Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


831-ubc_1992_spring_roberts_william.pdf [ 4.2MB ]
JSON: 831-1.0086476.json
JSON-LD: 831-1.0086476-ld.json
RDF/XML (Pretty): 831-1.0086476-rdf.xml
RDF/JSON: 831-1.0086476-rdf.json
Turtle: 831-1.0086476-turtle.txt
N-Triples: 831-1.0086476-rdf-ntriples.txt
Original Record: 831-1.0086476-source.json
Full Text

Full Text

HUMMINGBIRDS' CONCENTRATION PREFERENCES AND THE ENERGETICS OF NECTAR FEEDING: PREDICTIONS, TESTS, AND IMPLICATIONS FOR OPTIMAL FORAGING THEORY AND POLLINATION BIOLOGY by WILLIAM MARK ROBERTS B.Sc., The University of British Columbia, 1987 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ZOOLOGY  We accept this thesis as conforming  THE UNIVERSITY OF BRITISH COLUMBIA April 1992 © William Mark Roberts, 1992  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Department of ^ZOOLOGY The University of British Columbia Vancouver, Canada  Date ^27  DE-6 (2/88)  APRIL 1992  ii ABSTRACT An important issue in pollination biology and foraging theory is that average nectar sugar concentrations in hummingbird-pollinated plants are less than half those preferred by birds in published choice tests. One current explanation for this discrepancy is that low concentrations maximize birds' energy intake rates. Previous workers have suggested that birds may prefer low concentrations at the nectar pool volumes characteristic of the flowers they visit, which are much lower than volumes used in all previous choice tests. I used three approaches to study this issue. I modelled hummingbird visits to flowers on three temporal scales: tongue loading, the licking cycle, and entire visits to flowers. The nectar concentration that maximizes energy intake rate increases with the temporal scale of integration, so that optimal nectar concentration for the licking cycle is higher than predicted by models that integrate over only the loading phase of single licks. Since birds must position, insert, and withdraw their bills in addition to licking nectar, the optimum at the scale of flower visits is even higher. This "overhead time cost" of handling flower morphology, for most non-traplining hummingbirds under most natural conditions, is as great or greater than the cost of handling nectar. My modelling suggests that for these birds, the potential variation in the fine-scale factors that determine nectar intake rate during licking has little effect on flower handling time, and therefore is unlikely to determine optimal nectar concentration or the profitability of visiting flowers.  iii To test the models' validity, I measured fine-scale parameters of hummingbird licking with a photodetector array that monitored movement of the tongue and nectar pool meniscus. The results allowed me to reject previous hypotheses about the details of licking, but they supported the qualitative model prediction that optimal nectar concentration is low at the time scale of licking. To determine whether hummingbirds prefer concentrations that maximize energy intake rates over the licking cycle, over feeder visits or over foraging bouts, I tested concentration preferences at low nectar pool volume with a computer-controlled food delivery and activity-monitoring system. Birds preferred the highest concentration provided, which maximized energy intake rates over foraging bouts but not over finer time scales. The low nectar sugar concentrations characteristic of flowers pollinated by hummingbirds are not accounted for by birds' preferences nor by the energetics of nectar extraction.  iv  TABLE OF CONTENTS ABSTRACT  ^ii  TABLE OF CONTENTS ^  iv  LIST OF TABLES ^  vi  LIST OF FIGURES ^  vii  ACKNOWLEDGEMENTS ^  viii  PREFACE  ^1  INTRODUCTION  ^2  CHAPTER 1. THE PROBLEM OF TEMPORAL SCALE IN OPTIMIZATION: THREE CONTRASTING VIEWS OF HUMMINGBIRD VISITS TO FLOWERS ^7 The fluid mechanics of nectar intake  ^8  Intake rate over the loading phase of licking  ^10  Energy intake rate over the licking cycle  ^15  Energy intake rate over a feeding visit  ^23  Limitations of the models  ^27  Nectar intake parameters in nature and the laboratory  ^28  Nectar volume in nature  ^31  Implications for field manipulations  ^33  Implications at fine temporal scales: intake rate and optimal concentration  ^33  Implications at coarser temporal scales  ^36  CHAPTER 2. LICKING BEHAVIOUR AND THE ENERGETICS OF THE LICKING CYCLE  ^42  Materials and methods  ^43  Results  ^47  Conclusions  ^51  V  CHAPTER 3. HUMMINGBIRDS' CONCENTRATION PREFERENCES AT LOW VOLUME AND THE ENERGETICS OF FEEDING VISITS AND FORAGING BOUTS ^57 Materials and methods  ^57  Results  ^61  Conclusions  ^64  DISCUSSION  ^68  Implications for optimal foraging theory  ^69  Implications for pollination biology  ^71  BIBLIOGRAPHY ^  81  APPENDIX 1. GLOSSARY OF TERMS USED IN CHAPTER 1  ^95  APPENDIX 2. SAMPLE SIZES IN FIGURES 11 AND 12  ^96  vi LIST OF TABLES Table^  Page  1.  Nectar uptake parameters for hummingbirds  ^29  2.  Analysis of variance of energy intake rates during licking with concentration at five nectar pool volumes  ^51  3.  Bill lengths and body weights of experimental birds  ^58  4.  Analysis of variance of energy intake rates for feeding visits and foraging bouts  ^62  5. Sample sizes in volume and energy intake rate graphs  ^96  vii  LIST OF FIGURES Figure^  Page  1.  A hierarchy of temporal scales of hummingbird foraging  ^8  2.  Intake rates during tongue loading as a function of sucrose concentration  ^12  3.  Energy intake rates during the licking cycle  ^16  4.  Contour plots of the number of licks required to empty a nectar pool as a function of concentration ^20  5.  Energy intake rate during the licking cycle for 3 nectar pool volumes under constant volume and constant frequency licking  ^22  6.  Handling times and intake rates during a feeding visit for 4 nectar pool volumes at 4 durations of handling time overhead under constant volume licking ^24  7.  Handling times and intake rates during a feeding visit for 4 nectar pool volumes at 4 durations of handling time overhead under constant frequency licking ^25  8.  Recession of the fluid meniscus within single visits  ^48  9.  Variation in licking behaviour within single visits  ^49  Variation in parameters of licking behaviour with concentration  ^50  10.  11. Volume intake rates for feeding visits of 4 rufous hummingbirds at five concentrations 12.  Energy intake rates for feeding visits and for foraging bouts, and concentration preferences  ^62  ^63  13. Generalized representation of two food types corresponding to dilute and concentrated nectar.... ^66  viii  ACKNOWLEDGEMENTS I wish to thank several people for their help and support: Lee Gass gave advice and suggestions on all aspects of my research and thesis. Gayle Brown and Gordon McIntyre helped with computer programming and bird care. My Research Committee, Robert Blake, John Gosline and Carl Walters, provided suggestions for my experiments and thesis. Robert Blake also generously allowed me to use his digital oscilloscope. Don Brandys provided the technical expertise to design and build the electronic hardware used in my experiments. Tom Daniel enthusiastically responded to work in progress and suggested future directions. William W. Roberts drew the equations. Andrew Fedoruk edited the penultimate draft of the thesis. The following provided assistance with previous versions of the manuscript "The problem of temporal scale in optimization: three contrasting views of hummingbird 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 offered helpful comments. A. Blachford, G. Landon, and D. Ludwig offered programming 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 to C. L. Gass.  1  PREFACE Chapter 1 and portions of the Introduction and Discussion of this thesis were derived from the manuscript, "The problem of temporal scale in optimization: three contrasting views of hummingbird visits to flowers", by Clifton Lee Gass and W. Mark Roberts, in press in The American Naturalist. I contributed the models and their predictions about the effect of time scale on optimal concentration to this manuscript, and Lee Gass contributed the consideration of nectar parameters in nature and the majority of the literature research. We were jointly responsible for all writing and graphics. Signed,  C. Lee Gass Date:^  A  2 INTRODUCTION A central notion of optimal foraging theory is that through evolution and/or learning, animals perform actions that increase their fitness. It has long been recognized that both costs and benefits of actions must be considered (MacArthur and Pianka 1966; Emlen 1966; Schoener 1971), but it has not always been clear what combination of costs and benefits may be optimized by a given animal in a given situation. Identifying costs and benefits and defining appropriate currencies is a critical problem (Pyke 1984; Stephens and Krebs 1986; Possingham 1989), and great effort has gone into its solution. It is particularly difficult to know over what temporal scale the costs and benefits of behaviour should be considered (Templeton and Lawlor 1981), especially since their consequences can be significant on a vast hierarchy of scales (e.g. Gass and Montgomerie 1981; Orians 1981; Allen and Starr 1982). Investigators usually use their biological intuition to select temporal scales (Stephens and Krebs 1986), but they may single out different temporal scales in the same system because their intuition is informed by different experience (Pyke and Waser 1981). Ignoring this fact can confound attempts to understand the economics of foraging. Stephens and Krebs (1986, Box 2.1) made this general point with a simple hypothetical example. In this thesis I make the point again in more detail, using both optimal foraging models and experiments to apply it to a real biological example, hummingbirds feeding at flowers.  3  Nectarivorous animals and the flowers that they visit are convenient systems in which to test foraging theory. Flowers are conspicuous and stationary, and the caloric value of nectar is readily quantifiable (e.g. Bolten et al. 1979; Trombulak 1990). Metabolic costs of a variety of activities have been measured in many 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 conditions which influence their energy balance, so they have proven to be well-suited for testing important issues in optimal foraging theory (e.g. DeBenedictis et al. 1978; Pyke 1978a; Hixon and Carpenter 1988; Mitchell 1989; Tamm 1989). Considerable attention has been focussed on the significance of the low sugar concentrations prevalent in most hummingbirdpollinated plants' nectar (e.g. Baker 1975; Bolten and Feinsinger 1978; Pyke and Waser 1981; Calder 1979; Heyneman 1983; Kingsolver and Daniel 1983; Plowright 1987; Sutherland and Vickery 1988). Sugar concentrations in flowers visited primarily by hummingbirds typically average 20 - 25 % sucrose equivalents (all concentrations reported are wt/wt), similar to the dilute nectars of butterfly-pollinated plants, but lower than mean concentrations of over 35 % in bee-pollinated flowers (Baker 1975; Pyke and Waser 1981; Heyneman 1983). One tropical plant produces nectar with a mean concentration of 24 % when hummingbirds visit it. Then, after its flower corollas fall, it  4  secretes nectar with concentrations of 41 - 51 % that is consumed by ants which presumably guard the plant (Gracie 1991). Floral characteristics of animal-pollinated plants appear to be closely coadapted with the behavioural, physiological and morphological characteristics of their pollinators. Flower colour (Miller and Miller 1971; Raven 1972; Stiles 1976; Bleiweiss 1990; Weiss 1991), and patterns of flower arrangement and nectar abundance in flowers (Whitham 1977; Pyke 1978b; Eckhart 1991; Itino et al. 1991) frequently correspond to pollinators' preferences and movement patterns. The sugar and amino acid composition of plants' nectar appears to be suited to the digestive constraints and nutritional requirements of the species that visit and pollinate them (Baker and Baker 1973, 1983, 1986; Gryl et al. 1990; Martinez del Rio 1990a,b; Freeman et al. 1991; Galetto 1991; Erhardt 1991a; but see Alm et. al 1990; Martini et al. 1990; Erhardt 1991b). Corolla morphology often provides a close fit to pollinators' bill or tongue size and shape (Feinsinger and Colwell 1978; Gill and Wolf 1978; Snow and Snow 1980; Nilsson 1988; Colwell 1989; Fenster 1991). Given this close correspondence between other characteristics of plants and the preferences of their pollinators, it is incongruous that in choice tests hummingbirds have not preferred artificial nectars as dilute as those offered by the plants they visit, but have instead chosen concentrations higher than 45 % (Van Riper 1958; Stiles 1976; Pyke and Waser 1981; Tam and Gass 1986).  5  Hummingbirds feed by licking with their forked, open-grooved tongues, into which nectar flows by capillary action (Weymouth et al. 1964; Hainsworth 1973; Ewald and Williams 1982). Increasing concentration increases nectar's caloric value and also increases its viscosity and thus decreases its fluid flow rate into the tongue grooves. Kingsolver and Daniel (1983) modelled hummingbird licking and predicted that the sugar concentration which optimizes birds' energy intake rates is 20 - 25 % sucrose for feeding on low nectar pool volumes, but 35 - 40 % for feeding on high volumes. Under this model, therefore, the discrepancy between nectar concentrations in nature and birds' observed choices might be an artifact, because volumes in most North American flowers are small (Chapter 1), whereas all published choice tests have used large volumes, usually infinite from the birds' point of view. The details of nectar uptake by hummingbirds are critical for 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 high frequency 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 they visit. Consequently, key assumptions of nectar feeding models have not previously been tested. In this thesis I investigate Kingsolver and Daniel's (1983) models within a conceptual framework of hierarchies of temporal scale. I also present measurements of parameters of licking at a  6  range of concentrations and nectar pool volumes, and test key assumptions of the models. Finally, I report results of concentration preference tests for hummingbirds at realistically low nectar pool volume. My findings challenge existing interpretations of patterns of nectar sugar concentration in nature, and demonstrate the critical importance of identifying appropriate time scales in both predictions and tests of optimal foraging theory.  