearch and thesis. Gayle Brown and Gordon McIntyre helped withcomputer programming and bird care. My Research Committee,Robert Blake, John Gosline and Carl Walters, provided suggestionsfor my experiments and thesis. Robert Blake also generouslyallowed me to use his digital oscilloscope. Don Brandys providedthe technical expertise to design and build the electronichardware used in my experiments. Tom Daniel enthusiasticallyresponded to work in progress and suggested future directions.William W. Roberts drew the equations. Andrew Fedoruk edited thepenultimate draft of the thesis. The following providedassistance with previous versions of the manuscript "The problemof temporal scale in optimization: three contrasting views ofhummingbird visits to flowers": D. Armstrong, G. Brown, W.Calder, L. Carpenter, R. Colwell, P. Feinsinger, F. Gill, F. R.Hainsworth, J. Kingsolver, G. McIntyre, R. Mitchell, G. Pyke, L.Rowe, R. Russell, G. Sutherland, S. Tamm, D. Taneyhill, H.Tiebout, J. Thomson, N. Waser, and R. Ydenberg all offeredhelpful comments. A. Blachford, G. Landon, and D. Ludwig offeredprogramming suggestions, and F. L. Carpenter, F. R. Hainsworth,R. Mitchell, and R. Montgomerie kindly lent unpublished data.This research was supported by NSERC operating grant 58-9876 toC. L. Gass.C. Lee Gass1PREFACEChapter 1 and portions of the Introduction and Discussion ofthis thesis were derived from the manuscript, "The problem oftemporal scale in optimization: three contrasting views ofhummingbird visits to flowers", by Clifton Lee Gass and W. MarkRoberts, in press in The American Naturalist. I contributed themodels and their predictions about the effect of time scale onoptimal concentration to this manuscript, and Lee Gasscontributed the consideration of nectar parameters in nature andthe majority of the literature research. We were jointlyresponsible for all writing and graphics.Signed,Date:^A2INTRODUCTIONA central notion of optimal foraging theory is that throughevolution and/or learning, animals perform actions that increasetheir fitness. It has long been recognized that both costs andbenefits of actions must be considered (MacArthur and Pianka1966; Emlen 1966; Schoener 1971), but it has not always beenclear what combination of costs and benefits may be optimized bya given animal in a given situation. Identifying costs andbenefits and defining appropriate currencies is a criticalproblem (Pyke 1984; Stephens and Krebs 1986; Possingham 1989),and great effort has gone into its solution.It is particularly difficult to know over what temporalscale the costs and benefits of behaviour should be considered(Templeton and Lawlor 1981), especially since their consequencescan be significant on a vast hierarchy of scales (e.g. Gass andMontgomerie 1981; Orians 1981; Allen and Starr 1982).Investigators usually use their biological intuition to selecttemporal scales (Stephens and Krebs 1986), but they may singleout different temporal scales in the same system because theirintuition is informed by different experience (Pyke and Waser1981). Ignoring this fact can confound attempts to understandthe economics of foraging. Stephens and Krebs (1986, Box 2.1)made this general point with a simple hypothetical example. Inthis thesis I make the point again in more detail, using bothoptimal foraging models and experiments to apply it to a realbiological example, hummingbirds feeding at flowers.3Nectarivorous animals and the flowers that they visit areconvenient systems in which to test foraging theory. Flowers areconspicuous and stationary, and the caloric value of nectar isreadily quantifiable (e.g. Bolten et al. 1979; Trombulak 1990).Metabolic costs of a variety of activities have been measured inmany nectarivores, most notably hummingbirds (Pearson 1950;Hainsworth and Wolf 1972a; Beuchat et al. 1979; Epting 1980;Powers and Nagy 1988; Suarez et al. 1990; Powers 1991).Hummingbirds also respond rapidly to perturbations of conditionswhich influence their energy balance, so they have proven to bewell-suited for testing important issues in optimal foragingtheory (e.g. DeBenedictis et al. 1978; Pyke 1978a; Hixon andCarpenter 1988; Mitchell 1989; Tamm 1989).Considerable attention has been focussed on the significanceof the low sugar concentrations prevalent in most hummingbird-pollinated plants' nectar (e.g. Baker 1975; Bolten and Feinsinger1978; Pyke and Waser 1981; Calder 1979; Heyneman 1983; Kingsolverand Daniel 1983; Plowright 1987; Sutherland and Vickery 1988).Sugar concentrations in flowers visited primarily by hummingbirdstypically average 20 - 25 % sucrose equivalents (allconcentrations reported are wt/wt), similar to the dilute nectarsof butterfly-pollinated plants, but lower than meanconcentrations of over 35 % in bee-pollinated flowers (Baker1975; Pyke and Waser 1981; Heyneman 1983). One tropical plantproduces nectar with a mean concentration of 24 % whenhummingbirds visit it. Then, after its flower corollas fall, it4secretes nectar with concentrations of 41 - 51 % that is consumedby ants which presumably guard the plant (Gracie 1991).Floral characteristics of animal-pollinated plants appear tobe closely coadapted with the behavioural, physiological andmorphological characteristics of their pollinators. Flowercolour (Miller and Miller 1971; Raven 1972; Stiles 1976;Bleiweiss 1990; Weiss 1991), and patterns of flower arrangementand nectar abundance in flowers (Whitham 1977; Pyke 1978b;Eckhart 1991; Itino et al. 1991) frequently correspond topollinators' preferences and movement patterns. The sugar andamino acid composition of plants' nectar appears to be suited tothe digestive constraints and nutritional requirements of thespecies that visit and pollinate them (Baker and Baker 1973,1983, 1986; Gryl et al. 1990; Martinez del Rio 1990a,b; Freemanet al. 1991; Galetto 1991; Erhardt 1991a; but see Alm et. al1990; Martini et al. 1990; Erhardt 1991b). Corolla morphologyoften provides a close fit to pollinators' bill or tongue sizeand shape (Feinsinger and Colwell 1978; Gill and Wolf 1978; Snowand Snow 1980; Nilsson 1988; Colwell 1989; Fenster 1991).Given this close correspondence between othercharacteristics of plants and the preferences of theirpollinators, it is incongruous that in choice tests hummingbirdshave not preferred artificial nectars as dilute as those offeredby the plants they visit, but have instead chosen concentrationshigher than 45 % (Van Riper 1958; Stiles 1976; Pyke and Waser1981; Tam and Gass 1986).5Hummingbirds feed by licking with their forked, open-groovedtongues, into which nectar flows by capillary action (Weymouth etal. 1964; Hainsworth 1973; Ewald and Williams 1982). Increasingconcentration increases nectar's caloric value and also increasesits viscosity and thus decreases its fluid flow rate into thetongue grooves. Kingsolver and Daniel (1983) modelledhummingbird licking and predicted that the sugar concentrationwhich optimizes birds' energy intake rates is 20 - 25 % sucrosefor feeding on low nectar pool volumes, but 35 - 40 % for feedingon high volumes. Under this model, therefore, the discrepancybetween nectar concentrations in nature and birds' observedchoices might be an artifact, because volumes in most NorthAmerican flowers are small (Chapter 1), whereas all publishedchoice tests have used large volumes, usually infinite from thebirds' point of view.The details of nectar uptake by hummingbirds are criticalfor models which predict optimal nectar sugar concentrations(Pyke and Waser 1981; Heyneman 1983; Kingsolver and Daniel 1983).Observing these details, however, has been hampered by the highfrequency at which hummingbirds lick (Ewald and Williams 1982;Paton and Collins 1989) and by the small size of their bills,tongues and both the nectar pools and the flowers that theyvisit. Consequently, key assumptions of nectar feeding modelshave not previously been tested.In this thesis I investigate Kingsolver and Daniel's (1983)models within a conceptual framework of hierarchies of temporalscale. I also present measurements of parameters of licking at a6range of concentrations and nectar pool volumes, and test keyassumptions of the models. Finally, I report results ofconcentration preference tests for hummingbirds at realisticallylow nectar pool volume. My findings challenge existinginterpretations of patterns of nectar sugar concentration innature, and demonstrate the critical importance of identifyingappropriate time scales in both predictions and tests of optimalforaging theory.7CHAPTER 1THE PROBLEM OF TEMPORAL SCALE IN OPTIMIZATION:THREE CONTRASTING VIEWS OF HUMMINGBIRD VISITS TO FLOWERSHere I show that different pictures of profitability emergefrom analyses of visits by hummingbirds to flowers on threetemporal scales that differ over a narrow range. Thesedifferences are sufficiently great to affect the design ofinvestigations and to alter conclusions about the evolution ofplants and their pollinators.The daily activity budgets of hummingbirds could be analyzedon several different temporal scales (Fig. 1). Most studies ofoptimal nectar concentration have considered flower visits(Hainsworth and Wolf 1976; Stiles 1976; Pyke and Waser 1981;Heyneman 1983; Kingsolver and Daniel 1983; Montgomerie 1984; Tammand Gass 1986; Stromberg and Johnsen 1990). Some studies haveexamined visits to inflorescences or plants (Pyke and Waser1981), and foraging bouts (Tamm 1989). I consider three temporalscales -- all within flower visits.At the finest scale I explore the fluid mechanics of nectarloading by a hummingbird's tongue while it contacts a pool ofnectar during a single lick, re-examining previous conclusionsabout the nectar concentration that maximizes loading rate. ThenI show that this optimal concentration increases systematicallyas the analysis is extended in time, for example to include bothloading and unloading phases of the licking cycle. At thecoarsest scale I consider the duration of entire visits toFORAGINGCYCLEFORAGINGBOUTperchn <hungry ?›y4fly to patchfly to flower1insert bill4<withdraw bill ?›4 y4 n^< satiated ?›Y 4fly to perchinsert tonguewithdraw tongueFLOWERVISITLICKINGCYCLE8flowers, including time not spent licking, over a range ofconditions.Figure 1. A hierarchy of temporal scales of hummingbirdforaging.The fluid mechanics of nectar intake Hummingbirds lick nectar from flowers with their forked,open-grooved tongues (Weymouth et al. 1964; Hainsworth 1973).Nectar enters the grooves by capillary action during the tongueloading phase of the licking cycle, while the tongue contacts thenectar pool (Hainsworth 1973; Ewald and Williams 1982). During9the unloading phase, the tongue retracts into the bill, whichsqueezes nectar into the mouth as the tongue extends for the nextlick (Ewald and Williams 1982).^Ewald and Williams (1982)estimated average licking frequency of Anna's hummingbirds(Calypte anna) at an artificial feeder to be 13.8 Hz, with amaximum of about 17 Hz.The energy content of nectar approximates a linear functionof sugar concentration by weight (but an accelerating function ofconcentration by volume; Bolten et al. 1979). Nectar viscosityis an exponentially increasing function of concentration, and asa result, volume flow rate decreases with concentration. Thecombination of increasing caloric content per unit volume anddecreasing volumetric intake rate with increasing sugarconcentration causes energy intake rate to peak at anintermediate concentration. At each time scale I consider, Irefer to this as the optimal concentration.Two theoretical models based on different assumptionspredict this optimum. Heyneman's (1983) steady-state, continuousnectar flow model (which applies to the loading phase only)predicts an optimum of 22 - 26 % sucrose by weight, butKingsolver and Daniel (1983) pointed out that nectar flow is notat steady state if induced by capillarity. Under this condition,flow rate is extremely high initially and decreases rapidly withtime. Their more realistic capillarity-induced, discontinuousflow model (which applies to the complete licking cycle) predictsoptima of 40 - 45 % when feeding from high volume nectar poolsrequiring many licks to empty. For small volumes that can be10loaded on a single lick, however, description of fluid flowrequires no unloading phase, so the two models convergemathematically and predict the same low optimal concentration.My aim here is to assess the significance of the biophysicalmodels when applied on longer time scales than those for whichthey were derived.Kingsolver and Daniel (1983) considered two of the manypossible licking behaviours that hummingbirds might employ. Intheir "EL" licking, the tongue loads to a constant volume acrossall concentrations; I refer to this as CV (constant load volume)licking. Loading time must increase with increasingconcentration because flow rate decreases. If unloading timeremains constant, then licking frequency must decrease. InKingsolver and Daniel's (1983) "ET" licking, frequency and itscomponents, loading and unloading time, are constant acrossconcentration; I refer to this as CF (constant frequency)licking. Again because flow rate decreases with increasingconcentration, volume loaded per lick must also decrease.Although real hummingbird licking behaviour is unlikely toprecisely follow either of these patterns, I restrict my analysesto them in order to enable comparisons with Kingsolver andDaniel's (1983) model results.Intake rate over the loading phase of lickingNectar flow during the loading phase of the licking cycle isessentially what Heyneman (1983) modelled. It is not surprising,therefore, that the 22 - 26 % optimal sugar concentration she11predicted accords with Kingsolver and Daniel's (1983) predictionexplicitly derived for loading. The dynamics of loading the twogrooves of a hummingbird tongue are described by(1) Vand(2) Enr3ycos8141Trr3ycos8epS PA(modified from Equation 8 in Kingsolver and Daniel 1983). V isvolume intake rate, E is energy intake rate, r is tongue grooveradius, and 1 is the distance to which nectar flows into thetongue grooves. All other symbols describe physical propertiesof sucrose solutions (see Appendix 1 for definitions).Holding loading distance, 1, constant in Equation 2 is thecondition for constant volume licking. Throughout my analyses ofCV licking, I assume 1 is tongue groove length, l g ; i.e. that thegrooves are filled completely. The solid curves in Figure 2depict the loading phase for a bird that exhibits this behaviour.Volume intake rate decreases rapidly with concentration, due toincreasing viscosity, g. The ascending portion of the energyintake rate curve (Fig. 2b) results from the increasing caloriccontent of food, Eps, while volume flow rate is still high. Thedescending portion at high concentration results from very lowflow rate, in spite of high caloric content. Inspection ofN/ \ \NB\N N20^40^60^800.