7 CHAPTER 1 THE PROBLEM OF TEMPORAL SCALE IN OPTIMIZATION: THREE CONTRASTING VIEWS OF HUMMINGBIRD VISITS TO FLOWERS  Here I show that different pictures of profitability emerge from analyses of visits by hummingbirds to flowers on three temporal scales that differ over a narrow range. These differences are sufficiently great to affect the design of investigations and to alter conclusions about the evolution of plants and their pollinators. The daily activity budgets of hummingbirds could be analyzed on several different temporal scales (Fig. 1). Most studies of optimal nectar concentration have considered flower visits (Hainsworth and Wolf 1976; Stiles 1976; Pyke and Waser 1981; Heyneman 1983; Kingsolver and Daniel 1983; Montgomerie 1984; Tamm and Gass 1986; Stromberg and Johnsen 1990). Some studies have examined visits to inflorescences or plants (Pyke and Waser 1981), and foraging bouts (Tamm 1989). I consider three temporal scales -- all within flower visits. At the finest scale I explore the fluid mechanics of nectar loading by a hummingbird's tongue while it contacts a pool of nectar during a single lick, re-examining previous conclusions about the nectar concentration that maximizes loading rate. Then I show that this optimal concentration increases systematically as the analysis is extended in time, for example to include both loading and unloading phases of the licking cycle. At the coarsest scale I consider the duration of entire visits to  8  flowers, including time not spent licking, over a range of conditions.  FORAGING CYCLE  perch  n  <hungry ?›  y4  FORAGING BOUT  fly to patch  fly to flower  1  FLOWER VISIT  insert bill  4  insert tongue withdraw tongue  <with  4 draw bill  LICKING CYCLE  ?›  y4  n^< satiated ?› Y  4  fly to perch  Figure 1. A hierarchy of temporal scales of hummingbird foraging.  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 tongue loading phase of the licking cycle, while the tongue contacts the nectar pool (Hainsworth 1973; Ewald and Williams 1982). During  9  the unloading phase, the tongue retracts into the bill, which squeezes nectar into the mouth as the tongue extends for the next lick (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 a maximum of about 17 Hz. The energy content of nectar approximates a linear function of sugar concentration by weight (but an accelerating function of concentration by volume; Bolten et al. 1979). Nectar viscosity is an exponentially increasing function of concentration, and as a result, volume flow rate decreases with concentration. The combination of increasing caloric content per unit volume and decreasing volumetric intake rate with increasing sugar concentration causes energy intake rate to peak at an intermediate concentration. At each time scale I consider, I refer to this as the optimal concentration. Two theoretical models based on different assumptions predict this optimum. Heyneman's (1983) steady-state, continuous nectar flow model (which applies to the loading phase only) predicts an optimum of 22 - 26 % sucrose by weight, but Kingsolver and Daniel (1983) pointed out that nectar flow is not at steady state if induced by capillarity. Under this condition, flow rate is extremely high initially and decreases rapidly with time. Their more realistic capillarity-induced, discontinuous flow model (which applies to the complete licking cycle) predicts optima of 40 - 45 % when feeding from high volume nectar pools requiring many licks to empty. For small volumes that can be  10  loaded on a single lick, however, description of fluid flow requires no unloading phase, so the two models converge mathematically and predict the same low optimal concentration. My aim here is to assess the significance of the biophysical models when applied on longer time scales than those for which they were derived. Kingsolver and Daniel (1983) considered two of the many possible licking behaviours that hummingbirds might employ. In their "EL" licking, the tongue loads to a constant volume across all concentrations; I refer to this as CV (constant load volume) licking. Loading time must increase with increasing concentration because flow rate decreases. If unloading time remains constant, then licking frequency must decrease. In Kingsolver and Daniel's (1983) "ET" licking, frequency and its components, loading and unloading time, are constant across concentration; I refer to this as CF (constant frequency) licking. Again because flow rate decreases with increasing concentration, volume loaded per lick must also decrease. Although real hummingbird licking behaviour is unlikely to precisely follow either of these patterns, I restrict my analyses to them in order to enable comparisons with Kingsolver and Daniel's (1983) model results. Intake rate over the loading phase of licking Nectar flow during the loading phase of the licking cycle is essentially what Heyneman (1983) modelled. It is not surprising, therefore, that the 22 - 26 % optimal sugar concentration she  11  predicted accords with Kingsolver and Daniel's (1983) prediction explicitly derived for loading. The dynamics of loading the two grooves of a hummingbird tongue are described by  (1)  V  nr3ycos8 141  and  (2)  E  Trr3ycos8epS PA  (modified from Equation 8 in Kingsolver and Daniel 1983). V is volume intake rate, E is energy intake rate, r is tongue groove radius, and 1 is the distance to which nectar flows into the tongue grooves. All other symbols describe physical properties of sucrose solutions (see Appendix 1 for definitions). Holding loading distance, 1, constant in Equation 2 is the condition for constant volume licking. Throughout my analyses of CV licking, I assume 1 is tongue groove length, l g ; i.e. that the grooves are filled completely. The solid curves in Figure 2 depict the loading phase for a bird that exhibits this behaviour. Volume intake rate decreases rapidly with concentration, due to increasing viscosity, g. The ascending portion of the energy intake rate curve (Fig. 2b) results from the increasing caloric content of food, Eps, while volume flow rate is still high. The descending portion at high concentration results from very low flow rate, in spite of high caloric content. Inspection of  12 .---. 75  E< 50  Z 25  0  0  DURATION OF ^ 28 42^83 ms LOADING PHASE 30  B E.  N  r4 20 /  z  \  N  \  \  10  N  0  N  20^40^60^80  NECTAR CONCENTRATION (%) Figure 2. Intake rates during tongue loading as a function of sucrose concentration. The solid curves describe constant volume licking, and the broken curves, constant frequency licking for three different values of tongue loading time. Arrows indicate the maximum concentrations at which the tongue can load completely under constant frequency licking. Tongue groove parameters are for rufous hummingbirds (Selasphorus rufus); r = 0.16 mm, l g = 11.8 mm (WMR, unpublished data).  13  Equation 2 reveals that although energy intake rate varies with tongue groove radius and nectar loading distance, optimal concentration is insensitive to both (Kingsolver and Daniel 1983). Optimal concentration is also independent of metabolic costs, which displace the curves downward without changing their form when subtracted from E. Therefore, an optimal concentration of 23.6 % for tongue loading under CV licking should be general across hummingbird size and morphology under these assumptions. Suppose, however, that hummingbirds cannot adjust loading time to hold lick volume constant across concentrations, and instead exhibit constant frequency licking and constant loading time, T1. Two cases are possible. Viscosity may be low enough to allow complete tongue loading during the loading phase, so that nectar loading distance equals tongue groove length, (3a)  1 = 1g  as I assumed for CV licking. Alternatively, viscosity may be too high to allow complete loading during T1 (i.e. 1 < l g ), so that 1 is limited by fluid dynamics instead of by l g :  (3b)  i . V rycoseT 2i.L  (which is Equation 3b of Kingsolver and Daniel 1983). For either case  14  (4)  E^2nr2lEpS Tt The broken lines in Figure 2 illustrate the effect on volume  and energy loading rates of switching from complete to incomplete loading (switching from my Equation 3a to 3b) at particular concentrations for three different values of loading time, Tl. Note that this switch occurs where the broken curves for constant frequency licking intersect the solid curves for constant volume licking. By definition, the CV curves result from modulation of loading time to allow exact, complete filling of the tongue grooves. At concentrations at which intake rates are less for CF than for CV licking (to the left of the solid CV curve in Figure 2a), loading time is longer than required to fully load the tongue. This wasted time results in lower intake rates than could be achieved were the bird not constrained to a fixed licking frequency with a fixed loading time. At concentrations above this threshold, volume and energy loading rates are higher for CF than for CV licking. It is counterintuitive at first that intake rates should be greater under conditions that do not allow complete loading, but because loading rate decreases dramatically with loading time (Equation 4), birds achieve higher rates during the loading phase if they load for less time and thus take smaller volumes per lick. For this case, the optimal concentration is higher for CF than for CV licking. The conclusion that optimal concentration during the loading phase is sensitive to details of licking  15  behaviour probably extends to patterns of licking other than the two considered here  (see  Kingsolver and Daniel 1983).  Energy intake rate over the licking cycle The 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, T u , is required to unload the tongue grooves on each lick, and including it in the rate averaging functions increases the optimal concentration. Licking from a non-depleting nectar pool. High volume artificial feeders typically used in tests of concentration preference and intake rate offer more food than birds can consume in 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 are exact multiples of tongue loading volume and can be consumed during single visits. For constant volume licking, energy intake rate over the complete cycle is  (  5  )  E - 277r2tepS -2 Ell 11- T ry c o s 8 u {  (incorporating Equation 3a of Kingsolver and Daniel 1983 in the denominator).  16  Figure 3a shows the effect of unloading time, T u , on energy intake rate.^Equation 5 reduces to Equation 2 when T u = 0, so the uppermost curve in Figure 3a is the same as the solid curve in Figure 2b. Note that optimal concentration is sensitive to even small increases in T u , which shift it upwards. At T u = 25 ms, near the 30 ms estimated for C. anna (Ewald and Williams 1982), optimal concentration is 28.9 %. The curves are increasingly flat with increasing T u , because the added time depresses intake rate. Hummingbirds would have to be more  CONSTANT VOLUME 20  ^  CONSTANT FREQUENCY  A  B  a 10  z a  z 0  0  20^40^60^0^20^40  60  SUCROSE CONCENTRATION (%)  Figure 3. Energy intake rates during the licking cycle. The curves indicate six unloading durations under constant volume licking (unloading time, T u ; ms), and six licking frequencies under constant frequency licking (frequency, f; Hz). T u is 42 ms at 12 Hz constant frequency licking, and this is comparable to T u = 50 ms under constant volume licking (bold curves). The bold line connecting the peaks of the curves illustrates the upward shift in optimal concentration with increasing T u or decreasing f. Tongue groove parameters are as before.  80  17  sensitive at long than at short T u to discriminate among concentrations on the basis of energy flux. This is equivalent to concluding that in order to select optimum nectar concentration, hummingbirds would require greater sensitivity to differences in energy intake rate if they evaluated intake over the entire licking cycle rather than over the loading phase only. Under constant frequency licking, the proportions of the cycle taken up by the loading and unloading phases could vary at any given licking frequency, f. Kingsolver and Daniel (1983) concluded that energy intake rate is maximized when the loading and unloading phases are exactly equal in duration; when tongue loading time is half the licking cycle and intake rates are averaged over the period of the cycle, 1 / f. Substituting this in the denominator of Equation 4 yields  (6  )^  E. 2nr2lEpSf  This doubling of the time constant in Equation 4 produces the same form of relationship between energy intake rate and concentration as shown in Figure 2; it merely halves the amplitude of the curves (Fig. 3b). Optimal concentration therefore varies in the same manner for both the loading phase alone and the complete licking cycle under CF behaviour. For most plausible licking frequencies, optimal concentration is 35.7 %; however, if Hainsworth's (1973) report of 2.7 Hz licking by black-chinned hummingbirds (Archilochus alexandri) is accepted  18  (but see Ewald and Williams 1982), optimal concentration could be higher than 43 %. Licking from a depleting nectar pool. The preceding analysis lacks realism in that I have imagined birds feeding from nectar pools which are either infinite or contain integral multiples of lick volume. Flowers are not this obliging in nature, so volume loaded per lick, V1, must vary, at least on the last lick, which loads whatever nectar has not been already taken. The assumption that hummingbirds remove all nectar is approximately satisfied in many systems (e.g. Gass and Montgomerie 1981; Wolf and Hainsworth 1983), but since there are important exceptions (e.g. Whitham 1977; Wolf and Stiles 1989) it should always be tested in practice. Because empirical studies have demonstrated that handling time approximates a direct linear function of nectar pool volume (Hainsworth and Wolf 1972b; Wolf et al. 1972, 1975; Wolf 1975; Wolf and Wolf 1976; Gass and Montgomerie 1981), this variable must be a component of analyses of intake rate optimization. If nectar pool volume, V p , is less than meal size, the total time spent licking increases in stepwise fashion with the number of licks, n, required to load it. If I assume that all licks load the same amount, except for the last if pool volume is not an integral multiple of tongue loading volume, then for both CV and CF licking, n = Vp / V1, rounded up to the nearest whole lick. I shall also assume that the last lick takes as much time as each of the previous ones, even when it does not obtain as much nectar.  