---. 75E-< 50Z 250 012DURATION OFLOADING PHASE^28 42^83 ms30E.r4 20z10NECTAR CONCENTRATION (%)Figure 2. Intake rates during tongue loading as a function ofsucrose concentration. The solid curves describe constantvolume licking, and the broken curves, constant frequencylicking for three different values of tongue loading time.Arrows indicate the maximum concentrations at which thetongue can load completely under constant frequency licking.Tongue groove parameters are for rufous hummingbirds(Selasphorus rufus); r = 0.16 mm, lg = 11.8 mm (WMR,unpublished data).13Equation 2 reveals that although energy intake rate varies withtongue groove radius and nectar loading distance, optimalconcentration is insensitive to both (Kingsolver and Daniel1983). Optimal concentration is also independent of metaboliccosts, which displace the curves downward without changing theirform when subtracted from E. Therefore, an optimal concentrationof 23.6 % for tongue loading under CV licking should be generalacross hummingbird size and morphology under these assumptions.Suppose, however, that hummingbirds cannot adjust loadingtime to hold lick volume constant across concentrations, andinstead exhibit constant frequency licking and constant loadingtime, T1. Two cases are possible. Viscosity may be low enoughto allow complete tongue loading during the loading phase, sothat nectar loading distance equals tongue groove length,(3a) 1 = 1gas I assumed for CV licking. Alternatively, viscosity may be toohigh to allow complete loading during T1 (i.e. 1 < l g), so that 1is limited by fluid dynamics instead of by l g :(3b) i . V rycoseT2i.L(which is Equation 3b of Kingsolver and Daniel 1983). For eithercase14E^2nr2lEpS TtThe broken lines in Figure 2 illustrate the effect on volumeand energy loading rates of switching from complete to incompleteloading (switching from my Equation 3a to 3b) at particularconcentrations for three different values of loading time, Tl.Note that this switch occurs where the broken curves for constantfrequency licking intersect the solid curves for constant volumelicking. By definition, the CV curves result from modulation ofloading time to allow exact, complete filling of the tonguegrooves. At concentrations at which intake rates are less for CFthan for CV licking (to the left of the solid CV curve in Figure2a), loading time is longer than required to fully load thetongue. This wasted time results in lower intake rates thancould be achieved were the bird not constrained to a fixedlicking frequency with a fixed loading time. At concentrationsabove this threshold, volume and energy loading rates are higherfor CF than for CV licking.It is counterintuitive at first that intake rates should begreater under conditions that do not allow complete loading, butbecause loading rate decreases dramatically with loading time(Equation 4), birds achieve higher rates during the loading phaseif they load for less time and thus take smaller volumes perlick. For this case, the optimal concentration is higher for CFthan for CV licking. The conclusion that optimal concentrationduring the loading phase is sensitive to details of licking(4)15behaviour probably extends to patterns of licking other than thetwo considered here (see Kingsolver and Daniel 1983).Energy intake rate over the licking cycleThe previous section dealt with the loading phase only.Strictly speaking, "intake" has not yet occurred at this stage,as the nectar has yet to be removed from the tongue and ingested.Some time, Tu , is required to unload the tongue grooves on eachlick, and including it in the rate averaging functions increasesthe optimal concentration.Licking from a non-depleting nectar pool. High volumeartificial feeders typically used in tests of concentrationpreference and intake rate offer more food than birds can consumein a visit, and every lick can load the same volume of nectar.When averaged over all licks, therefore, intake rates at such"infinite" sources are equivalent to those for volumes that areexact multiples of tongue loading volume and can be consumedduring single visits.For constant volume licking, energy intake rate over thecomplete cycle is( 5 ) E - 277r2tepS {-2El  11- Tury c o s 8(incorporating Equation 3a of Kingsolver and Daniel 1983 in thedenominator).A20^40^60^0^20^40SUCROSE CONCENTRATION (%)20a10zaz00B60 8016Figure 3a shows the effect of unloading time, T u , on energyintake rate.^Equation 5 reduces to Equation 2 when Tu = 0, sothe uppermost curve in Figure 3a is the same as the solid curvein Figure 2b. Note that optimal concentration is sensitive toeven small increases in Tu , which shift it upwards. At T u = 25ms, near the 30 ms estimated for C. anna (Ewald and Williams1982), optimal concentration is 28.9 %. The curves areincreasingly flat with increasing Tu , because the added timedepresses intake rate. Hummingbirds would have to be moreCONSTANT VOLUME^CONSTANT FREQUENCYFigure 3. Energy intake rates during the licking cycle. Thecurves indicate six unloading durations under constantvolume licking (unloading time, Tu ; ms), and six lickingfrequencies under constant frequency licking (frequency,f; Hz). Tu is 42 ms at 12 Hz constant frequency licking,and this is comparable to Tu = 50 ms under constant volumelicking (bold curves). The bold line connecting the peaksof the curves illustrates the upward shift in optimalconcentration with increasing Tu or decreasing f. Tonguegroove parameters are as before.17sensitive at long than at short Tu to discriminate amongconcentrations on the basis of energy flux. This is equivalentto concluding that in order to select optimum nectarconcentration, hummingbirds would require greater sensitivity todifferences in energy intake rate if they evaluated intake overthe entire licking cycle rather than over the loading phase only.Under constant frequency licking, the proportions of thecycle taken up by the loading and unloading phases could vary atany given licking frequency, f. Kingsolver and Daniel (1983)concluded that energy intake rate is maximized when the loadingand unloading phases are exactly equal in duration; when tongueloading time is half the licking cycle and intake rates areaveraged over the period of the cycle, 1 / f. Substituting thisin the denominator of Equation 4 yields( 6 )^ E. 2nr2lEpSfThis doubling of the time constant in Equation 4 producesthe same form of relationship between energy intake rate andconcentration as shown in Figure 2; it merely halves theamplitude of the curves (Fig. 3b). Optimal concentrationtherefore varies in the same manner for both the loading phasealone and the complete licking cycle under CF behaviour. Formost plausible licking frequencies, optimal concentration is35.7 %; however, if Hainsworth's (1973) report of 2.7 Hz lickingby black-chinned hummingbirds (Archilochus alexandri) is accepted18(but see Ewald and Williams 1982), optimal concentration could behigher than 43 %.Licking from a depleting nectar pool. The precedinganalysis lacks realism in that I have imagined birds feeding fromnectar pools which are either infinite or contain integralmultiples of lick volume. Flowers are not this obliging innature, so volume loaded per lick, V1, must vary, at least on thelast lick, which loads whatever nectar has not been alreadytaken. The assumption that hummingbirds remove all nectar isapproximately satisfied in many systems (e.g. Gass andMontgomerie 1981; Wolf and Hainsworth 1983), but since there areimportant exceptions (e.g. Whitham 1977; Wolf and Stiles 1989) itshould always be tested in practice. Because empirical studieshave demonstrated that handling time approximates a direct linearfunction of nectar pool volume (Hainsworth and Wolf 1972b; Wolfet al. 1972, 1975; Wolf 1975; Wolf and Wolf 1976; Gass andMontgomerie 1981), this variable must be a component of analysesof intake rate optimization.If nectar pool volume, Vp , is less than meal size, the totaltime spent licking increases in stepwise fashion with the numberof licks, n, required to load it. If I assume that all licksload the same amount, except for the last if pool volume is notan integral multiple of tongue loading volume, then for both CVand CF licking, n = Vp / V1, rounded up to the nearest wholelick. I shall also assume that the last lick takes as much timeas each of the previous ones, even when it does not obtain asmuch nectar.19Under constant volume licking, loading time is modulated tomaintain constant tongue loading volume at all concentrations.Under constant frequency licking, however, loading volumedecreases with concentration. If either concentration or lickingfrequency are low enough, the tongue can load fully in less thanor exactly the duration of the loading phase. Under myassumptions, V1 would then be the tongue groove capacity, 2yr 2 1g .At concentrations and/or frequencies too high to permit fullgroove loading,( 7 ) %ft r. 27Tr2 _ ^rrcose94/4.1For CV licking, the number of licks, n, is invariant withconcentration for a given nectar pool volume, VP (Fig. 4). Thenumber of licks is a complex function of concentration and volumeunder CF licking, however. The discontinuity between thestraight and curvilinear segments of the isopleths marks themaximum concentration at which viscosity is still low enough toallow complete groove loading over the loading phase, T1.Consider low frequency licking, 6 Hz, from low concentrationnectar. Under this condition, viscosity is low enough andloading rate high enough that the tongue can fully load in lessthan or exactly T1. In this example the tongue loads fully atall concentrations less than 33 %. This threshold is reached atlower concentration at higher frequency, because less time is84.1 60 4—400 2ra_.040^0^40^0^40^80NECTAR CONCENTRATION (%)41 50 584 4 4\^\ \3 3 32 2 21 1 1841 60 4,_.00 2ci.0020CONSTANT VOLUMETu = 250^100^404^ 4^ 43^ 3^ 32^ 2^ 2CONSTANT FREQUENCYF = 6^12^18Figure 4. Contour plots of the number of licks, n, required toempty a nectar pool, Vp , as a function of concentration.Panels indicate three values of unloading time, Tu (ms),under constant volume licking, and frequency, f underconstant frequency licking. For clarity, I graph only thefirst ten licks for constant frequency licking, numberingonly the first four, and include maximum n (at maximum V 13,and concentration) in the corner. Vertical lines indicatethe maximum concentration at which the tongue can loadcompletely during loading time, T1, under constant frequencylicking. Tongue groove parameters are as before, with V1 =1.9 gl for rufous hummingbirds (WMR, unpublished data).21available for loading, so that tongue loading is complete onlybelow 9 % at 18 Hz.Including nectar pool volume in energy intake ratecalculations produces dramatic, qualitative differences betweenconstant volume and constant frequency licking behaviour. Forthe former,(8)V E pSE- P^n[ILE + Tr7COSe UjIf nectar pool volume, Vp , is not an integral multiple of tongueloading volume, V1, the last lick takes less volume than previouslicks. This is equivalent to decreasing loading distance, 1, inEquation 8. As noted above, optimal concentration is insensitiveto variation in tongue groove parameters for CV licking (Fig.5a). However, decreasing pool volume decreases average energyintake rate at all concentrations, because the diminishedenergetic return of the last lick is an increasing proportion oftotal harvest.For CF licking, the energy intake rate isE .  