19  Under constant volume licking, loading time is modulated to maintain constant tongue loading volume at all concentrations. Under constant frequency licking, however, loading volume decreases with concentration. If either concentration or licking frequency are low enough, the tongue can load fully in less than or exactly the duration of the loading phase. Under my assumptions, V1 would then be the tongue groove capacity, 2yr 2 1 g . At concentrations and/or frequencies too high to permit full groove loading,  (7)  %ft r. 27Tr2 _  ^rrcose9 4/4.1  For CV licking, the number of licks, n, is invariant with concentration for a given nectar pool volume, V P (Fig. 4). The number of licks is a complex function of concentration and volume under CF licking, however. The discontinuity between the straight and curvilinear segments of the isopleths marks the maximum concentration at which viscosity is still low enough to allow complete groove loading over the loading phase, T1. Consider low frequency licking, 6 Hz, from low concentration nectar. Under this condition, viscosity is low enough and loading rate high enough that the tongue can fully load in less than or exactly T1. In this example the tongue loads fully at all concentrations less than 33 %. This threshold is reached at lower concentration at higher frequency, because less time is  20  CONSTANT VOLUME ^ ^ Tu = 250 100 40  8  4  4.1  4  ^  4  6 3  0  ^  ^  3  ^  3  4  —4 0 0 2 ra_.  2  ^  2  ^  2  0 CONSTANT FREQUENCY ^ ^ F = 6 12 8  41  18  50 \^\ \  41 0  6  4  4  4  3  3  3  2  2  2  1  1  1  58  4  ,_. 0 0 2 ci.  0  0  ^ ^ 40^0^40^0 40 80 NECTAR CONCENTRATION (%)  Figure 4. Contour plots of the number of licks, n, required to empty a nectar pool, V p , as a function of concentration. Panels indicate three values of unloading time, T u (ms), under constant volume licking, and frequency, f under constant frequency licking. For clarity, I graph only the first ten licks for constant frequency licking, numbering only the first four, and include maximum n (at maximum V 13, and concentration) in the corner. Vertical lines indicate the maximum concentration at which the tongue can load completely during loading time, T1, under constant frequency licking. Tongue groove parameters are as before, with V1 = 1.9 gl for rufous hummingbirds (WMR, unpublished data).  21  available for loading, so that tongue loading is complete only below 9 % at 18 Hz. Including nectar pool volume in energy intake rate calculations produces dramatic, qualitative differences between constant volume and constant frequency licking behaviour. For the former,  V E pS E- ^ P +T  (8)  ILE r7COSe  n[  Uj  If nectar pool volume, Vp , is not an integral multiple of tongue loading volume, V1, the last lick takes less volume than previous licks. This is equivalent to decreasing loading distance, 1, in Equation 8. As noted above, optimal concentration is insensitive to variation in tongue groove parameters for CV licking (Fig. 5a). However, decreasing pool volume decreases average energy intake rate at all concentrations, because the diminished energetic return of the last lick is an increasing proportion of total harvest. For CF licking, the energy intake rate is  (9)  E . VpEpSf n  where n is derived using tongue loading volume, V1, from Equation 7. Note that the increasing portions of the energy intake rate curves in Figure 5b are not straight, but slightly concave  22  upwards. This is because sugar content per unit volume is an exponential function of concentration (wt/total wt). The relationship between energy intake rate and concentration is extremely complex at all realistic pool volumes (Fig. 5b). Consider the curve for 1 Al of nectar in the 12 Hz example illustrated in Figure 5b. Beginning at 0 %, energy intake rate increases steadily with concentration up to a threshold beyond which viscosity is so high and loading rate so low that the 42 ms loading phase is insufficient to load the pool on one lick. At a slightly higher concentration, another lick is required to load  CONSTANT VOLUME 12  ^  CONSTANT FREQUENCY  A  B  <4 6  z 0  z 0  0  20^40^60^0^20  40  60  80  SUCROSE CONCENTRATION (%)  Figure 5. Energy intake rate during the licking cycle for three nectar pool volumes, V D (Al), under constant volume and constant frequency licking. The vertical line connecting the peaks of the curves for constant volume licking illustrates the independence of optimal concentration and V P under this behaviour. For constant volume licking, unloading time (T u ) = 50 ms, and for constant frequency licking, frequency (f) = 12 Hz. Tongue groove parameters are as before.  23  the miniscule residual volume. Since intake is now averaged over two licks instead of one, it drops sharply. This sawtooth pattern continues as concentration increases and more licks are required to remove the same volume. The curves are less jagged at greater pool volume because the energetics of the last lick play a decreasing role in the energetics of the visit as volume increases. The family of "curves" for any licking frequency are all bounded by the case in which nectar pool volume is infinite, which for the case illustrated in Figure 5b is analogous to that described by the curve for f = 12 Hz in Figure 3b. Energy intake rate over a feeding visit Handling time at flowers, Th, is longer than required to lick nectar. The bird must position its bill and insert it into the flower corolla at the start of the visit, and withdraw it at the end. The time required to do this, Ti, is an overhead cost paid regardless of the amount of nectar in the flower. Although Ti varies with flower and bird morphology (Wolf et al. 1975) and experience (unpublished observations; see also Laverty 1980 for bumblebees), and should also vary with bird agility, it should be independent of licking behaviour. Including the overhead cost of handling flowers, Ti, in analyses of feeding energetics for CV and CF licking results in  VpepS  (10)^E -  n  2µt 2+ T U] + Ti rycose  24  and  respectively. Increasing Ti always decreases energy intake rates over feeding visits. Adding Ti also increases optimal nectar concentration for both types of licking (Figs. 6 and 7), for the same reason that adding unloading time shifts the optimum upward in constant  Ti = 0.0  0.5  1.0  1.5  4 3  HANDLING TIME (s)  2  30  VOLUME INTAKE RATE (Alb)  20 10 12  ENERGY INTAKE RATE (W)  9 6 3 0 0  ^  40  ^ ^ 0  40^0^40  ^ ^ ^ 0 40 80  SUCROSE CONCENTRATION (7.)  Figure 6. Handling times and intake rates during a feeding visit for four nectar pool volumes, VD , at four durations of handling 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 (T u ) = 50 ms and tongue groove parameters are as before.  25  Ti = 0.0  ^  0.5  ^  1.0  ^  1.5  4 3  HANDLING TIME^2 (s) 30  VOLUME^20 INTAKE RATE 10 12 9  ENERGY INTAKE RATE 6 (W)  3 0 0  ^  40  ^  0  ^  40^0^40  ^ ^ ^ 40 BO 0  SUCROSE CONCENTRATION (7.)  Figure 7. Handling times and intake rates during a feeding visit for four nectar pool volumes, Vp , at four durations of handling time overhead, Ti, under constant frequency licking. From top to bottom in each panel, curves indicate V = 10, 2.5, 0.5 and 0 gl. f = 12 Hz and tongue groove parameters are as before.  volume licking (Fig. 3a). In both cases, time is added to the denominator of a relationship that generates a rate across concentration. Because tongue loading time, the other term of the denominator, increases with concentration, the added time influences the rate proportionally less at high concentration. In other words, the overhead cost of handling flowers enhances the advantage of the high caloric quality of concentrated nectar by offsetting the disadvantage of slow loading. The optimum shifts upward at all pool volumes but more so at low than at high volume; fewer licks and less time are required to harvest small  26  nectar pools, so the overhead is a larger proportion of total handling time (Figs. 6 and 7). Adding the overhead time also reduces the jaggedness of the curves that describe constant frequency licking (Fig. 7), for the same reason that it affects optimal concentration. The heights of all steps of all handling time curves at each Ti are equal, because each extra lick adds a constant amount of time regardless of nectar volume or concentration. The curves become smoother with increasing overhead time, however, because these increments in duration are relatively smaller proportions of total handling time at high than at low Ti. As with the shift in optimal concentration, curve smoothing is more pronounced at low than at high volume, because the overhead time is a larger proportion of total handling time. Although energy intake rate, optimal concentration, and the complexity of the intake rate curves are all sensitive to variation in both nectar pool volume and the overhead cost of handling flowers at all values of these parameters, they are most sensitive at combinations of low volume and low overhead. Increasing overhead slightly has a large effect on intake rate when overhead and pool volume are both near zero and far less effect when they are large. In general, overhead time reduces the influence of fluid dynamics and the details of licking behaviour on optimal nectar concentration, and increases the relative importance of the gross energy return from feeding visits. As energy intake rate is considered over successively longer time scales, from the loading  27  phase up to complete visits, optimal concentration shifts upwards. The time scale over which hummingbirds average energy intake rate, if indeed this is the currency to which they respond, must play a major role in determining optimal nectar concentration. Limitations of the models Following Kingsolver and Daniel (1983), my models assume that only the tips of the tongue grooves contact the nectar pool. If more of the tongue were immersed, as it routinely is at feeders, fluid might enter the open grooves along their length, possibly speeding loading (Hainsworth 1973; Kingsolver and Daniel 1983; Feinsinger 1987; Paton and Collins 1989). This is supported by Montgomerie's (1984) conclusion from high-volume laboratory tests that handling time is a decelerating positive function of volume. Nectar might also adhere to the external surface of the tongue. Such factors should increase optimal concentration by releasing nectar loading rate from the constraints of fluid dynamics, i.e. from viscosity. Therefore, these models are most applicable to flowers with small nectar pools or long corollas, which do not allow appreciable immersion. It is probably unrealistic to assume that hummingbirds lick at one constant frequency throughout a feeding visit, that they maintain this frequency across all concentrations, and that the loading and unloading phases are equal. I expect that even within a single visit these components would vary, for instance to adjust for the receding fluid meniscus during licking. Tongue  28  loading volume should be greater with deeper immersion, but decrease during licking as the pool is depleted (see above, and  Feinsinger 1987). However, no experimental evidence yet exists to allow discrimination between constant volume, constant frequency, or other possible licking behaviours. I have arbitrarily adopted the assumption of equal loading and unloading phases in CF licking to preserve compatibility with Kingsolver and Daniel's (1983) analysis. The assumption that intake rate during the licking cycle does not vary with overhead cost (in reality, that intake rate is independent of flower morphology) is unrealistic. Tongue immersion depth and/or loading time should decrease for a given pool volume with tongue extension distance and therefore with flower corolla length. Handling time increases dramatically only near maximum corolla length (Wolf and Hainsworth 1971; Montgomerie 1984; Temeles and Roberts, in review), so immersion depth may be partly conserved, but it must decrease to zero at maximum extension. Intake rate would still decrease if birds conserved loading time by decreasing licking frequency as tongue extension increased (Ewald and Williams 1982). Insufficient information is available to evaluate this assumption rigorously. Nectar intake parameters in nature and the laboratory Nectar intake parameters in Table 1, for real birds at flowers and feeders, suggest some general patterns to consider when interpreting my theoretical results. First, intake over the licking cycle is typically slower at flowers than at high volume  Table 1. Details of estimates of nectar uptake parameters for hummingbirds. 40  Vp  V (Ws)  Ti (s)  48  -20-120  2.6  1.26  Wolf et al. 1972  a  H. rostrata  40  -20-120  4.0  1.3  Wolf et al. 1972  a  37  H. imbricata  25  -20-120  3.7  0.8  Wolf et al. 1972  a  4.5  19  H. imbricata  25  -20-120  7.7  1.11  Wolf et al. 1972  a  F  -3.5  -17  Castilleja miniata  -26  0-10  8.3  1.22  Gass and Montgomerie 1981  b  S. rufus  F  -3.5  -17  Ipomopsis aggregata  26  0.5-20  23.3  0.37  R. Mitchell. pers. comm.  c  S. flammula  ?  2.7  12.8  Tropaeolum sp.  10-12  0.03-0.35  13  0.03  Hainsworth and Wolf 1972 b  d  Archilochus alexandri  F  -3.3  -23  Penstemon barbatus  -10-12  0.14  1.0  0.84  F.R. Hainsworth, pers. comm.  d  A. alexandri  M  -3.3  -23  P. pseudosFectabilis  25-30  02-5.35  4.35  0.35  F.R. Hainsworth, pers. comm.  d  A. alexandri  F  -3.3  -23  P. pseudospectabilis  25-30  0.1-4.3  5.56  0.35  F.R. Hainsworth, pers. comm.  d  A. alexandri  M  -3.3  -23  Bouvardia ternifolia  20-35  0.18-3.9  3.11  0.32  F.R. Hainsworth, pers. comm.  d  Cynanthus latirostris  M  -3.2  18-21  P. pseudospectabilis  25-30  0.5-4.8  8.33  038  F.R. Hainsworth, pers. comm.  d  Eugenes fulgens  M  8.3-10  31-32.4  P. pseuodspectabllis  25-30  ?  5.88  0.58  F.R. Hainsworth, pers. comm.  d  Amazilia tzacatl  ?  5.0  20  E. fulgens  M  8.3-10.0  S. rufus  F  S. rufus  F  Plant Species  Corolla (nun)  37  Heliconia tortuosa  6.0  37  ?  6.0  ?  Selasphorus rufus  Sex  Weight (g)  Bill (mm)  Phaethornis superciliosus  ?  6.0  P. superciliosus  ?  