VpEpSf nwhere n is derived using tongue loading volume, V1, from Equation7. Note that the increasing portions of the energy intake ratecurves in Figure 5b are not straight, but slightly concave(9)A8040 6020^40^60^0^20SUCROSE CONCENTRATION (%)12<4 6z0z00B22upwards. This is because sugar content per unit volume is anexponential function of concentration (wt/total wt). Therelationship between energy intake rate and concentration isextremely complex at all realistic pool volumes (Fig. 5b).Consider the curve for 1 Al of nectar in the 12 Hz exampleillustrated in Figure 5b. Beginning at 0 %, energy intake rateincreases steadily with concentration up to a threshold beyondwhich viscosity is so high and loading rate so low that the 42 msloading phase is insufficient to load the pool on one lick. At aslightly higher concentration, another lick is required to loadCONSTANT VOLUME^CONSTANT FREQUENCYFigure 5. Energy intake rate during the licking cycle for threenectar pool volumes, VD (Al), under constant volume andconstant frequency licking. The vertical line connectingthe peaks of the curves for constant volume lickingillustrates the independence of optimal concentration and V Punder this behaviour. For constant volume licking,unloading time (Tu) = 50 ms, and for constant frequencylicking, frequency (f) = 12 Hz. Tongue groove parametersare as before.23the miniscule residual volume. Since intake is now averaged overtwo licks instead of one, it drops sharply. This sawtoothpattern continues as concentration increases and more licks arerequired to remove the same volume.The curves are less jagged at greater pool volume becausethe energetics of the last lick play a decreasing role in theenergetics of the visit as volume increases. The family of"curves" for any licking frequency are all bounded by the case inwhich nectar pool volume is infinite, which for the caseillustrated in Figure 5b is analogous to that described by thecurve for f = 12 Hz in Figure 3b.Energy intake rate over a feeding visit Handling time at flowers, Th, is longer than required tolick nectar. The bird must position its bill and insert it intothe flower corolla at the start of the visit, and withdraw it atthe end. The time required to do this, Ti, is an overhead costpaid regardless of the amount of nectar in the flower. AlthoughTi varies with flower and bird morphology (Wolf et al. 1975) andexperience (unpublished observations; see also Laverty 1980 forbumblebees), and should also vary with bird agility, it should beindependent of licking behaviour.Including the overhead cost of handling flowers, Ti, inanalyses of feeding energetics for CV and CF licking results inVpepS(10)^E -n 2µt2+ TU] + TirycoseTi = 0.0 0.5 1.0 1.524andrespectively. Increasing Ti always decreases energy intake ratesover feeding visits.Adding Ti also increases optimal nectar concentration forboth types of licking (Figs. 6 and 7), for the same reason thatadding unloading time shifts the optimum upward in constant43HANDLINGTIME(s)230VOLUME 20INTAKE RATE(Alb) 10129ENERGYINTAKE RATE 6(W)300^40^0^40^0^40^0^40^80SUCROSE CONCENTRATION (7.)Figure 6. Handling times and intake rates during a feeding visitfor four nectar pool volumes, VD , at four durations ofhandling time overhead, Ti, under constant volume licking.From top to bottom in each panel, curves indicate VD = 10,2.5, .5 and 0 gl. Unloading time (Tu) = 50 ms and tonguegroove parameters are as before.25Ti = 0.0^0.5^1.0^1.543HANDLINGTIME^2(s)30VOLUME^20INTAKE RATE10129ENERGYINTAKE RATE 6(W)300^40^0^40^0^40^0^40^BOSUCROSE CONCENTRATION (7.)Figure 7. Handling times and intake rates during a feeding visitfor four nectar pool volumes, Vp , at four durations ofhandling time overhead, Ti, under constant frequencylicking. From top to bottom in each panel, curves indicateV = 10, 2.5, 0.5 and 0 gl. f = 12 Hz and tongue grooveparameters are as before.volume licking (Fig. 3a). In both cases, time is added to thedenominator of a relationship that generates a rate acrossconcentration. Because tongue loading time, the other term ofthe denominator, increases with concentration, the added timeinfluences the rate proportionally less at high concentration.In other words, the overhead cost of handling flowers enhancesthe advantage of the high caloric quality of concentrated nectarby offsetting the disadvantage of slow loading. The optimumshifts upward at all pool volumes but more so at low than at highvolume; fewer licks and less time are required to harvest small26nectar pools, so the overhead is a larger proportion of totalhandling time (Figs. 6 and 7).Adding the overhead time also reduces the jaggedness of thecurves that describe constant frequency licking (Fig. 7), for thesame reason that it affects optimal concentration. The heightsof all steps of all handling time curves at each Ti are equal,because each extra lick adds a constant amount of time regardlessof nectar volume or concentration. The curves become smootherwith increasing overhead time, however, because these incrementsin duration are relatively smaller proportions of total handlingtime at high than at low Ti. As with the shift in optimalconcentration, curve smoothing is more pronounced at low than athigh volume, because the overhead time is a larger proportion oftotal handling time.Although energy intake rate, optimal concentration, and thecomplexity of the intake rate curves are all sensitive tovariation in both nectar pool volume and the overhead cost ofhandling flowers at all values of these parameters, they are mostsensitive at combinations of low volume and low overhead.Increasing overhead slightly has a large effect on intake ratewhen overhead and pool volume are both near zero and far lesseffect when they are large.In general, overhead time reduces the influence of fluiddynamics and the details of licking behaviour on optimal nectarconcentration, and increases the relative importance of the grossenergy return from feeding visits. As energy intake rate isconsidered over successively longer time scales, from the loading27phase up to complete visits, optimal concentration shiftsupwards. The time scale over which hummingbirds average energyintake rate, if indeed this is the currency to which theyrespond, must play a major role in determining optimal nectarconcentration.Limitations of the models Following Kingsolver and Daniel (1983), my models assumethat only the tips of the tongue grooves contact the nectar pool.If more of the tongue were immersed, as it routinely is atfeeders, fluid might enter the open grooves along their length,possibly speeding loading (Hainsworth 1973; Kingsolver and Daniel1983; Feinsinger 1987; Paton and Collins 1989). This issupported by Montgomerie's (1984) conclusion from high-volumelaboratory tests that handling time is a decelerating positivefunction of volume. Nectar might also adhere to the externalsurface of the tongue. Such factors should increase optimalconcentration by releasing nectar loading rate from theconstraints of fluid dynamics, i.e. from viscosity. Therefore,these models are most applicable to flowers with small nectarpools or long corollas, which do not allow appreciable immersion.It is probably unrealistic to assume that hummingbirds lickat one constant frequency throughout a feeding visit, that theymaintain this frequency across all concentrations, and that theloading and unloading phases are equal. I expect that evenwithin a single visit these components would vary, for instanceto adjust for the receding fluid meniscus during licking. Tongue28loading volume should be greater with deeper immersion, butdecrease during licking as the pool is depleted (see above, andFeinsinger 1987). However, no experimental evidence yet existsto allow discrimination between constant volume, constantfrequency, or other possible licking behaviours. I havearbitrarily adopted the assumption of equal loading and unloadingphases in CF licking to preserve compatibility with Kingsolverand Daniel's (1983) analysis.The assumption that intake rate during the licking cycledoes not vary with overhead cost (in reality, that intake rate isindependent of flower morphology) is unrealistic. Tongueimmersion depth and/or loading time should decrease for a givenpool volume with tongue extension distance and therefore withflower corolla length. Handling time increases dramatically onlynear maximum corolla length (Wolf and Hainsworth 1971;Montgomerie 1984; Temeles and Roberts, in review), so immersiondepth may be partly conserved, but it must decrease to zero atmaximum extension. Intake rate would still decrease if birdsconserved loading time by decreasing licking frequency as tongueextension increased (Ewald and Williams 1982). Insufficientinformation is available to evaluate this assumption rigorously.Nectar intake parameters in nature and the laboratoryNectar intake parameters in Table 1, for real birds atflowers and feeders, suggest some general patterns to considerwhen interpreting my theoretical results. First, intake over thelicking cycle is typically slower at flowers than at high volumeTable 1. Details of estimates of nectar uptake parameters for hummingbirds.Bird Species Sex Weight(g)Bill(mm)Plant Species Corolla(nun)Vp40V(Ws)Ti(s)Source NotesHermits at flowersPhaethornis superciliosus ? 6.0 37 Heliconia tortuosa 48 -20-120 2.6 1.26 Wolf et al. 1972 aP. superciliosus ? 6.0 37 H. rostrata 40 -20-120 4.0 1.3 Wolf et al. 1972 aP. superciliosus ? 6.0 37 H. imbricata 25 -20-120 3.7 0.8 Wolf et al. 1972 aThalurania furcata ? 4.5 19 H. imbricata 25 -20-120 7.7 1.11 Wolf et al. 1972 aNon-hermits at flowersSelasphorus rufus F -3.5 -17 Castilleja miniata -26 0-10 8.3 1.22 Gass and Montgomerie 1981 bS. rufus F -3.5 -17 Ipomopsis aggregata 26 0.5-20 23.3 0.37 R. Mitchell. pers. comm. cS. flammula ? 2.7 12.8 Tropaeolum sp. 10-12 0.03-0.35 13 0.03 Hainsworth and Wolf 1972 b dArchilochus alexandri F -3.3 -23 Penstemon barbatus -10-12 0.14 1.0 0.84 F.R. Hainsworth, pers. comm. dA. alexandri M -3.3 -23 P. pseudosFectabilis 25-30 02-5.35 4.35 0.35 F.R. Hainsworth, pers. comm. dA. alexandri F -3.3 -23 P. pseudospectabilis 25-30 0.1-4.3 5.56 0.35 F.R. Hainsworth, pers. comm. dA. alexandri M -3.3 -23 Bouvardia ternifolia 20-35 0.18-3.9 3.11 0.32 F.R. Hainsworth, pers. comm. dCynanthus latirostris M -3.2 18-21 P. pseudospectabilis 25-30 0.5-4.8 8.33 038 F.R. Hainsworth, pers. comm. dEugenes fulgens M 8.3-10 31-32.4 P. pseuodspectabllis 25-30 ? 5.88 0.58 F.R. Hainsworth, pers. comm. dAmazilia tzacatl ? 5.0 20 IL imbricata 25 20-120 4.3 0.7 Wolf et al. 1972 d1121111211111ILlitallE. fulgens M 8.3-10.0 31-32.4 feeder 10 0-20 46.0 0.28 Hainsworth et al. 1983 eS. rufus F 3.5 -17 feeder 13.5 0-20 23.1 0.52 This study fS. rufus F 33 17 feeder 7 0.5-20 24.4 0.44 R. Mitchell, pers. comm. c30Table 1, Notes: In every case, V is the reciprocal of b in therelationship Th = Ti + bVp .indicates that the parameter was not given in the source; itwas estimated from related studies by the same authors, frompopulation figures in other sources, from field notes, orfrom personal communications.a d Th estimated in the field by stopwatchmovie frames. VP estimated indirectlymeasured time since last visit to eachmean of hourly nectar production rate.included in calculations.and/or by countingas the product offlower and populationRevisits notb^Th estimated in the field by stopwatch, beginning at dawn.V manipulated by adding 5 or 10 Al of sucrose solution tosamples of flowers during the night. Each sample wasassumed to contain the amount added plus the population meanat dawn for unmanipulated flowers. Revisits were includedin calculations, but were few.Th estimated in the field by stopwatch. Vpadding sucrose solution to empty flowers or manipulated byfeeders.efTh estimated in the laboratory for 0 and 20 Al by countingmovie frames.Th measured automatically in the laboratory by computer,which monitored a photodarlington triggered by the bill oninsertion and withdrawal. Vp = 0 , 2 , 4, 6 , 8 , 10, 15 or20 Al. Mean for three birds.feeders. Thirteen of 14 volume intake rates at flowers are lessthan 10 Al/s and 8 are less than 5 Al/s, but all rates at feedersare greater than 23 Al/s. Second, the intake rate of a givenhummingbird species varies with plant species. For example,rufous hummingbird (Selasphorus rufus) females drank 2.8 timesfaster at scarlet gilia (Ipomopsis aggregata) than at Indianpaintbrush (Castilleja miniata). Third, overhead time variesgreatly among flowers: from near 0 s to 1.8 s. Fourth, overheadtime characterizes neither birds nor plants alone, but theirinteraction. One hermit hummingbird species had similar intakerates but different overhead costs at three flower species in the31same habitat. Three hermit species had similar intake rates butdifferent overhead costs at one flower species, in the samehabitat as above. These patterns probably reflect an interactionbetween some combination of the length and morphology of flowercorollas, including their curvature, and the length and curvatureof hummingbird bills and tongues.Nectar volume in natureIn contrast to the paucity of nectar intake parameters,there is abundant information on nectar standing crops. I willdescribe a few general patterns among hummingbirds to place mymodels into the perspective of natural variation in nectarvolume. Whenever standing crop was reported in sucrose or energyunits I converted to volume units when nectar concentration ormolarity was also reported (Bolten et al. 1979).On hummingbird territories. Across a wide range ofhummingbird and plant species, nectar standing crop per flower infeeding territories is low and relatively independent of nectarproduction rate.^Means are usually less than 4 Al, often lessthan 1 Al, and may approach zero under some conditions(Hainsworth and Wolf 1972b; Gass et al. 1976; Kuban 1977; Gass1978a; Kodric-Brown and Brown 1978; Pyke 1978a; Waser 1978; Brownand Kodric-Brown 1979; Montgomerie 1979; Waser and Price 1981;Hixon et al. 1983; Feinsinger et al. 1985; Wolf and Hainsworth1986; Armstrong 1987; Carpenter 1988). Standing crops ofCastilleja lineariafolia flowers in a set of S. rufus feeding32territories over two summer seasons averaged less than birds'tongue groove volumes (F. L. Carpenter, unpublished data; alsosee Carpenter 1988). In that study, the means for individualterritories were as low as 0.38 and 0.03 gl at some times.Volumes are usually higher inside feeding territories than innearby undefended areas (Gass 1978a; Hixon et al. 1983; Carpenterpers. comm.), but this pattern was reversed in a breeding systemin which males commuted from their territories to feed (Armstrong1987).On hummingbird traplines. The situation is different withhermits (Phaethorninae) and other hummingbirds in the diversegroup of Feinsinger and Colwell's (1978) specialized "high rewardtrapliners". These larger hummingbirds with longer, usuallydecurved bills visit flowers with long, usually curved corollasthat are widely dispersed except under human disturbance(Feinsinger 1987). Access to these flowers is limited byspecialized floral morphology to a small set of specializednectarivores, and the complex fit of floral and bill morphologymay require specialized positioning or inserting techniques thatincrease flower handling overhead. Flowers produce nectarcopiously and accumulate standing crops of up to several hundredmicrolitres (Feinsinger and Colwell 1978; Feinsinger et al. 1979,1985; Montgomerie 1979; Angehr 1980; Wolf and Gill 1980; Gill etal. 1982; Feinsinger 1983; Dobkin 1984; Gill 1987, 1988; Wolf andStiles 1989). Nectar volume decreased diurnally in some cases inone survey (Feinsinger et al. 1985), but this pattern was muchless widespread than with territorial hummingbirds.33Implications for field manipulations Several studies have added high-volume feeders toterritories (Collias and Collias 1968; Miller and Miller 1971;Pimm 1978; Ewald 1980; Pimm et al. 1985; Tamm 1985). Theseexperiments must be interpreted in terms of both reduced costsand increased benefits of high volume, and it is not always clearwhich of these contributes more to long-term net benefits. Useof supply rate limited feeders helps reduce available volume(Ewald 1983; Norton et al. 1982; Ewald and Bransfield 1987; Gill1988), but only marginally, and the reduction of costs due tocentralization of normally dispersed resources remains. Evenadding nectar to flowers (Gass and Sutherland 1985) or coveringthem for a time to allow standing crop to accumulate (Hixon etal. 1983) turns flowers into high-volume "feeders". There is noobvious way to completely avoid these problems when manipulatingfood supply, but results must be interpreted cautiously. Forexample, the net advantage of specializing on experimentallyenriched patches in one study resulted from increases inbenefits, not from decreases in costs, and this was not obvious apriori (Gass and Sutherland 1985). These general cautions arenot new (Gill 1978).Implications at fine temporal scales: intake rate and optimal concentrationMany published handling times, most estimates of nectarintake parameters (Table 1), and all tests of concentrationpreference have been based on much larger volumes than non-34traplining hummingbirds normally encounter in nature (Gass 1974;Hainsworth and Wolf 1976; Kingsolver and Daniel 1983; Montgomerie1984; Tamm and Gass 1986; Gass 1988; Paton and Collins 1989;Stromberg and Johnsen 1990). In light of my model results, thismismatch of conditions makes interpretation of these studiesdifficult. Investigators have compared their results withHeyneman's (1983) and Kingsolver and Daniel's (1983) predictionsof optimal concentration (Tamm and Gass 1986; Stromberg andJohnsen 1990). Heyneman's (1983) prediction is based on tongueloading rate only, however, and therefore it does not apply tothe high volumes used in those experiments because they requiredmany licks. Since the volume loaded per lick has been estimatedonly roughly and indirectly (Ewald and Williams 1982), it is notyet possible to define the domain in which single-lick modelsmight apply.The above considerations pertain to both constant volume andconstant frequency licking. Additional considerations apply toconstant frequency licking, in which the jagged optimizationfunctions (Fig. 5) would confound predictions and complicatetests of optimal concentration, especially at the low volumesthat non-traplining hummingbirds normally encounter. Mitchelland Paton (1990) concluded that for three Australian honeyeaterspecies the optimum did not shift to low concentration at lowpool volume, in contrast to Kingsolver and Daniel's (1983)prediction. They stressed, however, that their results may notbe a relevant test of the model, since honeyeater tongues differ35considerably in morphology from the hummingbird tongues for whichit was derived.Nectar intake is a more complex process than previouslymodelled, and it is still not completely understood. No lickingparameters have previously been measured under rigorous,realistically low-volume conditions, and I modelled only two ofseveral plausible types of licking. Tongue extension, immersiondepth, loading volume, and licking frequency are difficult toestimate but must be accurately measured before biophysicalmodels can be applied to reality with confidence (Kingsolver andDaniel 1983; Paton and Collins 1989).One example of how assumptions about details of licking canbias interpretations is Pyke and Waser's (1981) conclusion thatoptimal concentration for hummingbirds -- over the licking cycle,over complete flower visits, and over visits to inflorescences --is at least 55 %. They based this conclusion on Hainsworth's(1973) cinematic analysis of visits to high volume feeders by A.alexandri and blue-throated hummingbirds (Lampornis clemenciae).However, Ewald and Williams (1982) pointed out that Hainsworth'sslow camera could have missed many licks. Based on high-speedcinematography of a different species (C. anna), they concludedthat licking frequency was 13.8 Hz, 4.6-fold faster thanHainsworth's estimate. Pyke and Waser (1981) may therefore haveincorporated an overestimation of the duration of the lickingcycle in their calculations, and because optimal concentrationshould increase with this duration (Fig. 3), their prediction ofhigh optimal concentration is not surprising. To the extent that36optimal concentration depends on intake rate, then, theirconclusions about the significance of dilute hummingbird nectarsare precarious. Tamm and Gass (1986) later concluded thatoptimal concentration is 40 - 45 %, based on measured intakerates during feeding visits over a wide range of concentrations.Another problem is that investigators often fail to specifyprecisely how intake rate was estimated (e.g. Hainsworth and Wolf1979; Hainsworth 1981; Schuchmann and Abersfelder 1986; Paton andCollins 1989). My analysis makes it clear that precision indefining rates and temporal scales is crucial to avoidingconfusion and misinterpretation (see Wolf et al. 1975; Gill andWolf 1979).Implications at coarser temporal scales Given the sensitivity of energy intake rate and optimalconcentration to temporal scale of integration, it is crucial tochoose appropriate temporal scales when interpreting experimentalresults and when considering coevolution of plants andpollinators (Feinsinger 1987; Gass 1988; Paton and Collins 1989).The problem of temporal scale of integration is likely to provecrucial in other systems as well (see Kacelnik 1984).^However,no generally applicable guidelines yet exist to identify thescales most relevant to fitness. This section provides contextfor considering this issue.In the introduction hummingbird foraging biology waspresented in hierarchical terms. In general, interactions amongevents at similar scales in the same system tend to be more3 7tightly coupled than events at different scales (Simon 1973), andthe following spatial scales represent discrete and successivelyhigher hierarchical levels and longer temporal scales: flowers;inflorescences; patches of flowering plants; territories,traplines, or home ranges; habitats; and geographic ranges (Gassand Montgomerie 1981). Studies of optimization in foraging haveusually considered only one of these scales, and usually arelatively fine one. However, the consequences of fine-scaledactions cascade upward in temporal scale, so processes atdifferent scales clearly interact (Allen and Starr 1982; Gass1985). Perhaps if it were easier to simultaneously consider thefull range of scales and their interaction, biological intuitionwould be better able to identify relevant scales for study ofparticular systems.Just as I demonstrated above at three fine scales, energyintake rate continues to decrease with increasing scale in mysystem. I suggest that the following pattern of changegeneralizes across systems. Consider energy intake rate at thethree adjacent scales that I considered earlier: the tongueloading phase of the licking cycle, the whole licking cycle, andhandling time at flowers. Tongue loading is directly productive,because nectar is taken up, and energy intake rate increases ifnectar quantity and quality are sufficient. Tongue unloading isnot directly productive, but it takes time, and because thisincreases the denominator of a rate whose numerator is constantduring unloading, energy intake rate always decreases during thisphase. This alternation between productive and non-productive38phases as time and energy accumulate during licking accounts forthe jagged optimization curves in Figure 5 and 7 (see Stephensand Krebs 1986 for discussion of this phenomenon in a differentcontext). Intake rate decreases again and a new hierarchicallevel is reached when non-productive flower handling overhead andtravel to the next flower are added to the denominator of theequation.Similar alternation of productive and non-productive phasesresults in discrete, successively longer temporal scales ofintegration. To complete a foraging bout, hummingbirds must notonly lick nectar from flowers, but pay the time and energyoverhead of handling each flower and moving between flowers oninflorescences, between inflorescences in patches, betweenpatches in territories or on traplines, and between perches andthe first and last patches visited. Addition of perching timebetween bouts completes the foraging cycle, and accumulation offoraging cycles completes the foraging day.Energy intake rate is higher over a period that includes anyproductive phase than over the period that excludes it. However,the rate should progressively decrease at successively higherhierarchical levels and longer temporal scales. Average intakerate decreases and optimal concentration increases whenever non-productive time is accumulated. For example, adding travel timebetween flowers to flower handling time is mathematicallyequivalent to adding overhead time to licking; in both casesintake rate decreases and optimal concentration increases. Thelatter effect, however, is asymptotic (Fig. 3); jumping from39tongue loading to flower visits can increase the predictedoptimum more than jumping from flower visits to foraging bouts(contrast Heyneman 1983).Now consider the effect on energy intake rate of variationin its components at each hierarchical level. I showed thatbecause all licks from non-depleting nectar pools are equivalent,energy intake rate for a series of licks is the same as for anyone of them. It should be true at all hierarchical levels thatenergy intake rate over a series of cycles is the same as for anycomplete cycle, but only if the components of energy intake rateare invariant or compensatory and the rate is invariant amongcycles. In practice, extrapolating from one cycle up to seriesshould be undertaken with caution, given the variability of patchquality (Gass and Sutherland 1985), habitat quality (Gass andMontgomerie 1981; Hixon et al. 1983), and meteorologicalconditions (Calder 1976; Gass and Lertzman 1980). Volume andconcentration of nectar, length, width, and shape of flowercorollas, and spacing of flowers, inflorescences and patches havebeen examined, but usually in separate studies, and only rarelyhave variation or interaction among factors been considered instudies of optimization in hummingbird systems (but see Pyke1978a; Gill 1988).If energy intake rate varies among cycles, as it usuallydoes in nature, it is difficult to imagine birds averaging overless than entire series unless they use a sliding window or somecomplex way to discount past variation while they forage (e.g.Green 1980). Animals probably integrate the costs and benefits40of foraging over whole hierarchical levels and the scales atwhich they integrate are therefore discontinuously distributed.Both from foragers' and biologists' points of view, thisdiscontinuous structure should simplify the practical problem ofevaluating the consequences of action (see Gass 1985 fordiscussion of the cognitive benefits of hierarchical decision-making