P. superciliosus Thalurania furcata  Bird Species  Source  Notes  Hermits at flowers  Non-hermits at flowers  IL imbricata  25  20-120  4.3  0.7  Wolf et al. 1972  d  31-32.4  feeder  10  0-20  46.0  0.28  Hainsworth et al. 1983  e  3.5  -17  feeder  13.5  0-20  23.1  0.52  This study  f  33  17  feeder  7  0.5-20  24.4  0.44  R. Mitchell, pers. comm.  c  1121111211111ILlitall  30 Table 1, Notes: In every case, V is the reciprocal of b in the relationship Th = Ti + bV p . indicates that the parameter was not given in the source; it was estimated from related studies by the same authors, from population figures in other sources, from field notes, or from personal communications. a  d Th estimated in the field by stopwatch and/or by counting movie frames. VP estimated indirectly as the product of measured time since last visit to each flower and population mean of hourly nectar production rate. Revisits not included in calculations. b^Th estimated in the field by stopwatch, beginning at dawn. V manipulated by adding 5 or 10 Al of sucrose solution to samples of flowers during the night. Each sample was assumed to contain the amount added plus the population mean at dawn for unmanipulated flowers. Revisits were included in calculations, but were few.  Th estimated in the field by stopwatch. Vp manipulated by adding sucrose solution to empty flowers or feeders.  e  Th estimated in the laboratory for 0 and 20 Al by counting movie frames.  f  Th measured automatically in the laboratory by computer, which monitored a photodarlington triggered by the bill on insertion and withdrawal. V p = 0 2 , 4, 6 8 , 10, 15 or 20 Al. Mean for three birds. ,  ,  feeders. Thirteen of 14 volume intake rates at flowers are less than 10 Al/s and 8 are less than 5 Al/s, but all rates at feeders are greater than 23 Al/s. Second, the intake rate of a given hummingbird species varies with plant species. For example, rufous hummingbird (Selasphorus rufus) females drank 2.8 times faster at scarlet gilia (Ipomopsis aggregata) than at Indian paintbrush (Castilleja miniata). Third, overhead time varies greatly among flowers: from near 0 s to 1.8 s. Fourth, overhead time characterizes neither birds nor plants alone, but their interaction. One hermit hummingbird species had similar intake rates but different overhead costs at three flower species in the  31  same habitat. Three hermit species had similar intake rates but different overhead costs at one flower species, in the same habitat as above. These patterns probably reflect an interaction between some combination of the length and morphology of flower corollas, including their curvature, and the length and curvature of hummingbird bills and tongues.  Nectar volume in nature In contrast to the paucity of nectar intake parameters, there is abundant information on nectar standing crops. I will describe a few general patterns among hummingbirds to place my models into the perspective of natural variation in nectar volume. Whenever standing crop was reported in sucrose or energy units I converted to volume units when nectar concentration or molarity was also reported (Bolten et al. 1979).  On hummingbird territories. Across a wide range of hummingbird and plant species, nectar standing crop per flower in feeding territories is low and relatively independent of nectar production rate.^Means are usually less than 4 Al, often less than 1 Al, and may approach zero under some conditions (Hainsworth and Wolf 1972b; Gass et al. 1976; Kuban 1977; Gass 1978a; Kodric-Brown and Brown 1978; Pyke 1978a; Waser 1978; Brown and Kodric-Brown 1979; Montgomerie 1979; Waser and Price 1981; Hixon et al. 1983; Feinsinger et al. 1985; Wolf and Hainsworth 1986; Armstrong 1987; Carpenter 1988). Standing crops of Castilleja lineariafolia flowers in a set of S. rufus feeding  32  territories over two summer seasons averaged less than birds' tongue groove volumes (F. L. Carpenter, unpublished data; also see Carpenter 1988). In that study, the means for individual territories were as low as 0.38 and 0.03 gl at some times. Volumes are usually higher inside feeding territories than in nearby undefended areas (Gass 1978a; Hixon et al. 1983; Carpenter pers. comm.), but this pattern was reversed in a breeding system in which males commuted from their territories to feed (Armstrong 1987). On hummingbird traplines. The situation is different with hermits (Phaethorninae) and other hummingbirds in the diverse group of Feinsinger and Colwell's (1978) specialized "high reward trapliners". These larger hummingbirds with longer, usually decurved bills visit flowers with long, usually curved corollas that are widely dispersed except under human disturbance (Feinsinger 1987). Access to these flowers is limited by specialized floral morphology to a small set of specialized nectarivores, and the complex fit of floral and bill morphology may require specialized positioning or inserting techniques that increase flower handling overhead. Flowers produce nectar copiously and accumulate standing crops of up to several hundred microlitres (Feinsinger and Colwell 1978; Feinsinger et al. 1979, 1985; Montgomerie 1979; Angehr 1980; Wolf and Gill 1980; Gill et  al. 1982; Feinsinger 1983; Dobkin 1984; Gill 1987, 1988; Wolf and Stiles 1989). Nectar volume decreased diurnally in some cases in one survey (Feinsinger et al. 1985), but this pattern was much less widespread than with territorial hummingbirds.  33  Implications for field manipulations Several studies have added high-volume feeders to territories (Collias and Collias 1968; Miller and Miller 1971; Pimm 1978; Ewald 1980; Pimm et al. 1985; Tamm 1985). These experiments must be interpreted in terms of both reduced costs and increased benefits of high volume, and it is not always clear which of these contributes more to long-term net benefits. Use of supply rate limited feeders helps reduce available volume (Ewald 1983; Norton et al. 1982; Ewald and Bransfield 1987; Gill 1988), but only marginally, and the reduction of costs due to centralization of normally dispersed resources remains. Even adding nectar to flowers (Gass and Sutherland 1985) or covering them for a time to allow standing crop to accumulate (Hixon et al. 1983) turns flowers into high-volume "feeders". There is no obvious way to completely avoid these problems when manipulating food supply, but results must be interpreted cautiously. For example, the net advantage of specializing on experimentally enriched patches in one study resulted from increases in benefits, not from decreases in costs, and this was not obvious a priori (Gass and Sutherland 1985). These general cautions are not new (Gill 1978). Implications at fine temporal scales: intake rate and optimal concentration Many published handling times, most estimates of nectar intake parameters (Table 1), and all tests of concentration preference have been based on much larger volumes than non-  34  traplining hummingbirds normally encounter in nature (Gass 1974; Hainsworth and Wolf 1976; Kingsolver and Daniel 1983; Montgomerie 1984; Tamm and Gass 1986; Gass 1988; Paton and Collins 1989; Stromberg and Johnsen 1990). In light of my model results, this mismatch of conditions makes interpretation of these studies difficult. Investigators have compared their results with Heyneman's (1983) and Kingsolver and Daniel's (1983) predictions of optimal concentration (Tamm and Gass 1986; Stromberg and Johnsen 1990). Heyneman's (1983) prediction is based on tongue loading rate only, however, and therefore it does not apply to the high volumes used in those experiments because they required many licks. Since the volume loaded per lick has been estimated only roughly and indirectly (Ewald and Williams 1982), it is not yet possible to define the domain in which single-lick models might apply. The above considerations pertain to both constant volume and constant frequency licking. Additional considerations apply to constant frequency licking, in which the jagged optimization functions (Fig. 5) would confound predictions and complicate tests of optimal concentration, especially at the low volumes that non-traplining hummingbirds normally encounter. Mitchell and Paton (1990) concluded that for three Australian honeyeater species the optimum did not shift to low concentration at low pool volume, in contrast to Kingsolver and Daniel's (1983) prediction. They stressed, however, that their results may not be a relevant test of the model, since honeyeater tongues differ  35  considerably in morphology from the hummingbird tongues for which it was derived. Nectar intake is a more complex process than previously modelled, and it is still not completely understood. No licking parameters have previously been measured under rigorous, realistically low-volume conditions, and I modelled only two of several plausible types of licking. Tongue extension, immersion depth, loading volume, and licking frequency are difficult to estimate but must be accurately measured before biophysical models can be applied to reality with confidence (Kingsolver and Daniel 1983; Paton and Collins 1989). One example of how assumptions about details of licking can bias interpretations is Pyke and Waser's (1981) conclusion that optimal 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's slow camera could have missed many licks. Based on high-speed cinematography of a different species (C. anna), they concluded that licking frequency was 13.8 Hz, 4.6-fold faster than Hainsworth's estimate. Pyke and Waser (1981) may therefore have incorporated an overestimation of the duration of the licking cycle in their calculations, and because optimal concentration should increase with this duration (Fig. 3), their prediction of high optimal concentration is not surprising. To the extent that  36  optimal concentration depends on intake rate, then, their conclusions about the significance of dilute hummingbird nectars are precarious. Tamm and Gass (1986) later concluded that optimal concentration is 40 - 45 %, based on measured intake rates during feeding visits over a wide range of concentrations. Another problem is that investigators often fail to specify precisely how intake rate was estimated (e.g. Hainsworth and Wolf 1979; Hainsworth 1981; Schuchmann and Abersfelder 1986; Paton and Collins 1989). My analysis makes it clear that precision in defining rates and temporal scales is crucial to avoiding confusion and misinterpretation (see Wolf et al. 1975; Gill and Wolf 1979). Implications at coarser temporal scales Given the sensitivity of energy intake rate and optimal concentration to temporal scale of integration, it is crucial to choose appropriate temporal scales when interpreting experimental results and when considering coevolution of plants and pollinators (Feinsinger 1987; Gass 1988; Paton and Collins 1989). The problem of temporal scale of integration is likely to prove crucial in other systems as well (see Kacelnik 1984).^However, no generally applicable guidelines yet exist to identify the scales most relevant to fitness. This section provides context for considering this issue. In the introduction hummingbird foraging biology was presented in hierarchical terms. In general, interactions among events at similar scales in the same system tend to be more  37  tightly coupled than events at different scales (Simon 1973), and the following spatial scales represent discrete and successively higher hierarchical levels and longer temporal scales: flowers; inflorescences; patches of flowering plants; territories, traplines, or home ranges; habitats; and geographic ranges (Gass and Montgomerie 1981). Studies of optimization in foraging have usually considered only one of these scales, and usually a relatively fine one. However, the consequences of fine-scaled actions cascade upward in temporal scale, so processes at different scales clearly interact (Allen and Starr 1982; Gass 1985). Perhaps if it were easier to simultaneously consider the full range of scales and their interaction, biological intuition would be better able to identify relevant scales for study of particular systems. Just as I demonstrated above at three fine scales, energy intake rate continues to decrease with increasing scale in my system. I suggest that the following pattern of change generalizes across systems. Consider energy intake rate at the three adjacent scales that I considered earlier: the tongue loading phase of the licking cycle, the whole licking cycle, and handling time at flowers. Tongue loading is directly productive, because nectar is taken up, and energy intake rate increases if nectar quantity and quality are sufficient. Tongue unloading is not directly productive, but it takes time, and because this increases the denominator of a rate whose numerator is constant during unloading, energy intake rate always decreases during this phase. This alternation between productive and non-productive  38  phases as time and energy accumulate during licking accounts for the jagged optimization curves in Figure 5 and 7 (see Stephens and Krebs 1986 for discussion of this phenomenon in a different context). Intake rate decreases again and a new hierarchical level is reached when non-productive flower handling overhead and travel to the next flower are added to the denominator of the equation. Similar alternation of productive and non-productive phases results in discrete, successively longer temporal scales of integration. To complete a foraging bout, hummingbirds must not only lick nectar from flowers, but pay the time and energy overhead of handling each flower and moving between flowers on inflorescences, between inflorescences in patches, between patches in territories or on traplines, and between perches and the first and last patches visited. Addition of perching time between bouts completes the foraging cycle, and accumulation of foraging cycles completes the foraging day. Energy intake rate is higher over a period that includes any productive phase than over the period that excludes it. However, the rate should progressively decrease at successively higher hierarchical levels and longer temporal scales. Average intake rate decreases and optimal concentration increases whenever nonproductive time is accumulated. For example, adding travel time between flowers to flower handling time is mathematically equivalent to adding overhead time to licking; in both cases intake rate decreases and optimal concentration increases. The latter effect, however, is asymptotic (Fig.  3);  jumping from  39  tongue loading to flower visits can increase the predicted optimum more than jumping from flower visits to foraging bouts (contrast Heyneman 1983). Now consider the effect on energy intake rate of variation in its components at each hierarchical level. I showed that because all licks from non-depleting nectar pools are equivalent, energy intake rate for a series of licks