structures). For instance, it is convenient to considerlicking cycles as productive although they include non-productiveunloading time, flower visits as productive although they includeflower handling overhead time, and foraging bouts as productivealthough they include travel time.Clearly, the suggestion that hummingbirds might prefer lowconcentrations under low nectar volume conditions must be testedempirically. If hummingbirds express as clear concentrationpreferences at realistically low volumes as they do in laboratoryand field tests that use high volume, then it would be importantfor researchers to know the temporal scale at which thesepreferences maximize some fitness surrogate. Others haveacknowledged that time scale influences estimation andinterpretation of net energy intake (Pyke and Waser 1981;Hainsworth and Wolf 1983; Heyneman 1983; Kingsolver and Daniel1983; Kacelnik 1984; Feinsinger 1987), but the present study isthe first detailed, graphical exploration of this effect.My analyses reveal that, although the rate of nectar intakefrom flowers influences hummingbird energetics, this influence islikely to be most significant under conditions that only somespecies encounter in nature. Therefore I suggest that the effectof intake rate during flower visits should be significant tooptimally foraging birds only in special cases.4142CHAPTER 2LICKING BEHAVIOUR ANDTHE ENERGETICS OF THE LICKING CYCLEIn the analyses of the biophysical models of Kingsolver andDaniel (1983) presented in Chapter 1, I concluded thathummingbirds should prefer low nectar sugar concentrations onlyif their foraging decisions maximize energy intake rates at veryfine time scales. However, this possibility assumes that themodels accurately predict energy intake rates during licking,which in turn depends upon how accurately they capture keydetails of hummingbird nectar feeding.Only two previous studies have estimated parameters of thehummingbird licking cycle. Hainsworth (1973) and Ewald andWilliams (1982) used cinematography to investigate licking fromhigh volume feeders. As I discussed in Chapter 1, however,Hainsworth (1973) probably used too slow a camera speed tocapture all licks during feeding, and thus underestimated lickingfrequency and overestimated lick volume. Ewald and Williams(1982) used a higher camera speed, but unlike Hainsworth (1973)they did not film licking at a range of concentrations.Given the lack of information about hummingbird licking atdifferent concentrations and volumes, Kingsolver and Daniel(1983) made several assumptions which I preserved in myextensions of their models (Chapter 1). For example, I assumedthat only the tips of the tongue grooves contact the nectar poolduring licking, and that volume intake rate while licking is43independent of flower morphology, even though I pointed toevidence that these two assumptions are unrealistic. The presentstudy was designed to fill the existing gap in knowledge abouthummingbird licking, and in particular to discriminate betweenthe major alternative assumptions that hummingbirds exhibiteither Constant Volume or Constant Frequency licking. Toevaluate these and other model assumptions, I used an electronicphotodetector apparatus to measure parameters of hummingbirdlicking behaviour and to estimate energy intake rates at the timescale of the licking cycle, at a range of concentrations andvolumes.Materials and methods I tested one adult male rufous hummingbird between 3 Augustand 14 September 1991. This individual was captured at RosewallCreek on Vancouver Island in May 1991. Its bill length was 16.6mm from the tip to the base of the exposed culmen, and its weightranged from 3.3 to 4.7 g over the course of these tests.Although variations in body weight probably influenced the bird'soverall energy requirements and its hovering cost while feeding,I assumed that they did not affect the details of its lickingbehaviour. This bird had participated previously in tests ofspatial association learning which employed different methodsfrom the present experiment (see G. S. Brown, PhD thesis, fordetails). At all times when not in tests, the bird had freeaccess to a commercial hummingbird food formula (Nektar Plus;Nekton USA, Inc.) supplemented with soybean protein. During44these experiments, the bird was housed in a Plexiglas box (46 mmlong x 29 mm wide x 43 mm high).To measure parameters of licking behaviour at differentsucrose concentrations and volumes, I built a photodetector arrayand mounted it in the wall at the opposite end of the Plexiglasbox from the bird's perch. The array was a linear series of fourinfrared emitters facing a parallel series of four detectors(Motorola pin diode components MLED71 and MRD721 respectively) onthe opposite side of a feeder tube. This tube was ofborosilicate glass (Vitro Dynamics, Inc., ST-8100), closed at thefar end, with internal dimensions of 1 mm square by 16 mm deep.The tube was inserted into the array such that each emitter'slight passed horizontally across it to the matching detector onthe other side. The centres of the light beams were 4.65 mmapart, and were 1.55, 6.20, 10.85 and 15.50 mm from the feedertube opening (all distances are ± 0.05 mm). The cross-sectionalradius of each light beam was 0.86 mm. The tongue of the feedinghummingbird interrupted each of these light beams in sequence,and the resulting voltage reductions were monitored with aNicolet 4094/4851 four-channel digital oscilloscope. The feedertube admitted only the bird's tongue, so measurements encompassedonly the licking cycle and excluded the overhead time required toposition and insert the bill (Chapter 1). Breaking the lightbeam of the first emitter-detector unit triggered data recordingfrom all four channels of the oscilloscope.After every trial I covered the feeder array, then removedand visually inspected the feeder tube to determine if the bird45had emptied it. I then refilled the feeder tube for the nexttrial with a repeating dispenser. Nectar was dispensed into thefar end of the feeder tube from the opening, so the bird's tonguehad to travel farther to contact the nectar pool at low than athigh volumes. The cross-sectional area of the tube was 1 mm 2 , so1 Al of solution filled 1 mm of its length. Using thisrelationship, I confirmed the volume of sucrose solution that Idispensed by measuring the distance from the end of the tube tothe nectar pool meniscus with dial calipers (accurate ± 0.02 mm)before every trial. After reinserting the feeder tube into thearray, I removed the cover to begin the next trial.Licking behaviour was examined at twenty combinations ofsucrose concentration and nectar pool volume: 25, 35, 45 and 55 %at each of 1, 4, 8, 12 and 16 Al. I analyzed only those trialson which the bird fed without pausing and removed all the nectarprovided during a single probe of the feeder (45 % of alltrials). For each combination of concentration and volume,trials were continued until four uninterrupted feeding visits hadbeen recorded. Testing sessions lasted 45 min to 5 h, no morethan once each day.Using this protocol, I measured the number of licks and thetime (± 1 ms) required for the bird to remove food from thefeeder. For each trial I calculated average licking frequency(number of licks extraction time), average lick volume (nectarpool volume number of licks), and average volume intake rate(nectar pool volume extraction time) during licking. I also46calculated average energy intake rate, E, during licking with thefollowing equation:(12) E = --€11P---t POwhere e = energy content of sucrose = 16.48 (J/mg), S = sucroseconcentration (% wt/total wt), v = nectar pool volume (gl), t =time (s), andp = density of sucrose solution, obtained byfitting a curve to tabulated values (CRC Handbook) using theNONLIN procedure in SYSTAT (SYSTAT, Inc.); p= 1.8 X 10 -5 S 2 +3.725 X 10 -3 S + 0.999 (kg/1; corrected r 2 = 1).Because sucrose solution has a different refractive indexthan does air, nectar and air registered as different voltages onthe oscilloscope traces. I could therefore time the recession ofthe nectar pool meniscus past the four light beams during lickingon the 16 gl trials, when the nectar pool completely filled thefeeder tube. This allowed me to estimate changes in volume andenergy intake rates as the bird emptied the feeder. It was notpossible, however, to measure precisely the volume loaded on eachindividual lick, nor to measure the durations of the loading andunloading phases of the licking cycle.Although I also offered 65 % sucrose, the bird never emptiedthe feeder during a single visit at this concentration. The birdalso failed to empty the 55 % solution when only 1 gl wasprovided.To examine the significance of the effect of concentrationon energy intake rate during licking, I performed a Kruskal-47Wallis test on energy intake rates from all trials for eachnectar pool volume, using the NPAR procedure in SYSTAT. When asignificant effect was detected at a = 0.05, I performed anonparametric Tukey-type multiple comparison test (Zar, 1984) forall pairs of concentrations. At each concentration at 16 Al, Itested the goodness of fit of linear regression equations,derived using the procedure MGLH in SYSTAT, for both number oflicks and time against cumulative volume extracted duringlicking.Results The rate of nectar extraction within visits was notconstant; after an initial increase, both lick volume and volumeintake rate decreased as the hummingbird emptied the feeder (Fig.8). This effect was most striking at 55 % sucrose. Thedeparture of both of these relationships from linearity washighly significant at all concentrations (for everyconcentration, P < 0.0005; one-tailed F ratio, deviations fromlinearity DF = 2, within groups DF = 12). Licking frequency wasrelatively constant within visits at a given concentration, butvaried from 8.8 Hz at 25 % to 5.6 Hz at 55 % sucrose (Fig. 9; R 2= 0.990 and 0.986 for 25 and 55 % respectively).For all volumes provided, the number of licks the birdrequired to empty the feeder increased, and thus the averagevolume loaded per lick decreased with increasing concentration(Fig. 10). Average lick volume also depended on the volume25 45 35 55 25 35 45 55pG 121-42OO10^20^30^0^1^2^3^4^548NUMBER OF LICKS TIME (s)Figure 8. Recession of fluid meniscus within single visits.Lines connect means of four 16 gl trials for four sucroseconcentrations (%). Slopes of the lines describe lickvolume (left panel), and volume intake rate (right panel).Because volume measurements were taken at fixed points alongthe feeder array, the variation in these graphs is in numberof licks and time. Error bars give SE.provided, being higher at higher nectar pool volumes for allconcentrations.For all nectar pool volumes, the bird licked more slowlywith increasing concentration (Fig. 10). Unlike the case ofaverage lick volume, average licking frequency did not appear tobe a function of nectar pool volume.Time to extract nectar increased with increasingconcentration at all nectar pool volumes (Fig. 10). As a result,30-P0:1g=004 20 -wm20zm>p 10-e,-40200••491^2^3^4^5^6TIME (s)Figure 9. Licking frequency within single visits. Lines areleast-squares regressions, constrained to intercept theorigin, for the lowest and highest sucrose concentrationspresented in Figure 8: 25 % (hollow circles, dashed line)and 55 % (filled circles, solid line). Line slopes describelicking frequency. N = 16 for each concentration.average volume intake rate during licking decreased withincreasing concentration (Fig. 10). This decrease was morepronounced at higher than at lower feeder volumes. As withaverage lick volume, average volume intake rate increased withnectar pool volume. 01.2 -8a• 5-4  ^0.010-^ 504d 1.0 -U:*)1:4^'0 8 -W a,X 0.6 -O0.4 -;/)016^12^g• 0• .2 -0 ^10 -N=9-Uz›.4• 8-a:1 6 -W7 35 -6 -sW 5 -X4-z03 -oGC.)r4 2-W1-25 -0210-30 -5-50• 8 -Wg 6 -WZ 4 -w2• 2 -o25 35^450 1^055^ 25^35^45^55E-144 30 -1.E 201612 z 10 H440 -1SUCROSE CONCENTRATION (%)Figure 10. Variation in parameters of licking behaviour withconcentration. Lines connect means of four trials at eachconcentration for four nectar pool volumes (gl). Error barsgive SE. Wherever means overlap at different nectar poolvolumes, plots for each volume are staggered along the X-axis to allow them to be distinguished.51Average energy intake rate during licking increased withnectar pool volume; across the concentrations presented, the birdgained energy more than four times as rapidly at 16 Al as it didat 1 Al (Fig. 10). Kruskal-Wallis analyses of variance indicatedsignificant differences in energy intake rate with concentrationonly for the 1, 12 and 16 Al trials (Table 2). At each of thesethree nectar pool volumes, there was a significant differenceonly between the two concentrations which yielded the highest andlowest energy intake rates: respectively, 35 and 25 % for 1 Al(0.025 < P < 0.05), 25 and 55 % for 12 Al (0.01 < P < 0.025), and35 and 55 % for 16 Al (0.01 < P < 0.025).Table 2. Kruskal-Wallis analysis of variance of energy intakeduring licking with concentration. 1VOLUME (al)12 164 8H 6.500 2.140 5.316 9.419 8.404DF 2 3 3 3 3N 12 16 16 16 16P 0.039 0.544 0.150 0.024 0.038Conclusions As expected, hummingbird nectar feeding is more complex thanpreviously modelled. As sucrose concentration increased, thebird did not reduce licking frequency enough to keep lick volumeconstant, nor did it reduce lick volume enough to keep lickingfrequency constant. Licking behaviour falls into neither theConstant Volume nor the Constant Frequency categories envisagedby Kingsolver and Daniel (1983), and considered in Chapter 1.52Several of my results followed previously reported patternsof variation in nectar intake parameters. For example, energyand volume intake rates during licking were highest at highnectar pool volumes, when more of the tongue could be immersed(Fig. 10). This is consistent with the conclusion, based onearlier reports, that intake rates during the licking cycle arehigher at high volume feeders than at flowers (Chapter 1; seeTable 1). Previous measurements at the time scale of feedervisits have also shown that intake rates increase with increasingnectar pool volume (e.g. Montgomerie 1984). Similarly, thedecrease in volume intake rate during licking at increasingconcentration (Fig. 10) parallels results of earlier studies atcoarser time scales (e.g. Montgomerie 1984; Tamm and Gass 1986),and follows predictions of biophysical models of nectar feeding(Heyneman 1983; Kingsolver and Daniel 1983).Interestingly, licking frequency appears not to be afunction of nectar pool volume, even as the nectar pool recedesduring licking. It does, however, vary greatly withconcentration (Figs. 8 and 10). By licking more slowly withincreasing concentration, birds should partly conserve loadingtime and therefore lick volume, thus achieving higher volumeintake rates during licking than if licking frequency remainedconstant (Chapter 1).Hainsworth (1973) reported lower licking frequencies atconcentrations lower than 55 % -- the opposite of the pattern Ifound -- but his result may not be accurate because of the slowcamera speed he used (see Ewald and Williams 1982). However, the53lowest licking frequencies I measured, 4.9 - 5.9 Hz at 55 %sucrose on 16 Al trials, were near Hainsworth's (1973) value of4.7 Hz for Lampornis clemenciae feeding at this concentration.If Hainsworth's (1973) birds actually licked more slowly athigher concentration, then his film records would have captured alarger proportion of all licks at high than at low concentration.His measurements at 55 % sucrose may therefore be accurate, eventhough his low concentration measurements probably are not.Parameters of licking performance were lower in this studythan those reported by Ewald and Williams (1982). The highestaverage licking frequencies I measured, at 25 % sucrose on 12 Altrials, were 9.1 - 9.7 Hz, whereas Ewald and Williams' (1982)mean for Calypte anna feeding at approximately 22 % sucrose was13.8 Hz. The highest lick volumes and volume intake rates duringlicking I measured were 0.9 - 1.2 Al/lick and 7.3 - 10.4 Al/srespectively (both at 25 % on 16 Al), as compared to Ewald andWilliams' (1982) values of 1.2 Al/lick and 17 Al/s. Thesedifferences may relate to feeder design; it is likely thatbecause Ewald and Williams' (1982) feeder did not exclude birds'bills as mine did, licking performance was limited less than itmay have been in this study. As feeder design probablyinfluences the quantitative results of licking behaviour studies,application of these measurements to other situations should beundertaken with caution. Nevertheless, the qualitative patternsof variation in licking behaviour with concentration and nectarpool volume revealed in this study should apply generally.54As predicted in Chapter 1, lick volume decreased withinvisits as the nectar pool was depleted and tongue immersiondecreased (Fig. 8). Previous workers have suggested that deepimmersion should free tongue loading from the constraints ofcapillarity-induced nectar flow, yielding higher optimalconcentrations at high volumes (and deeper immersion) than at lowvolumes for which only the tongue tip can contact the nectar pool(Hainsworth 1973; Kingsolver and Daniel 1983). Contrary to thisprediction, however, energy intake rates were not maximized athigher concentrations at higher nectar pool volumes (Fig. 10).Apparently, the increased viscosity of high concentrations limitsloading rate even when nectar can enter the tongue grooves alongtheir length.Kingsolver and Daniel (1983) proposed that optimalconcentration is 20 - 25 % at 1 gl nectar pools because single-lick, continuous nectar flow models (Kingsolver and Daniel 1979;Heyneman 1983) should apply at this volume, but that optimalconcentration should shift to 35 - 40 % at high volumes. Myresults supported neither their suggestion that birds should lickonly once at 1 gl nectar pools, nor their prediction of an upwardshift in optimal concentration with increasing volume (Figs. 9and 10).My results did, however, support my conclusions about thedependence of optimal concentration on time scale. Idemonstrated in Chapter 1 that the predicted upward shift inoptimal concentration with increasing volume results fromincreasing the time scale of integration from tongue loading to55the licking cycle, and not from increasing volume per se. Inthis study, the bird took more than one lick at 1 Al nectarpools, so under model assumptions, optimal concentration would beexpected to be the same as at high volumes.Indeed, it may be unrealistic to imagine that hummingbirdswould lick only once even at volumes lower than 1 Al. Low volumenectar pools in flowers are often present as separate beads ordroplets which are difficult to extract (F. L. Carpenter, pers.comm.). Likewise, flowers with superior ovaries have nectardispersed around the ovary base (C. L. Gass, pers. comm.; seeLawrence 1955, especially Fig. 39). Birds would have to lickmany times to empty a flower under both of these conditions.Additionally, more than a single lick may be required to convincethem that a flower or feeder is empty, and because they can lickso rapidly, the time cost of double-checking would be miniscule.If birds lick more than once at all volumes, they would beexpected to choose the same concentrations at low volume thatthey choose at high volume. Clearly, low volume choice tests arerequired to address this issue.This experiment provides a basis for distinguishing betweentime scales at which hummingbirds' concentration preferencesmaximize their energy intake rates. For 12 and 16 Al nectarpools, 25 - 35 % sucrose yielded significantly higher energyintake rates at the time scale of the licking cycle than did55 %, and this is probably true for 1 Al nectar pools as well,given that the bird failed to extract the 55 % solution at thisvolume. If, therefore, birds maximize energy intake rates over56the duration of licking, they should be expected to prefer 25 -35 % over 55 % or higher concentrations.57CHAPTER 3HUMMINGBIRDS' CONCENTRATION PREFERENCES AT LOW VOLUMEAND THE ENERGETICS OF FEEDING VISITS AND FORAGING BOUTSIn my analyses of nectar feeding models (Chapter 1), Iconcluded that hummingbirds should prefer dilute nectars, in the20 - 25 % range predicted for low volumes and found on average intheir flowers, only if they maximize energy intake rate at thefine time scale of the tongue groove loading phase of licking.In Chapter 2 I reported that 25 - 35 % sucrose yields a higherenergy intake rate than 55 % sucrose at the time scale of thelicking cycle. To determine if, and at what time scale,concentration preferences coincide with optimal sucroseconcentrations, I measured both preferences and intake rates forrufous hummingbirds over a wide range of concentrations at a lowvolume similar to nectar standing crops found in nature.Materials and methods I tested the concentration preferences of four adult rufoushummingbirds (2 males, 2 females) between 13 November 1991 and 24January 1992. These individuals were captured between May andJuly 1990 at Rosewall Creek, Vancouver Island. The females hadlonger bills and were heavier on average than the males (Table3). At all times when not in tests, birds had free access toNektar-Plus supplemented with soybean protein. Previous to thepresent experiment, these individuals participated in tests ofspatial association learning which employed different methodsfrom mine (see G. S. Brown, PhD thesis, for details). In58addition, bird 5 was used in the licking behaviour study (Chapter2) .Table 3. Bill lengths and body weights of experimental birds. Bill^ Mass (g)Sex^length (mm)^Minimum^MaximumBird 4^M^16.7^2.8^3.9Bird 5^M 16.6 3.5 4.2Bird 27^F^17.8 3.3 4.4Bird 38^F 17.9^3.8^4.6Tests were conducted in an environment chamber at 25 ± 1 °C.An opaque partition divided the chamber into two compartments 136cm long X 16 cm wide X 66 cm high, allowing two birds to betested independently. One feeder was situated at either end ofeach compartment, and a perch was positioned halfway between thetwo feeders. Feeders were plastic tubes, 2 cm long with 2.4 mminternal diameter, mounted horizontally in the compartment wall,and marked by round orange Avery labels with central 3 mmdiameter holes. Birds' arrivals and departures from feeders andperches were detected by infrared photocells, and recorded by acomputer to 0.01 s. The computer also controlled food delivery(see Gass 1985; Tamm 1987, especially Fig. 2, for a generaldescription of the computer system).Tests began with 1 Al of a different concentration ofsucrose solution in each feeder. Thereafter, any feeder a birdvisited was resupplied with another 1 Al of the sameconcentration by a solenoid valve (General Valve Corp.), upon thebird's return to its perch. Each foraging bout yielded 1 Al at a59given feeder no matter how many times it was probed within thatbout, but birds could obtain food from both feeders on any bout.I tested preferences with all ten pairwise combinations ofthe five sucrose concentrations at 10 % increments from 25 to65 %. To control for possible positional biases (e.g. Cole etal. 1982; Tamm and Gass 1986; Wunderle and Martinez 1987) Iconducted two tests for each pair of concentrations onconsecutive days, with the positions of high and lowconcentrations reversed for the second test, and pooled theirresults. Because birds' feeder choices could be affected byhysteresis (Gass 1978b), I reversed the sequence ofconcentrations that I presented to the first two birds tested forthe other two.Visit durations are usually more variable and longer at thebeginning of a bird's exposure to new feeding conditions, anddecrease to an asymptotic level with increasing experience(unpubl. data; see Pyke 1984). I included a training sessionimmediately before every test to exclude this learning periodfrom my measure of concentration preference (for consideration ofthe effect of learning on food choice, see Hughes 1979; Mitchell1989). Concentration, volume and food delivery protocols in thetraining session were identical to those in that day's test.First, one feeder was covered with adhesive tape and the bird wasallowed to visit only the other. After the bird had made atleast 10 visits and visit durations were relatively stable, Ireversed the presentation, allowing the bird to feed only fromthe previously covered feeder until visit durations were stable60there also. The order in which I exposed feeders in the trainingsession was always the same. At the end of a training session,both feeders were briefly (< 1 min) covered while the datacollection program was started, then both were exposed to beginthe test proper. I had to open the doors of the environmentchamber briefly (< 5 s) in order to cover and uncover thefeeders, but birds exhibited no signs of disturbance within 20 safter these intrusions.Visit durations recorded by the computer were whole feedingvisits, including the time to insert and withdraw the bill fromthe feeder as well as the time spent licking. I calculatedvolume intake rates averaged over feeding visits, and energyintake rates averaged over both visits and foraging bouts, usingonly those bouts on which the bird probed the feeder just onceand then returned to its perch (91.8 - 93.9 % of all bouts foreach bird). Of these, I considered to be outliers any feedingvisits longer than 1.99 s and shorter than 0.20 s (0.6 - 4.7 % ofall visits on single-probe bouts), and any foraging bouts longerthan 5.99 s (0.2 - 0.7 % of all single-probe bouts on whichvisits were not outliers). I excluded these outliers from intakerate analyses. Energy intake rates were calculated usingEquation 12 (Chapter 2). I pooled energy intake rates forfeeding visits and foraging bouts from all tests for eachconcentration for each of the four birds, and used the means ofthese data in statistical tests. I tested for a significanteffect of concentration on energy intake rate using Friedman's61nonparametric analysis of variance for repeated measures from theNPAR procedure in SYSTAT (SYSTAT, Inc. 1990).Statistical analyses of preference were based on the volumetaken from each feeder (i.e. 1 gl X number of bouts on which eachfeeder was visited), for the first 100 gl consumed in each testfor each pair of concentrations. I tested the significance ofresults for each pair of concentrations for each bird, at a =0.05, against the null hypothesis of no preference using Chi-square goodness of fit with Yates' correction for continuity(Zar, 1984).Results As expected, visit durations increased and thus volumeintake rates for feeding visits decreased with