is the same as for any one of them. It should be true at all hierarchical levels that energy intake rate over a series of cycles is the same as for any complete cycle, but only if the components of energy intake rate are invariant or compensatory and the rate is invariant among cycles. In practice, extrapolating from one cycle up to series should be undertaken with caution, given the variability of patch quality (Gass and Sutherland 1985), habitat quality (Gass and Montgomerie 1981; Hixon et al. 1983), and meteorological conditions (Calder 1976; Gass and Lertzman 1980). Volume and concentration of nectar, length, width, and shape of flower corollas, and spacing of flowers, inflorescences and patches have been examined, but usually in separate studies, and only rarely have variation or interaction among factors been considered in studies of optimization in hummingbird systems (but see Pyke 1978a; Gill 1988). If energy intake rate varies among cycles, as it usually does in nature, it is difficult to imagine birds averaging over less than entire series unless they use a sliding window or some complex way to discount past variation while they forage (e.g. Green 1980). Animals probably integrate the costs and benefits  40  of foraging over whole hierarchical levels and the scales at which they integrate are therefore discontinuously distributed. Both from foragers' and biologists' points of view, this discontinuous structure should simplify the practical problem of evaluating the consequences of action (see Gass 1985 for discussion of the cognitive benefits of hierarchical decisionmaking structures). For instance, it is convenient to consider licking cycles as productive although they include non-productive unloading time, flower visits as productive although they include flower handling overhead time, and foraging bouts as productive although they include travel time. Clearly, the suggestion that hummingbirds might prefer low concentrations under low nectar volume conditions must be tested empirically. If hummingbirds express as clear concentration preferences at realistically low volumes as they do in laboratory and field tests that use high volume, then it would be important for researchers to know the temporal scale at which these preferences maximize some fitness surrogate. Others have acknowledged that time scale influences estimation and interpretation of net energy intake (Pyke and Waser 1981; Hainsworth and Wolf 1983; Heyneman 1983; Kingsolver and Daniel 1983; Kacelnik 1984; Feinsinger 1987), but the present study is the first detailed, graphical exploration of this effect. My analyses reveal that, although the rate of nectar intake from flowers influences hummingbird energetics, this influence is likely to be most significant under conditions that only some species encounter in nature. Therefore I suggest that the effect  41  of intake rate during flower visits should be significant to optimally foraging birds only in special cases.  42 CHAPTER 2 LICKING BEHAVIOUR AND THE ENERGETICS OF THE LICKING CYCLE  In the analyses of the biophysical models of Kingsolver and Daniel (1983) presented in Chapter 1, I concluded that hummingbirds should prefer low nectar sugar concentrations only if their foraging decisions maximize energy intake rates at very fine time scales. However, this possibility assumes that the models accurately predict energy intake rates during licking, which in turn depends upon how accurately they capture key details of hummingbird nectar feeding. Only two previous studies have estimated parameters of the hummingbird licking cycle. Hainsworth (1973) and Ewald and Williams (1982) used cinematography to investigate licking from high volume feeders. As I discussed in Chapter 1, however, Hainsworth (1973) probably used too slow a camera speed to capture all licks during feeding, and thus underestimated licking frequency 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 at different concentrations and volumes, Kingsolver and Daniel (1983) made several assumptions which I preserved in my extensions of their models (Chapter 1). For example, I assumed that only the tips of the tongue grooves contact the nectar pool during licking, and that volume intake rate while licking is  43  independent of flower morphology, even though I pointed to evidence that these two assumptions are unrealistic. The present study was designed to fill the existing gap in knowledge about hummingbird licking, and in particular to discriminate between the major alternative assumptions that hummingbirds exhibit either Constant Volume or Constant Frequency licking. To evaluate these and other model assumptions, I used an electronic photodetector apparatus to measure parameters of hummingbird licking behaviour and to estimate energy intake rates at the time scale of the licking cycle, at a range of concentrations and volumes. Materials and methods I tested one adult male rufous hummingbird between 3 August and 14 September 1991. This individual was captured at Rosewall Creek on Vancouver Island in May 1991. Its bill length was 16.6 mm from the tip to the base of the exposed culmen, and its weight ranged from 3.3 to 4.7 g over the course of these tests. Although variations in body weight probably influenced the bird's overall energy requirements and its hovering cost while feeding, I assumed that they did not affect the details of its licking behaviour. This bird had participated previously in tests of spatial association learning which employed different methods from the present experiment (see G. S. Brown, PhD thesis, for details). At all times when not in tests, the bird had  free  access to a commercial hummingbird food formula (Nektar Plus; Nekton USA, Inc.) supplemented with soybean protein. During  44  these experiments, the bird was housed in a Plexiglas box (46 mm long x 29 mm wide x 43 mm high). To measure parameters of licking behaviour at different sucrose concentrations and volumes, I built a photodetector array and mounted it in the wall at the opposite end of the Plexiglas box from the bird's perch. The array was a linear series of four infrared emitters facing a parallel series of four detectors (Motorola pin diode components MLED71 and MRD721 respectively) on the opposite side of a feeder tube. This tube was of borosilicate glass (Vitro Dynamics, Inc., ST-8100), closed at the far end, with internal dimensions of 1 mm square by 16 mm deep. The tube was inserted into the array such that each emitter's light passed horizontally across it to the matching detector on the other side. The centres of the light beams were 4.65 mm apart, and were 1.55, 6.20, 10.85 and 15.50 mm from the feeder tube opening (all distances are ± 0.05 mm). The cross-sectional radius of each light beam was 0.86 mm. The tongue of the feeding hummingbird interrupted each of these light beams in sequence, and the resulting voltage reductions were monitored with a Nicolet 4094/4851 four-channel digital oscilloscope. The feeder tube admitted only the bird's tongue, so measurements encompassed only the licking cycle and excluded the overhead time required to position and insert the bill (Chapter 1). Breaking the light beam of the first emitter-detector unit triggered data recording from all four channels of the oscilloscope. After every trial I covered the feeder array, then removed and visually inspected the feeder tube to determine if the bird  45  had emptied it. I then refilled the feeder tube for the next trial with a repeating dispenser. Nectar was dispensed into the far end of the feeder tube from the opening, so the bird's tongue had to travel farther to contact the nectar pool at low than at high volumes. The cross-sectional area of the tube was 1 mm 2 , so 1 Al of solution filled 1 mm of its length. Using this relationship, I confirmed the volume of sucrose solution that I dispensed by measuring the distance from the end of the tube to the nectar pool meniscus with dial calipers (accurate ± 0.02 mm) before every trial. After reinserting the feeder tube into the array, I removed the cover to begin the next trial. Licking behaviour was examined at twenty combinations of sucrose concentration and nectar pool volume: 25, 35, 45 and 55 % at each of 1, 4, 8, 12 and 16 Al. I analyzed only those trials on which the bird fed without pausing and removed all the nectar provided during a single probe of the feeder (45 % of all trials). For each combination of concentration and volume, trials were continued until four uninterrupted feeding visits had been recorded. Testing sessions lasted 45 min to 5 h, no more than once each day. Using this protocol, I measured the number of licks and the time (± 1 ms) required for the bird to remove food from the feeder. For each trial I calculated average licking frequency (number of licks extraction time), average lick volume (nectar pool volume number of licks), and average volume intake rate (nectar pool volume extraction time) during licking. I also  46  calculated average energy intake rate, E, during licking with the following equation:  E = --€11P--t  (12)  PO  where e = energy content of sucrose = 16.48 (J/mg), S = sucrose concentration (% wt/total wt), v = nectar pool volume (gl), t = time (s), andp = density of sucrose solution, obtained by fitting a curve to tabulated values (CRC Handbook) using the NONLIN 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 index than does air, nectar and air registered as different voltages on the oscilloscope traces. I could therefore time the recession of the nectar pool meniscus past the four light beams during licking on the 16 gl trials, when the nectar pool completely filled the feeder tube. This allowed me to estimate changes in volume and energy intake rates as the bird emptied the feeder. It was not possible, however, to measure precisely the volume loaded on each individual lick, nor to measure the durations of the loading and unloading phases of the licking cycle. Although I also offered 65 % sucrose, the bird never emptied the feeder during a single visit at this concentration. The bird also failed to empty the 55 % solution when only 1 gl was provided. To examine the significance of the effect of concentration on energy intake rate during licking, I performed a Kruskal-  47  Wallis test on energy intake rates from all trials for each nectar pool volume, using the NPAR procedure in SYSTAT. When a significant effect was detected at a = 0.05, I performed a nonparametric Tukey-type multiple comparison test (Zar, 1984) for all pairs of concentrations. At each concentration at 16 Al, I tested the goodness of fit of linear regression equations, derived using the procedure MGLH in SYSTAT, for both number of licks and time against cumulative volume extracted during licking. Results The rate of nectar extraction within visits was not constant; after an initial increase, both lick volume and volume intake rate decreased as the hummingbird emptied the feeder (Fig. 8). This effect was most striking at 55 % sucrose. The departure of both of these relationships from linearity was highly significant at all concentrations (for every concentration, P < 0.0005; one-tailed F ratio, deviations from linearity DF = 2, within groups DF = 12). Licking frequency was relatively constant within visits at a given concentration, but varied from 8.8 Hz at 25 % to 5.6 Hz at 55 % sucrose (Fig. 9; R = 0.990 and 0.986 for 25 and 55 % respectively). For all volumes provided, the number of licks the bird required to empty the feeder increased, and thus the average volume loaded per lick decreased with increasing concentration (Fig. 10). Average lick volume also depended on the volume  2  48  25 45 35  55  25 35 45  55  pG 12 1-4  2  O O  10^20^30^0^1^2^3^4^5 NUMBER OF LICKS^  TIME (s)  Figure 8. Recession of fluid meniscus within single visits. Lines connect means of four 16 gl trials for four sucrose concentrations (%). Slopes of the lines describe lick volume (left panel), and volume intake rate (right panel). Because volume measurements were taken at fixed points along the feeder array, the variation in these graphs is in number of licks and time. Error bars give SE.  provided, being higher at higher nectar pool volumes for all concentrations. For all nectar pool volumes, the bird licked more slowly with increasing concentration (Fig. 10). Unlike the case of average lick volume, average licking frequency did not appear to be a function of nectar pool volume. Time to extract nectar increased with increasing concentration at all nectar pool volumes (Fig. 10). As a result,  49  30-  P0  •  :1 g= 0  •  04 20 w m 2 0  z m >p e ,-4  10-  0  2 0 0 1^2^3^4^5^6 TIME (s)  Figure 9. Licking frequency within single visits. Lines are least-squares regressions, constrained to intercept the origin, for the lowest and highest sucrose concentrations presented in Figure 8: 25 % (hollow circles, dashed line) and 55 % (filled circles, solid line). Line slopes describe licking frequency. N = 16 for each concentration.  average volume intake rate during licking decreased with increasing concentration (Fig. 10). This decrease was more pronounced at higher than at lower feeder volumes. As with average lick volume, average volume intake rate increased with nectar pool volume.  • ••  • • •  50 7  35 -  6-  30 -  s W 5-  0  X z 0  C.)  r oG  4  25 -  43-  2  2-  10-  W  1-  5-  0^ 10 -  0 1.2 -  9-  4d 1.0 U :*) 1:4^ W0' 8 a,  N = ›.4 U  z  a  8-  X 0.6 O  :1 6 -  0.4 ;/) 8 0 12^ 16^ g 0 .2 -  W a  -  54  ^0.0 50  10-^  40 -1  • W  8-  g W  6-  44  Z w  4-  .E 20  • o  2-  E-1  2  16 12 4  0  30 -1  z 10 H  35^45 55^ 251^0 25^35^45^55 SUCROSE CONCENTRATION (%)  Figure 10. Variation in parameters of licking behaviour with concentration. Lines connect means of four trials at each concentration for four nectar pool volumes (gl). Error bars give SE. Wherever means overlap at different nectar pool volumes, plots for each volume are staggered along the Xaxis to allow them to be distinguished.  51  Average energy intake rate during licking increased with nectar pool volume; across the concentrations presented, the bird gained energy more than four times as rapidly at 16 Al as it did at 1 Al (Fig. 10). Kruskal-Wallis analyses of variance indicated significant differences in energy intake rate with concentration only for the 1, 12 and 16 Al trials (Table 2). At each of these three nectar pool volumes, there was a significant difference only between the two concentrations which yielded the highest and lowest 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), and 35 and 55 % for 16 Al (0.01 < P < 0.025).  