increasingconcentration (Fig. 11). Despite their longer bills, the femalebirds did not achieve consistently higher volume intake ratesthan did the males. Round trip travel time between perch andfeeder, exclusive of handling time, averaged 1.30 - 1.69 s foreach bird.Energy intake rates differed significantly with sucroseconcentration (Table 4). At the relatively fine time scale offeeding visits, energy intake rates peaked at intermediateconcentrations in the presented range: 55 % sucrose in two birds,and 45 % in the other two (Fig. 12, column 1). Over the coarsertime scale of foraging bouts, however, energy intake rates ofthree birds peaked at the highest concentration available, 65 %sucrose, and the remaining bird's energy intake rates peaked at4S277.543 -^5ill4k^38g 4wNd4 2 -Hzw1 -.400 ^1^I^I^1^I25^35^45^55^65SUCROSE CONCENTRATION (%)Figure 11. Volume intake rates for feeding visits of four rufoushummingbirds at five concentrations. Each line connectsmeans for one bird (numerical labels identify individualbirds; error bars give SE; n is reported in Table 5,Appendix 2).Table 4. Friedman's analysis of variance of energy intake ratesfor feeding visits and foraging bouts with concentration. Intake rates for^DF^X^W^P62Feeding visitsForaging bouts4 13.400 0.837 0.0094 15.400 0.962 0.004the two highest concentrations, 55 and 65 % (Mann-Whitney U-test;n = 515 bouts at 55 %, 587 bouts at 65 %; P = 0.833; Fig. 13,column 2).35 %8 -645 %4-55 %BIRD 465 %wraus 25 % 35 % 45 % 55 %020 ^8-W%^ BIRDS45 %55 %65 %venue 25 % 35 % 45 % 55 %64-2640 ^25^35^45^55^65^ 25^35^45^55^65SUCROSE CONCENTRATION (%)035 %45 %55 %65 %Vera" 25 % 35 % 45 % 55 %BIRD 3820 -1063CALCULATED OVER FEEDING VISIT^CALCULATED OVER FORAGING BOUT CONCENTRATION PREFERENCES$35 %64-45 %55 %2-^ 65%toms 25 % 35 % 45 % 55 %0 ^s30 20 -10 -03020 -81184^10-0 ^30 -v20 -10-1030Figure 12. Energy intake rates for feeding visits and foragingbouts, and concentration preferences of the same birds as inFigure 11. In energy intake rate graphs, lines connectmeans (error bars give SE; n for each mean reported in Table5, Appendix 2). In preference graphs, each square depictsthe outcome of a Chi-square analysis of two choice tests ata pair of concentrations. Dark shading indicatessignificant preference for the higher concentrationpresented. Light shading indicates no preference. In casesof significant preference, r> 3.841. Birds neverexpressed significant preference for the lowerconcentration.64All birds either preferred the higher concentration of eachpair presented, or else preferred neither concentration.Whenever they preferred neither, the two concentrations were only10 % apart (Fig. 12, column 3).Conclusions This experiment is the first to test concentrationpreferences of hummingbirds at a volume comparable to the lownectar pool volumes prevalent in nature (see Chapter 1). Myfinding that birds preferred the highest concentration availableaccords with results of earlier high volume choice tests. In theonly high volume study that provided concentrations as high as65 % sucrose, Tam and Gass (1986) found that birds took morefrom the weaker solution when the mean concentration of the twooffered was above 55 % sucrose. This preference, however, wassignificant only for presentations of 65 % vs. 60 %, and nochoices were offered between 65 % and concentrations lower than60 %.In the present study, hummingbirds generally preferredsucrose concentrations which maximized their energy intake ratesat the coarse time scale of foraging bouts, even when this didnot maximize energy intake rates at the finer time scale offeeder visits. Those cases of failure to express preference donot necessarily indicate that birds were unable to distinguishbetween the concentrations. On the contrary, it is reasonable toassume that these nectarivores, which possess taste buds(Weymouth et al. 1964) and a sense of taste (Stromberg and65Johnsen 1990), can distinguish between the concentrationspresented in this study; even human tasters can readily tell themapart (pers. obs.; see e.g. Monneuse et al. 1991). A moreplausible explanation for the failure to express preference isthat the difference between the two feeders' energetic yields mayhave been insufficient to elicit preference from all individualson the basis of concentration. This possibility is supported bythe observation that these cases occurred when sucroseconcentrations were only 10 % apart. Alternatively, a weakpreference for one of the two concentrations may have been maskedby a stronger preference for one of the two feeder positions.The sensitivity of optimal concentration to the time periodover which rates are calculated, demonstrated with measuredvalues in Figure 12, is depicted more generally with thediscrete-marginal-value theorem representation in Figure 13.This representation can be compared with the cases of birds 5, 27and 38 in Figure 12, where food "D" would be 45 % sucrose, andfood "C", 65 % sucrose. The slopes of the solid lines in Figure13 connecting the energy gain and time coordinates of both foodsto the abscissa, describe gross energy intake rates averaged overfeeding visits. The slopes of the dashed lines, which encompasstravel time, describe energy intake rates averaged over foragingbouts. A given volume of dilute nectar ("D") has a lower grosscaloric value than the same volume of concentrated nectar ("C"),but has a shorter handling time. For feeding visits, thisshorter handling time results in a higher energy intake rate atdilute than at concentrated solutions. For foraging bouts,66TRAVEL TIME^HANDLING TIMEFEEDING VISITFORAGING BOUTFigure 13. Generalized representation of two food typescorresponding to dilute and concentrated nectar ("D" and "C"respectively). D has low caloric value and handling time; Chas high caloric value and handling time. The slopes of thesolid and dashed lines connecting foods to abscissa areenergy intake rates for feeding visits and foraging boutsrespectively (after Stephens et al. 1986; Hainsworth 1989).however, travel time effectively outweighs the advantage ofshorter handling time, so that the concentrated solution yields ahigher energy intake rate than does the dilute.67All birds preferred 65 % sucrose to less concentratedsolutions. Although this preference maximized energy intakerates over foraging bouts, and not over feeding visits, it doesnot demonstrate that hummingbirds monitor rates on either ofthese scales, or even that energy intake rate is the currency ofconcern to birds (see Montgomerie et al. 1984; Hixon andCarpenter 1988; Tam 1989). In this case, choosing theconcentration which is optimal at the time scale of foragingbouts could have resulted from application of a simple rule ofthumb like "Always choose the sweetest solution available"(Hainsworth and Wolf 1976; Tamm and Gass 1986).68DISCUSSIONThe adaptive significance of the low concentrations ofnectar prevalent in hummingbird-pollinated flowers is a centralissue in pollination biology (e.g. Bolten and Feinsinger 1978;Calder 1979; Pyke and Waser 1981; Plowright 1987; Sutherland andVickery 1988; Mitchell and Paton 1990). Mean nectarconcentration of North American and many tropical hummingbird-pollinated plants is in the range predicted to be optimal byHeyneman (1983) and by Kingsolver and Daniel (1983) for lowvolume sources (Baker 1975; Feinsinger 1987). However,previously reported energy intake rates during feeding visits andconcentration preferences of hummingbirds in the laboratorypeaked in the range Kingsolver and Daniel (1983) predicted forhigh volume (Tamm and Gass 1986; Chapter 3). This observedpreference for concentrations roughly twice what flowers offer innature has complicated understanding of the evolution of thepresumably coevolved plant-pollinator system (Pyke and Waser1981; Feinsinger 1987; Gass 1988).Interestingly, most flowers visited by non-traplininghummingbirds usually contain nectar pools near to or less thanthe volume of the tongue grooves, whereas all publishedpreference tests used much larger volumes (usually infinite fromthe birds' perspective; e.g. Hainsworth and Wolf 1976;Montgomerie et al. 1984; Tamm and Gass 1986; Tamm 1989).Following Kingsolver and Daniel's (1983) prediction of differentoptimal concentrations for different nectar pool volumes, it wastempting to infer that the discrepancy between the higher nectar69concentrations birds prefer and the lower concentrations flowersprovide them is just an artifact introduced by testing preferenceand intake rate at inappropriately large volumes.As I showed in Chapter 1, however, biophysical modelssuggest that hummingbirds should prefer concentrations as low asflowers provide only if they average costs and benefits over theloading phase of single licks alone. Conversely, the same modelspredict that preference for higher concentrations should beexpected even at very low volume sources if birds average overtotal handling time or longer. My tests of these predictionsconfirmed the dependence of optimal concentration on the timescale of integration, and revealed that hummingbirds prefer highconcentrations even at realistically low volume sources. Birds'choices maximized their energy intake rates at the time scale offoraging bouts, but not at the time scales of feeding visits orthe licking cycle.Implications for optimal foraging theoryPrevious workers who have focussed their analyses on thetime scale of feeder visits have concluded that hummingbirds'foraging decisions do not always maximize energy intake rates(Hainsworth and Wolf 1976; Montgomerie et al. 1984). My resultssuggest that reinterpretation of these studies may reveal thatbirds' foraging decisions did maximize energy intake rates, butover longer time periods than feeder visits.Travel time is only one of several possible time componentsthat might be important. Referring back to Figure 13, whenever70the "faster" food type provides even a marginally lower totalenergetic reward than the "slower", there will be some time scaleover which the latter yields a higher energy intake rate. Inreality, however, whether or not this type should be preferreddepends on a complex interaction of temporal, nutritional,behavioural and other constraints, which are discussed in depthelsewhere (e.g. Sih 1980; Pyke 1984; Stephens et al. 1986; Calderet al. 1990; Lima 1991; Murray 1991).In an earlier experiment that distinguished between timescales of energy intake rate maximization, Stephens et al. (1986)showed that honeybees (Apis mellifera ligustica) made foragingdecisions consistent with rate maximization over coarser timescales than feeding visits. In contrast, Barkan and Withiam(1989) found that black-capped chickadees (Parus atricapillus)selected foods which maximized energy intake rates duringfeeding, but not over longer periods. Their experiment generateddifferent handling times by varying the thickness of tape thatbirds had to peck through in order to obtain food. This imposeda delay between the start of food "handling" and actuallybeginning feeding which was different for the different foodchoices.Barkan and Withiam (1989) pointed out that their result mayhave been generated by a well-established psychologicalphenomenon in which animals, apparently lacking "self-control",choose immediately available foods with smaller energetic rewardsover more rewarding foods when access to the latter is delayed.Conversely, in my protocol the only analogous delay was the time71nominally required to insert the bill into the feeder, whichshould not have differed among feeders. Instead, variation inhandling times with concentration resulted from differentextraction rates during feeding itself (Fig. 11). Investigatorsinto food choices should be aware that the validity ofpredictions may depend critically on what behavioural componentsare included in the category "handling time", and that preferencecould be sensitive to the sources of variation in handling time(Houston 1991).It is unclear exactly how either foragers or experimentersshould estimate costs and benefits of action at any hierarchicallevel or any temporal scale. While the positive and negativeconsequences of fine-scale events must ultimately determinefitness, it is unclear how or on what temporal scale eitheranimals or biologists should integrate them. It is clear from myanalyses, though, that to predict optimal behaviour on the basisof fine-scale events is dangerous unless the contribution ofthese components to higher level processes is understood.Implications for pollination biologyFlower nectar of hummingbird-pollinated plants is typicallylow in amino acids, and pollen is an insignificant source ofenergy and protein for hummingbirds (Brice et al. 1989), sonectar sugar is the principal benefit birds obtain from visitingflowers. Hummingbirds' sugar concentration preferences overridetheir preferences for colour or sugar type (Collias and Collias1968; Stiles 1976). Nevertheless, I have demonstrated that the72energetic effects of decreasing fluid flow rates with increasingnectar concentration, which are large at the fine time scale offeeding visits, diminish at the coarser time scale of foragingbouts. Over these longer time periods, gross energetic reward,which is a function of concentration and nectar pool volume (seeMontgomerie 1984), influences energy intake rate more than