Table 2. Kruskal-Wallis analysis of variance of energy intake during licking with concentration. VOLUME (al) 1 4 8 12 16 6.500 H 2.140 5.316 9.419 8.404 DF 2 3 3 3 3 N 12 16 16 16 16 P 0.039 0.544 0.150 0.024 0.038 Conclusions As expected, hummingbird nectar feeding is more complex than previously modelled. As sucrose concentration increased, the bird did not reduce licking frequency enough to keep lick volume constant, nor did it reduce lick volume enough to keep licking frequency constant. Licking behaviour falls into neither the Constant Volume nor the Constant Frequency categories envisaged by Kingsolver and Daniel (1983), and considered in Chapter 1.  52  Several of my results followed previously reported patterns of variation in nectar intake parameters. For example, energy and volume intake rates during licking were highest at high nectar pool volumes, when more of the tongue could be immersed (Fig. 10). This is consistent with the conclusion, based on earlier reports, that intake rates during the licking cycle are higher at high volume feeders than at flowers (Chapter 1; see Table 1). Previous measurements at the time scale of feeder visits have also shown that intake rates increase with increasing nectar pool volume (e.g. Montgomerie 1984). Similarly, the decrease in volume intake rate during licking at increasing concentration (Fig. 10) parallels results of earlier studies at coarser 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 a function of nectar pool volume, even as the nectar pool recedes during licking. It does, however, vary greatly with concentration (Figs. 8 and 10). By licking more slowly with increasing concentration, birds should partly conserve loading time and therefore lick volume, thus achieving higher volume intake rates during licking than if licking frequency remained constant (Chapter 1). Hainsworth (1973) reported lower licking frequencies at concentrations lower than 55 % -- the opposite of the pattern I found -- but his result may not be accurate because of the slow camera speed he used (see Ewald and Williams 1982). However, the  53  lowest licking frequencies I measured, 4.9 - 5.9 Hz at 55 % sucrose on 16 Al trials, were near Hainsworth's (1973) value of 4.7 Hz for Lampornis clemenciae feeding at this concentration. If Hainsworth's (1973) birds actually licked more slowly at higher concentration, then his film records would have captured a larger proportion of all licks at high than at low concentration. His measurements at 55 % sucrose may therefore be accurate, even though his low concentration measurements probably are not. Parameters of licking performance were lower in this study than those reported by Ewald and Williams (1982). The highest average licking frequencies I measured, at 25 % sucrose on 12 Al trials, were 9.1 - 9.7 Hz, whereas Ewald and Williams' (1982) mean for Calypte anna feeding at approximately 22 % sucrose was 13.8 Hz. The highest lick volumes and volume intake rates during licking I measured were 0.9 - 1.2 Al/lick and 7.3 - 10.4 Al/s respectively (both at 25 % on 16 Al), as compared to Ewald and Williams' (1982) values of 1.2 Al/lick and 17 Al/s. These differences may relate to feeder design; it is likely that because Ewald and Williams' (1982) feeder did not exclude birds' bills as mine did, licking performance was limited less than it may have been in this study. As feeder design probably influences the quantitative results of licking behaviour studies, application of these measurements to other situations should be undertaken with caution. Nevertheless, the qualitative patterns of variation in licking behaviour with concentration and nectar pool volume revealed in this study should apply generally.  54  As predicted in Chapter 1, lick volume decreased within visits as the nectar pool was depleted and tongue immersion decreased (Fig. 8). Previous workers have suggested that deep immersion should free tongue loading from the constraints of capillarity-induced nectar flow, yielding higher optimal concentrations at high volumes (and deeper immersion) than at low volumes for which only the tongue tip can contact the nectar pool (Hainsworth 1973; Kingsolver and Daniel 1983). Contrary to this prediction, however, energy intake rates were not maximized at higher concentrations at higher nectar pool volumes (Fig. 10). Apparently, the increased viscosity of high concentrations limits loading rate even when nectar can enter the tongue grooves along their length. Kingsolver and Daniel (1983) proposed that optimal concentration is 20 - 25 % at 1 gl nectar pools because singlelick, continuous nectar flow models (Kingsolver and Daniel 1979; Heyneman 1983) should apply at this volume, but that optimal concentration should shift to 35 - 40 % at high volumes. My results supported neither their suggestion that birds should lick only once at 1 gl nectar pools, nor their prediction of an upward shift in optimal concentration with increasing volume (Figs. 9 and 10). My results did, however, support my conclusions about the dependence of optimal concentration on time scale. I demonstrated in Chapter 1 that the predicted upward shift in optimal concentration with increasing volume results from increasing the time scale of integration from tongue loading to  55  the licking cycle, and not from increasing volume per se. In this study, the bird took more than one lick at 1 Al nectar pools, so under model assumptions, optimal concentration would be expected to be the same as at high volumes. Indeed, it may be unrealistic to imagine that hummingbirds would lick only once even at volumes lower than 1 Al. Low volume nectar pools in flowers are often present as separate beads or droplets which are difficult to extract (F. L. Carpenter, pers. comm.). Likewise, flowers with superior ovaries have nectar dispersed around the ovary base (C. L. Gass, pers. comm.; see Lawrence 1955, especially Fig. 39). Birds would have to lick many times to empty a flower under both of these conditions. Additionally, more than a single lick may be required to convince them that a flower or feeder is empty, and because they can lick so rapidly, the time cost of double-checking would be miniscule. If birds lick more than once at all volumes, they would be expected to choose the same concentrations at low volume that they choose at high volume. Clearly, low volume choice tests are required to address this issue. This experiment provides a basis for distinguishing between time scales at which hummingbirds' concentration preferences maximize their energy intake rates. For 12 and 16 Al nectar pools, 25 - 35 % sucrose yielded significantly higher energy intake rates at the time scale of the licking cycle than did 55 %, and this is probably true for 1 Al nectar pools as well, given that the bird failed to extract the 55 % solution at this volume. If, therefore, birds maximize energy intake rates over  56  the duration of licking, they should be expected to prefer 25 35 % over 55 % or higher concentrations.  57 CHAPTER 3 HUMMINGBIRDS' CONCENTRATION PREFERENCES AT LOW VOLUME AND THE ENERGETICS OF FEEDING VISITS AND FORAGING BOUTS  In my analyses of nectar feeding models (Chapter 1), I concluded that hummingbirds should prefer dilute nectars, in the 20 - 25 % range predicted for low volumes and found on average in their flowers, only if they maximize energy intake rate at the fine time scale of the tongue groove loading phase of licking. In Chapter 2 I reported that 25 - 35 % sucrose yields a higher energy intake rate than 55 % sucrose at the time scale of the licking cycle. To determine if, and at what time scale, concentration preferences coincide with optimal sucrose concentrations, I measured both preferences and intake rates for rufous hummingbirds over a wide range of concentrations at a low volume similar to nectar standing crops found in nature. Materials and methods I tested the concentration preferences of four adult rufous hummingbirds (2 males, 2 females) between 13 November 1991 and 24 January 1992. These individuals were captured between May and July 1990 at Rosewall Creek, Vancouver Island. The females had longer bills and were heavier on average than the males (Table 3). At all times when not in tests, birds had free access to Nektar-Plus supplemented with soybean protein. Previous to the present experiment, these individuals participated in tests of spatial association learning which employed different methods from mine (see G. S. Brown, PhD thesis, for details). In  58  addition, bird 5 was used in the licking behaviour study (Chapter 2) .  Table 3. Bill lengths and body weights of experimental birds. ^Bill^ Mass (g) Sex length (mm)^Minimum^Maximum Bird 4^M^16.7^2.8^3.9 Bird 5^M^16.6^3.5^4.2 Bird 27^F^17.8^3.3^4.4 Bird 38^F^17.9^3.8^4.6  Tests were conducted in an environment chamber at 25 ± 1 °C. An opaque partition divided the chamber into two compartments 136 cm long X 16 cm wide X 66 cm high, allowing two birds to be tested independently. One feeder was situated at either end of each compartment, and a perch was positioned halfway between the two feeders. Feeders were plastic tubes, 2 cm long with 2.4 mm internal diameter, mounted horizontally in the compartment wall, and marked by round orange Avery labels with central 3 mm diameter holes. Birds' arrivals and departures from feeders and perches were detected by infrared photocells, and recorded by a computer to 0.01 s. The computer also controlled food delivery (see Gass 1985; Tamm 1987, especially Fig. 2, for a general description of the computer system). Tests began with 1 Al of a different concentration of sucrose solution in each feeder. Thereafter, any feeder a bird visited was resupplied with another 1 Al of the same concentration by a solenoid valve (General Valve Corp.), upon the bird's return to its perch. Each foraging bout yielded 1 Al at a  59  given feeder no matter how many times it was probed within that bout, but birds could obtain food from both feeders on any bout. I tested preferences with all ten pairwise combinations of the five sucrose concentrations at 10 % increments from 25 to 65 %. To control for possible positional biases (e.g. Cole et al. 1982; Tamm and Gass 1986; Wunderle and Martinez 1987) I conducted two tests for each pair of concentrations on consecutive days, with the positions of high and low concentrations reversed for the second test, and pooled their results. Because birds' feeder choices could be affected by hysteresis (Gass 1978b), I reversed the sequence of concentrations that I presented to the first two birds tested for the other two. Visit durations are usually more variable and longer at the beginning of a bird's exposure to new feeding conditions, and decrease to an asymptotic level with increasing experience (unpubl. data; see Pyke 1984). I included a training session immediately before every test to exclude this learning period from my measure of concentration preference (for consideration of the effect of learning on food choice, see Hughes 1979; Mitchell 1989). Concentration, volume and food delivery protocols in the training session were identical to those in that day's test. First, one feeder was covered with adhesive tape and the bird was allowed to visit only the other. After the bird had made at least 10 visits and visit durations were relatively stable, I reversed the presentation, allowing the bird to feed only from the previously covered feeder until visit durations were stable  60  there also. The order in which I exposed feeders in the training session was always the same. At the end of a training session, both feeders were briefly (< 1 min) covered while the data collection program was started, then both were exposed to begin the test proper. I had to open the doors of the environment chamber briefly (< 5 s) in order to cover and uncover the feeders, but birds exhibited no signs of disturbance within 20 s after these intrusions. Visit durations recorded by the computer were whole feeding visits, including the time to insert and withdraw the bill from the feeder as well as the time spent licking. I calculated volume intake rates averaged over feeding visits, and energy intake rates averaged over both visits and foraging bouts, using only those bouts on which the bird probed the feeder just once and then returned to its perch (91.8 - 93.9 % of all bouts for each bird). Of these, I considered to be outliers any feeding visits longer than 1.99 s and shorter than 0.20 s (0.6 - 4.7 % of all visits on single-probe bouts), and any foraging bouts longer than 5.99 s (0.2 - 0.7 % of all single-probe bouts on which visits were not outliers). I excluded these outliers from intake rate analyses. Energy intake rates were calculated using Equation 12 (Chapter 2). I pooled energy intake rates for feeding visits and foraging bouts from all tests for each concentration for each of the four birds, and used the means of these data in statistical tests. I tested for a significant effect of concentration on energy intake rate using Friedman's  61  nonparametric analysis of variance for repeated measures from the NPAR procedure in SYSTAT (SYSTAT, Inc. 1990). Statistical analyses of preference were based on the volume taken from each feeder (i.e. 1 gl X number of bouts on which each feeder was visited), for the first 100 gl consumed in each test for each pair of concentrations. I tested the significance of results for each pair of concentrations for each bird, at a = 0.05, against the null hypothesis of no preference using Chisquare goodness of fit with Yates' correction for continuity (Zar, 1984). Results As expected, visit durations increased and thus volume intake rates for feeding visits decreased with increasing concentration (Fig. 11). Despite their longer bills, the female birds did not achieve consistently higher volume intake rates than did the males. Round trip travel time between perch and feeder, exclusive of handling time, averaged 1.30 - 1.69 s for each bird. Energy intake rates differed significantly with sucrose concentration (Table 4). At the relatively fine time scale of feeding visits, energy intake rates peaked at intermediate concentrations in the presented range: 55 % sucrose in two birds, and 45 % in the other two (Fig. 12, column 1). Over the coarser time scale of foraging bouts, however, energy intake rates of three birds peaked at the highest concentration available, 65 % sucrose, and the remaining bird's energy intake rates peaked at  ^  62  4 S  27 7.54 ill 3 -^5 k^38 4 4 g w Nd 4 2 H z w .4 0  1-  0  1^I^I^1^I 25^35^45^55^65 SUCROSE CONCENTRATION (%)  Figure 11. Volume intake rates for feeding visits of four rufous hummingbirds at five concentrations. Each line connects means for one bird (numerical labels identify individual birds; error bars give SE; n is reported in Table 5, Appendix 2).  