doesconcentration alone. Patterns of nectar concentration inhummingbird-pollinated plants cannot be explained byhummingbirds' preferences nor by the energetics of nectarextraction.Accounting for dilute nectars on the basis of sugar flowrates alone is likely to generate incorrect predictions. Forexample, Heyneman (1983) concluded that travel costs interritorial hummingbirds were far outweighed by costs duringnectar feeding, based on the close fit between sugarconcentrations of their flowers and the 20 - 26 % sucrose thatmaximized energy intake rates during tongue groove loading in hermodel. The present study contradicts this conclusion;incorporating travel times of only about 1.5 seconds into myenergy intake rate calculations increased measured optimalconcentrations 10 - 20 % above those for feeding visits alone(Fig. 13), as the theoretical results of Chapter 1 predicted itshould.The above considerations also apply to nectarivores otherthan hummingbirds. May (1988) found that nectar concentrationwas uncorrelated with butterflies' energy intake rates or amountof sugar per flower in one butterfly-pollinated plant, and73correlated only weakly in another. He argued that it wasunlikely that concentration would be used by butterflies as abasis for selecting flowers. Both measured and predicted energyintake rates for butterflies (calculated over handling time) peakat 30 - 40 % sucrose (Pivnick and McNeil 1985; May 1985; Boggs1988; Daniel et al. 1989) not the 20 - 25 % found in butterfly-pollinated flowers and predicted by an earlier model (Kingsolverand Daniel 1979). Neither are bees' energy intake ratesmaximized at the sugar concentrations their flowers provide. Aswith hummingbirds, when travel time is included in energy intakerate calculations, the optimal sucrose concentration forbumblebees increases to 50-65% (Harder 1986), which issubstantially higher than the average concentration in bee-pollinated flowers.The question remains of why hummingbird flowers secretedilute nectar. It is improbable that hummingbirds are limited byconstraints of water balance or digestion from taking advantageof high sugar concentrations. Floral nectars providehummingbirds considerable excess of water above theirrequirements (Calder 1979; Calder and Hiebert 1983; see Weathersand Stiles 1989). Efficiency of digesting sucrose inhummingbirds is > 97 % (Hainsworth 1974; Martinez del Rio 1990a),and intestinal sucrase activity is up to 118 times higher than inpasserines (Martinez del Rio 1990b). Contrary to earlier reports(Diamond et al. 1986; Karasov et al. 1986), physiological ratesof nectar processing do not appear to limit the frequency of74hummingbirds' feeding bouts (Tiebout 1989; Martinez del Rio,pers. comm.).Bolten and Feinsinger (1978) suggested that dilute nectarmight deter bees, which may be less reliable and efficientpollinators of some plants than hummingbirds (see Sazima andSazima 1990). In one plant species, hummingbirds deposit 10times as much pollen per flower stigma per visit as bees, andboth fruit and seed production increase with pollen loaddeposited (Bertin 1982, 1990). Low sugar concentration alone,however, is not sufficient to deter bees. Pleasants and Waser(1985) observed bumblebees (Bombus appositus) visiting Ipomopsisaggregata, a typical hummingbird-pollinated flower with anaverage nectar sugar concentration of 26 % (Pyke and Waser 1981).This flower's corolla is longer than the proboscis of bumblebees,so it normally excludes them, but in a year when nectar standingcrop was higher than usual, bees were able to harvest nectar thataccumulated and filled the corolla tube. There is no consistentrelationship between the accessibility of a species' nectar tobees and its sugar concentration (Pyke and Waser 1981).Earlier I argued that sugar concentration is likely to beimportant to hummingbirds only under special conditions. Onesuch condition was revealed by the failure of the hummingbird inthe licking cycle experiment to empty 65 % solutions from thefeeder, and also by its failure to empty 55 % when only 1 Al wasoffered (Chapter 2). These solutions were probably too viscousfor this male to extract easily from the end of the 16 mm longfeeder tube, near the limit of its tongue extension (unpubl.75data; Temeles and Roberts, in review). Within feeding visits,volume intake rate during licking decreased more dramatically asthe nectar pool receded at high than at low concentration (Fig.8). This suggests that hummingbirds may prefer lowconcentrations in flowers with very long corollas where the timeand energy costs of harvesting nectar would be high, and thusthat concentration preference may depend on corolla length.Furthermore, as female hummingbirds' tongues are longer thanmales° (Johnsgard 1983; Paton and Collins 1989; Temeles andRoberts, in review), females may not be constrained by corollalength to as great an extent, and may prefer higherconcentrations than males under identical conditions. Both ofthese possibilities await testing.Just how meaningful is the observation of low average sugarconcentrations in hummingbird-pollinated plants? Focussing onpatterns of average concentrations tends to obscure the fact thatthere is considerable variation in concentrations in hummingbird-pollinated flowers (see Kingsolver and Daniel 1983). Nectars of17 species in Arizona and Colorado ranged from 8 - 43 % sucroseequivalents (Hainsworth 1973), and of 11 species in Mexico, 18 -29 % (Arizmendi and Ornelas 1990). Within a single family(Bromeliaceae) of hummingbird-pollinated plants in Argentina, 20species ranged from 16 - 48 % (Bernardello et al. 1991). Evenwithin individual flowers, nectar concentration varies greatlyafter secretion with environmental factors, particularly ambienthumidity (Plowright 1981; Bertsch 1983; Mohr and Jay 1990).Corolla morphology contributes to the maintenance of dilute76nectar in low humidity by sheltering the nectar pool fromevaporation (Corbet et al. 1979; Plowright 1987). The dilutenectar in hummingbird-pollinated flowers could therefore bemerely a consequence of possessing long corollas which excludeother pollinators (Plowright 1987). Indeed, the persistence ofsuch wide variation argues against nectar concentration beingsubject to strong selection pressure from hummingbirds.The importance of presentation schemes in choice tests.Offering pollinators sugar in nectar is expensive for plants.For instance, up to 37 % of daily photosynthetic productionduring blossoming is secreted as nectar sugar in the commonmilkweed (Asclepias syriaca; Southwick 1984). Sugar secretion innectar is constrained by weather and plants' other physiologicalrequirements (Michaud 1990; Harder and Cruzan 1990), and somespecies may reabsorb sugar from unvisited flowers to reclaiminvested energy (BUrquez and Corbet 1991). As Mitchell and Paton(1990) pointed out, to compare pollinators' concentrationpreferences with equal nectar pool volumes suggests that plantsshould achieve different concentrations by investing vastlyunequal energetic rewards in nectar. Given the high cost ofsugar secretion, it is more realistic under many conditions toconsider pollinators' concentration preferences for the sameamount of sugar packaged in different amounts of water; Mitchelland Paton's (1990) "Equal Sugar" presentation scheme.In "Equal Volume" presentations, Mitchell and Paton (1990)found that honeyeaters' energy intake rates during feeding peakedat 30 - 50 % sucrose, but in their Equal Sugar presentation, New77Holland honeyeaters (Phylidonyris novaehollandiae) maximizedenergy intake rates during feeding visits at about 20 %. Becausethe amount of sugar was the same at all concentrations, thismeasured optimum holds at all time scales (i.e. the optimum willnot shift upwards with increasing temporal scale of integration).The authors suggested that their result could account for thedilute nectars of bird-pollinated plants. However, they did notperform the critical test of this suggestion and determinewhether or not their birds preferred 20 % sucrose under EqualSugar conditions.Energy intake rates of hummingbirds have not been measuredunder an Equal Sugar presentation scheme. Even if these peakedat low concentration as for honeyeaters, however, there may bereasons other than energy intake rate for choosing high over lowconcentrations. One possibility relates to the property of EqualSugar presentations that at high concentrations the given amountof sugar is available in a smaller volume than it is at lowconcentrations. Large meals increase body mass and thereforeflight cost, and are sometimes avoided (DeBenedictis et al. 1978;Montgomerie et al. 1984; Tamm 1989; Carpenter et al. 1991;Tiebout 1991; see Schmid-Hempel et al. 1985 for honeybees).Hummingbirds might therefore choose high concentrations thatyield more energy per unit volume consumed (see Montgomerie etal. 1984) than low concentrations, even if the latter yieldedhigher energy intake rates under Equal Sugar conditions.Obviously, preference tests at realistic volumes using an Equal78Sugar presentation scheme are required to investigate thesealternatives.Should plants provide what pollinators prefer? A majorassumption of attempts to correlate optimal sugar concentrationsfor pollinators with concentrations in floral nectar is thatplants should offer pollinators what they prefer in order tosecure and maintain their services (see Gass 1988). Suggestedbenefits of such a strategy include increased visitation ratesand pollinator fidelity (Wolf et al. 1972; Waser 1986). However,this assumption neglects the fact that plant fitness is affectednot only by pollinator visitation, but also by the amount ofenergy invested in nectar rewards. Furthermore, althoughexamples abound of pollinator visitation rates increasing withincreasing nectar reward (e.g. Abrol 1990; Klinkhamer and de Jong1990; Delesalle and Buchmann 1991; Jennersten and Kwak 1991), thepositive relationship between visitation rates and plantreproductive success is neither simple nor linear (Zimmerman1983; Carpenter 1988; Sutherland and Vickery 1988; Ashman andStanton 1991; Real and Rathcke 1991; Waser and Price 1991).Likewise, the relationship between nectar reward andvisitation rate is neither simple nor linear. Although flowersmust present enough nectar to secure the attention of potentialpollinators, if the rewards they offered were too large, theirvisitors would not need to visit as many other flowers and couldbecome less efficient pollinators (Baker 1975; Heinrich 1975).The proposition that large rewards can reduce nectarivores'79foraging movements has been supported by experimental enrichmentsof flowers (Gass and Sutherland 1985).In at least one case, smaller nectar pools resulted inhigher visitation rates (Pyke 1980). Bumblebees (Bombusflavifrons) visited flowers in a patch of larkspur (Delphiniumbarbeyi) at twice the rate they did in a contiguous patch ofmonkshood (Aconitum columbianum), even though Delphinium flowersoffer less than half the volume of Aconitum flowers and nectarsugar concentrations are similar in both plant species (41.3 %and 40.1 % respectively). By visiting Delphinium flowers morefrequently, bees obtained similar net energy intake rates at bothpatches.Similarly, while pollinator infidelity has been shown todecrease plant reproductive success in some cases (Feinsinger etal. 1988; Feinsinger and Tiebout 1991), in others the loss ofpollen due to indiscriminate foraging has little effect(Feinsinger et al. 1986; Feinsinger et al. 1991). In addition,even specialized plants can sometimes "compensate" for theabsence of their principal pollinators by attracting other taxa(Wolf and Stiles 1989).Clearly, plant-pollinator systems are not amenable toexplanations based on simple assumptions (Carpenter 1983; Gass1988). 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Plant reproduction and optimal foraging:experimental nectar manipulations in Delphinium nelsonii.Oikos 41:57-63.95APPENDIX 1GLOSSARY OF TERMS USED IN CHAPTER 1CF = constant licking frequency across concentrationCV = constant load volume per lick across concentration= energy constant of sucrose = 16500^(j*g-1)E^= energy intake rate^ (W)f^= licking frequency (Hz)1^= distance of fluid flow into tongue groove^(m)1g = tongue groove length^ (m)n^= number of licks to load nectar poolr^= tongue groove radius^ (m)S^= sucrose concentration (%; wt/total wt)Th = total time spent at flower = T1 + Tu + Ti^(s)Ti = "overhead" time to handle flower morphology^(s)T1 = duration of loading phase of licking cycle^(s)Tu = duration of unloading phase^ (s)V^= volume intake rate^ (m3*s-1)V1 = nectar volume loaded per lick^ (m3)V^= nectar pool volume^ (m3)p^= fluid density coefficient = 1000 + 5.37 S^(kg*m-3)A^= viscosity= exp[0.00076 S2 + 0.012 S - 6.892]^(kg*ml*s-1)= surface tension coefficient= 7.18 10-2 + 7.11 10- S^ (N*m-1)8^= contact angle = 0^ (°)96APPENDIX 2SAMPLE SIZES IN FIGURES 11 AND 12Table 5. Sample sizes in volume and energy intake rate graphs(Figures 11 and 12).25Feeding visitsconcentration65^25Foraging bouts65Sucrose35^45^55(%)35^45^55Bird 4 10 254 396 428 641 9 254 394 427 633Bird 5 163 215 273 495 539 162 214 273 495 538Bird 27 32 238 374 474 610 31 236 372 474 608Bird 38 127 245 313 516 589 126 243 310 515 587

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