Table 4. Friedman's analysis of variance of energy intake rates for feeding visits and foraging bouts with concentration. ^ Intake rates for^DF^X ^W P 0.837 Feeding visits 13.400 0.009 4 0.962 Foraging bouts 4 15.400 0.004  the 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).  63 CALCULATED OVER FEEDING VISIT^CALCULATED OVER FORAGING BOUT CONCENTRATION PREFERENCES  30  8 35 %  BIRD 4  6  20 -  45 % 4-  55 %  10 2  65 % wraus 25 % 35 % 45 % 55 %  0 30  0^ 8-  W%^  6  20 -  BIRDS  45 % 4-  811  55 %  84^10-  2  65 % venue  0 ^ 30 -  25 % 35 % 45 % 55 %  0  $  v 35 %  6 20 -  45 % 4-  55 %  10-1 2-^  65% toms  0 30  25 % 35 % 45 % 55 %  0^  s  35 %  6 20 -  BIRD 38  45 % 4 55 %  10 65 % Vera" 25 % 35 % 45 % 55 %  0  0^  25^35^45^55^65^  25^35^45^55^65  SUCROSE CONCENTRATION (%)  Figure 12. Energy intake rates for feeding visits and foraging bouts, and concentration preferences of the same birds as in Figure 11. In energy intake rate graphs, lines connect means (error bars give SE; n for each mean reported in Table 5, Appendix 2). In preference graphs, each square depicts the outcome of a Chi-square analysis of two choice tests at a pair of concentrations. Dark shading indicates significant preference for the higher concentration presented. Light shading indicates no preference. In cases of significant preference, 3.841. Birds never expressed significant preference for the lower concentration.  r>  64  All birds either preferred the higher concentration of each pair presented, or else preferred neither concentration. Whenever they preferred neither, the two concentrations were only 10 % apart (Fig. 12, column 3). Conclusions This experiment is the first to test concentration preferences of hummingbirds at a volume comparable to the low nectar pool volumes prevalent in nature (see Chapter 1). My finding that birds preferred the highest concentration available accords with results of earlier high volume choice tests. In the only high volume study that provided concentrations as high as 65 % sucrose, Tam and Gass (1986) found that birds took more from the weaker solution when the mean concentration of the two offered was above 55 % sucrose. This preference, however, was significant only for presentations of 65 % vs. 60 %, and no choices were offered between 65 % and concentrations lower than 60 %. In the present study, hummingbirds generally preferred sucrose concentrations which maximized their energy intake rates at the coarse time scale of foraging bouts, even when this did not maximize energy intake rates at the finer time scale of feeder visits. Those cases of failure to express preference do not necessarily indicate that birds were unable to distinguish between the concentrations. On the contrary, it is reasonable to assume that these nectarivores, which possess taste buds (Weymouth et al. 1964) and a sense of taste (Stromberg and  65  Johnsen 1990), can distinguish between the concentrations presented in this study; even human tasters can readily tell them apart (pers. obs.; see e.g. Monneuse et al. 1991). A more plausible explanation for the failure to express preference is that the difference between the two feeders' energetic yields may have been insufficient to elicit preference from all individuals on the basis of concentration. This possibility is supported by the observation that these cases occurred when sucrose concentrations were only 10 % apart. Alternatively, a weak preference for one of the two concentrations may have been masked by a stronger preference for one of the two feeder positions. The sensitivity of optimal concentration to the time period over which rates are calculated, demonstrated with measured values in Figure 12, is depicted more generally with the discrete-marginal-value theorem representation in Figure 13. This representation can be compared with the cases of birds 5, 27 and 38 in Figure 12, where food "D" would be 45 % sucrose, and food "C", 65 % sucrose. The slopes of the solid lines in Figure 13 connecting the energy gain and time coordinates of both foods to the abscissa, describe gross energy intake rates averaged over feeding visits. The slopes of the dashed lines, which encompass travel time, describe energy intake rates averaged over foraging bouts. A given volume of dilute nectar ("D") has a lower gross caloric value than the same volume of concentrated nectar ("C"), but has a shorter handling time. For feeding visits, this shorter handling time results in a higher energy intake rate at dilute than at concentrated solutions. For foraging bouts,  66  TRAVEL TIME^HANDLING TIME FEEDING VISIT FORAGING BOUT  Figure 13. Generalized representation of two food types corresponding to dilute and concentrated nectar ("D" and "C" respectively). D has low caloric value and handling time; C has high caloric value and handling time. The slopes of the solid and dashed lines connecting foods to abscissa are energy intake rates for feeding visits and foraging bouts respectively (after Stephens et al. 1986; Hainsworth 1989).  however, travel time effectively outweighs the advantage of shorter handling time, so that the concentrated solution yields a higher energy intake rate than does the dilute.  67  All birds preferred 65 % sucrose to less concentrated solutions. Although this preference maximized energy intake rates over foraging bouts, and not over feeding visits, it does not demonstrate that hummingbirds monitor rates on either of these scales, or even that energy intake rate is the currency of concern to birds (see Montgomerie et al. 1984; Hixon and Carpenter 1988; Tam 1989). In this case, choosing the concentration which is optimal at the time scale of foraging bouts could have resulted from application of a simple rule of thumb like "Always choose the sweetest solution available" (Hainsworth and Wolf 1976; Tamm and Gass 1986).  68 DISCUSSION The adaptive significance of the low concentrations of nectar prevalent in hummingbird-pollinated flowers is a central issue in pollination biology (e.g. Bolten and Feinsinger 1978; Calder 1979; Pyke and Waser 1981; Plowright 1987; Sutherland and Vickery 1988; Mitchell and Paton 1990). Mean nectar concentration of North American and many tropical hummingbirdpollinated plants is in the range predicted to be optimal by Heyneman (1983) and by Kingsolver and Daniel (1983) for low volume sources (Baker 1975; Feinsinger 1987). However, previously reported energy intake rates during feeding visits and concentration preferences of hummingbirds in the laboratory peaked in the range Kingsolver and Daniel (1983) predicted for high volume (Tamm and Gass 1986; Chapter 3). This observed preference for concentrations roughly twice what flowers offer in nature has complicated understanding of the evolution of the presumably coevolved plant-pollinator system (Pyke and Waser 1981; Feinsinger 1987; Gass 1988). Interestingly, most flowers visited by non-traplining hummingbirds usually contain nectar pools near to or less than the volume of the tongue grooves, whereas all published preference tests used much larger volumes (usually infinite from the 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 different optimal concentrations for different nectar pool volumes, it was tempting to infer that the discrepancy between the higher nectar  69  concentrations birds prefer and the lower concentrations flowers provide them is just an artifact introduced by testing preference and intake rate at inappropriately large volumes. As I showed in Chapter 1, however, biophysical models suggest that hummingbirds should prefer concentrations as low as flowers provide only if they average costs and benefits over the loading phase of single licks alone. Conversely, the same models predict that preference for higher concentrations should be expected even at very low volume sources if birds average over total handling time or longer. My tests of these predictions confirmed the dependence of optimal concentration on the time scale of integration, and revealed that hummingbirds prefer high concentrations even at realistically low volume sources. Birds' choices maximized their energy intake rates at the time scale of foraging bouts, but not at the time scales of feeding visits or the licking cycle.  Implications for optimal foraging theory Previous workers who have focussed their analyses on the time 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 results suggest that reinterpretation of these studies may reveal that birds' foraging decisions did maximize energy intake rates, but over longer time periods than feeder visits. Travel time is only one of several possible time components that might be important. Referring back to Figure 13, whenever  70  the "faster" food type provides even a marginally lower total energetic reward than the "slower", there will be some time scale over which the latter yields a higher energy intake rate. In reality, however, whether or not this type should be preferred depends on a complex interaction of temporal, nutritional, behavioural and other constraints, which are discussed in depth elsewhere (e.g. Sih 1980; Pyke 1984; Stephens et al. 1986; Calder  et al. 1990; Lima 1991; Murray 1991). In an earlier experiment that distinguished between time scales of energy intake rate maximization, Stephens et al. (1986) showed that honeybees (Apis mellifera ligustica) made foraging decisions consistent with rate maximization over coarser time scales than feeding visits. In contrast, Barkan and Withiam (1989) found that black-capped chickadees (Parus atricapillus) selected foods which maximized energy intake rates during feeding, but not over longer periods. Their experiment generated different handling times by varying the thickness of tape that birds had to peck through in order to obtain food. This imposed a delay between the start of food "handling" and actually beginning feeding which was different for the different food choices. Barkan and Withiam (1989) pointed out that their result may have been generated by a well-established psychological phenomenon in which animals, apparently lacking "self-control", choose immediately available foods with smaller energetic rewards over more rewarding foods when access to the latter is delayed. Conversely, in my protocol the only analogous delay was the time  71  nominally required to insert the bill into the feeder, which should not have differed among feeders. Instead, variation in handling times with concentration resulted from different extraction rates during feeding itself (Fig. 11). Investigators into food choices should be aware that the validity of predictions may depend critically on what behavioural components are included in the category "handling time", and that preference could be sensitive to the sources of variation in handling time (Houston 1991). It is unclear exactly how either foragers or experimenters should estimate costs and benefits of action at any hierarchical level or any temporal scale. While the positive and negative consequences of fine-scale events must ultimately determine fitness, it is unclear how or on what temporal scale either animals or biologists should integrate them. It is clear from my analyses, though, that to predict optimal behaviour on the basis of fine-scale events is dangerous unless the contribution of these components to higher level processes is understood.  Implications for pollination biology Flower nectar of hummingbird-pollinated plants is typically low in amino acids, and pollen is an insignificant source of energy and protein for hummingbirds (Brice et al. 1989), so nectar sugar is the principal benefit birds obtain from visiting flowers. Hummingbirds' sugar concentration preferences override their preferences for colour or sugar type (Collias and Collias 1968; Stiles 1976). Nevertheless, I have demonstrated that the  72  energetic effects of decreasing fluid flow rates with increasing nectar concentration, which are large at the fine time scale of feeding visits, diminish at the coarser time scale of foraging bouts. Over these longer time periods, gross energetic reward, which is a function of concentration and nectar pool volume (see Montgomerie 1984), influences energy intake rate more than does concentration alone. Patterns of nectar concentration in hummingbird-pollinated plants cannot be explained by hummingbirds' preferences nor by the energetics of nectar extraction. Accounting for dilute nectars on the basis of sugar flow rates alone is likely to generate incorrect predictions. For example, Heyneman (1983) concluded that travel costs in territorial hummingbirds were far outweighed by costs during nectar feeding, based on the close fit between sugar concentrations of their flowers and the 20 - 26 % sucrose that maximized energy intake rates during tongue groove loading in her model. The present study contradicts this conclusion; incorporating travel times of only about 1.5 seconds into my energy intake rate calculations increased measured optimal concentrations 10 - 20 % above those for feeding visits alone (Fig. 13), as the theoretical results of Chapter 1 predicted it should. The above considerations also apply to nectarivores other than hummingbirds. May (1988) found that nectar concentration was uncorrelated with butterflies' energy intake rates or amount of sugar per flower in one butterfly-pollinated plant, and  73  correlated only weakly in another. He argued that it was unlikely that concentration would be used by butterflies as a basis for selecting flowers. Both measured and predicted energy intake rates for butterflies (calculated over handling time) peak at 30 - 40 % sucrose (Pivnick and McNeil 1985; May 1985; Boggs 1988; Daniel et al. 1989) not the 20 - 25 % found in butterflypollinated flowers and predicted by an earlier model (Kingsolver and Daniel 1979). Neither are bees' energy intake rates maximized at the sugar concentrations their flowers provide. As with hummingbirds, when travel time is included in energy intake rate calculations, the optimal sucrose concentration for bumblebees increases to 50-65% (Harder 1986), which is substantially higher than the average concentration in beepollinated flowers. The question remains of why hummingbird flowers secrete dilute nectar. It is improbable that hummingbirds are limited by constraints of water balance or digestion from taking advantage of high sugar concentrations. Floral nectars provide hummingbirds considerable excess of water above their requirements (Calder 1979; Calder and Hiebert 1983; see Weathers and Stiles 1989). Efficiency of digesting sucrose in hummingbirds is > 97 % (Hainsworth 1974; Martinez del Rio 1990a), and intestinal sucrase activity is up to 118 times higher than in passerines (Martinez del Rio 1990b). Contrary to earlier reports (Diamond et al. 1986; Karasov et al. 1986), physiological rates of nectar processing do not appear to limit the frequency of  74  hummingbirds' feeding bouts (Tiebout 1989; Martinez del Rio, pers. comm.). Bolten and Feinsinger (1978) suggested that dilute nectar might deter bees, which may be less reliable and efficient pollinators of some plants than hummingbirds (see Sazima and Sazima 1990). In one plant species, hummingbirds deposit 10 times as much pollen per flower stigma per visit as bees, and both fruit and seed production increase with pollen load deposited (Bertin 1982, 1990). Low sugar concentration alone, however, is not sufficient to deter bees. Pleasants and Waser (1985) observed bumblebees (Bombus appositus) visiting Ipomopsis aggregata, a typical hummingbird-pollinated flower with an average 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 standing crop was higher than usual, bees were able to harvest nectar that accumulated and filled the corolla tube. There is no consistent relationship between the accessibility of a species' nectar to bees and its sugar concentration (Pyke and Waser 1981). Earlier I argued that sugar concentration is likely to be important to hummingbirds only under special conditions. One such condition was revealed by the failure of the hummingbird in the licking cycle experiment to empty 65 % solutions from the feeder, and also by its failure to empty 55 % when only 1 Al was offered (Chapter 2). These solutions were probably too viscous for this male to extract easily from the end of the 16 mm long feeder tube, near the limit of its tongue extension (unpubl.  75  data; Temeles and Roberts, in review). Within feeding visits, volume intake rate during licking decreased more dramatically as the nectar pool receded at high than at low concentration (Fig. 8). This suggests that hummingbirds may prefer low concentrations in flowers with very long corollas where the time and energy costs of harvesting nectar would be high, and thus that concentration preference may depend on corolla length. Furthermore, as female hummingbirds' tongues are longer than males° (Johnsgard 1983; Paton and Collins 1989; Temeles and Roberts, in review), females may not be constrained by corolla length to as great an extent, and may prefer higher concentrations than males under identical conditions. Both of these possibilities await testing. Just how meaningful is the observation of low average sugar concentrations in hummingbird-pollinated plants? Focussing on patterns of average concentrations tends to obscure the fact that there is considerable variation in concentrations in hummingbirdpollinated flowers (see Kingsolver and Daniel 1983). Nectars of 17 species in Arizona and Colorado ranged from 8 - 43 % sucrose equivalents (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, 20 species ranged from 16 - 48 % (Bernardello et al. 1991). Even within individual flowers, nectar concentration varies greatly after secretion with environmental factors, particularly ambient humidity (Plowright 1981; Bertsch 1983; Mohr and Jay 1990). Corolla morphology contributes to the maintenance of dilute  76  nectar in low humidity by sheltering the nectar pool from evaporation (Corbet et al. 1979; Plowright 1987). The dilute nectar in hummingbird-pollinated flowers could therefore be merely a consequence of possessing long corollas which exclude other pollinators (Plowright 1987). Indeed, the persistence of such wide variation argues against nectar concentration being subject 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 production during blossoming is secreted as nectar sugar in the common milkweed (Asclepias syriaca; Southwick 1984). Sugar secretion in nectar is constrained by weather and plants' other physiological requirements (Michaud 1990; Harder and Cruzan 1990), and some species may reabsorb sugar from unvisited flowers to reclaim invested energy (BUrquez and Corbet 1991). As Mitchell and Paton (1990) pointed out, to compare pollinators' concentration preferences with equal nectar pool volumes suggests that plants should achieve different concentrations by investing vastly unequal energetic rewards in nectar. Given the high cost of sugar secretion, it is more realistic under many conditions to consider pollinators' concentration preferences for the same amount of sugar packaged in different amounts of water; Mitchell and Paton's (1990) "Equal Sugar" presentation scheme. In "Equal Volume" presentations, Mitchell and Paton (1990) found that honeyeaters' energy intake rates during feeding peaked at 30 - 50 % sucrose, but in their Equal Sugar presentation, New  77  Holland honeyeaters (Phylidonyris novaehollandiae) maximized energy intake rates during feeding visits at about 20 %. Because the amount of sugar was the same at all concentrations, this measured optimum holds at all time scales (i.e. the optimum will not shift upwards with increasing temporal scale of integration). The authors suggested that their result could account for the dilute nectars of bird-pollinated plants. However, they did not perform the critical test of this suggestion and determine whether or not their birds preferred 20 % sucrose under Equal Sugar conditions. Energy intake rates of hummingbirds have not been measured under an Equal Sugar presentation scheme. Even if these peaked at low concentration as for honeyeaters, however, there may be reasons other than energy intake rate for choosing high over low concentrations. One possibility relates to the property of Equal Sugar presentations that at high concentrations the given amount of sugar is available in a smaller volume than it is at low concentrations. Large meals increase body mass and therefore flight 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 that yield more energy per unit volume consumed (see Montgomerie et al. 1984) than low concentrations, even if the latter yielded higher energy intake rates under Equal Sugar conditions. Obviously, preference tests at realistic volumes using an Equal  78  Sugar presentation scheme are required to investigate these alternatives. Should plants provide what pollinators prefer? A major assumption of attempts to correlate optimal sugar concentrations for pollinators with concentrations in floral nectar is that plants should offer pollinators what they prefer in order to secure and maintain their services (see Gass 1988). Suggested benefits of such a strategy include increased visitation rates and pollinator fidelity (Wolf et al. 1972; Waser 1986). However, this assumption neglects the fact that plant fitness is affected not only by pollinator visitation, but also by the amount of energy invested in nectar rewards. Furthermore, although examples abound of pollinator visitation rates increasing with increasing nectar reward (e.g. Abrol 1990; Klinkhamer and de Jong 1990; Delesalle and Buchmann 1991; Jennersten and Kwak 1991), the positive relationship between visitation rates and plant reproductive success is neither simple nor linear (Zimmerman 1983; Carpenter 1988; Sutherland and Vickery 1988; Ashman and Stanton 1991; Real and Rathcke 1991; Waser and Price 1991). Likewise, the relationship between nectar reward and visitation rate is neither simple nor linear. Although flowers must present enough nectar to secure the attention of potential pollinators, if the rewards they offered were too large, their visitors would not need to visit as many other flowers and could become less efficient pollinators (Baker 1975; Heinrich 1975). The proposition that large rewards can reduce nectarivores'  79  foraging movements has been supported by experimental enrichments of flowers (Gass and Sutherland 1985). In at least one case, smaller nectar pools resulted in higher visitation rates (Pyke 1980). Bumblebees (Bombus flavifrons) visited flowers in a patch of larkspur (Delphinium barbeyi) at twice the rate they did in a contiguous patch of monkshood (Aconitum columbianum), even though Delphinium flowers offer less than half the volume of Aconitum flowers and nectar sugar concentrations are similar in both plant species (41.3 % and 40.1 % respectively). By visiting Delphinium flowers more frequently, bees obtained similar net energy intake rates at both patches. Similarly, while pollinator infidelity has been shown to decrease plant reproductive success in some cases (Feinsinger et al. 1988; Feinsinger and Tiebout 1991), in others the loss of pollen due to indiscriminate foraging has little effect (Feinsinger et al. 1986; Feinsinger et al. 1991). In addition, even specialized plants can sometimes "compensate" for the absence of their principal pollinators by attracting other taxa (Wolf and Stiles 1989). Clearly, plant-pollinator systems are not amenable to explanations based on simple assumptions (Carpenter 1983; Gass 1988). I believe that more emphasis should be placed on the plants' side of this coevolutionary story, and that models and experiments focussed on the consequences of parameters of nectar production for plant fitness (e.g. Pyke 1981; Campbell 1991;  80  Campbell et al. 1991) will have more explanatory and predictive value than those that focus on pollinator preferences alone.  81 BIBLIOGRAPHY Abrol, D. P. 1990. Energetics of nectar production in some apple cultivars as a predictor of floral choice by honeybees. Tropical Ecology 31:116-122. Alm, J., T. E. Ohnmeiss, J. Lanza and L. Vriesenga. 1990. Preference of cabbage white butterflies and honey bees for nectar that contains amino acids. Oecologia 84:53-57. Angehr, G. R. 1980. The role of interference competition in the organization of a guild of Panamanian hummingbirds. PhD thesis. Univ. Colorado. Boulder. Allen, T. F. H. and T. B. Starr. 1982. Hierarchy: perspectives for ecological complexity. Univ. Chicago Press. 310 pp. Arizmendi, M. C. and J. F. Ornelas. 1990. Hummingbirds and their floral resources in a tropical dry forest in Mexico. Biotropica 22:172-180. Armstrong, D. P. 1987. Economics of breeding territoriality in male calliope hummingbirds. Auk 104:242-253. Ashman, T.-L. and M. Stanton. 1991. Seasonal variation in pollination dynamics of sexually dimorphic Sidalcea oregana ssp. spicata (Malvaceae). Ecology 72:993-1003. Baker, H. G. 1975. Sugar concentration in nectars from hummingbird flowers. Biotropica 7:37-41. Baker, H. G. and I. Baker. 1973. Amino acids in nectar and their evolutionary significance. Nature 241:543-545. Baker, H. G. and I. Baker. 1983. Floral nectar sugar constituents in relation to pollinator type. pp. 117-141 In Handbook of experimental pollination ecology, Jones, C. E. and R. J. Riddle, eds. Van Nostrand Reinhold. New York, New York. Baker, H. G. and I. Baker. 1986. The occurrence and significance of amino acids in floral nectar. Plant. Syst. Evol. 151:175-186. Barkan, C. P. L. and M. L. Withiam. 1989. Profitability, rate maximization, and reward delay: a test of the simultaneousencounter model of prey choice with Parus atricapillus. Am. Nat. 134:254-272. Bernardello, L. M., L. Galetto and H. R. Juliani. 1991. Floral nectar, nectary structure and pollinators in some Argentinean Bromeliaceae. Ann. Bot. 67:401-411. Bertin, R. I. 1982. Floral biology, hummingbird pollination and fruit production of trumpet creeper (Campsis radicans, Bignoniaceae). Am. J. Bot. 69:122-134. Bertin, R. I. 1990. Effects of pollination intensity in Campsis radicans. Am. J. Bot. 77:178-187.  82 Bertsch, A. 1983. Nectar production of Epilobium angustifolium L. at different air humidities; nectar sugar in individual flowers and the optimal foraging theory. Oecologia 59:4048. Beuchat, C. A., S. B. Chaplin and M. L. Morton. 1979. Ambient temperature and the daily energetics of two species of hummingbirds, Calype anna and Selasphorus rufus. Physiol. Zool. 52:280-295. Bleiweiss, R. 1990. Spectral confusion by hummingbirds and the evolution of red coloration in their flowers: a new hypothesis (MUllerian mimicry/wavelength discrimination/shade/color name). Trans. Wisc. Acad. Sci. Arts Lett. 78:33-38. Boggs, C. L. 1988. Rates of nectar feeding in butterflies: effects of sex, size, age and nectar concentration. Funct. Ecol. 2:289-295. Bolten, A. B. and P. Feinsinger. 1978. Why do hummingbird flowers secrete dilute nectars? Biotropica 10:307-310. Bolten, A. B., P. Feinsinger, H. G. Baker, and I. Baker. 1979. On the calculation of sugar concentration in flower nectar. Oecologia 41:301-304. Brice, A. R., K. H. Dahl and C. R. Grau. 1989. Pollen digestibility by hummingbirds and psittacines. Condor 91:681-688. Brown, G. S. In prep. Spatial association learning in rufous hummingbirds. PhD Thesis. Univ. British Columbia. Brown, J. H. and A. Kodric-Brown. 1979. Convergence, competition, and mimicry in a temperate community of hummingbird-pollinated flowers. Ecology 60:1022-1035. Bdrquez, A. and S. A. Corbet. 1991. Do flowers reabsorb nectar? Funct. Ecol. 5:369-379. Calder, W. A. 1976. Energetics of small body size and high latitude: the rufous hummingbird in coastal Alaska. International J. Biometeorology 20:23-35. Calder, W. A. 1979. On the temperature-dependency of optimal nectar concentration for birds. J. Theor. Biol. 78:185-196. Calder, W. A., III, L. L. Calder and T. D. Fraizer. 1990. The hummingbird's restraint: a natural model for weight control. Experientia 46:999-1002. Calder, W. A., III and S. M. Hiebert. 1983. Nectar feeding, diuresis, and electrolyte replacement of hummingbirds. Physiol. Zool. 56:325-334.  83 Campbell, D. R. 1991. Effects of floral traits on sequential components of fitness in Ipomopsis aggregata. Am. Nat. 137:713-737. Campbell, D. R., N. M. Waser, M. V. Price, E. A. Lynch and R. J. Mitchell. 1991. Components of phenotypic selection: pollen export and flower corolla width in Ipomopsis aggregata. Evolution 45:1458-1467. Carpenter, F. L. 1983. Pollination energetics in avian communities: simple concepts and complex realities. pp. 215-234 In Handbook of experimental pollination ecology, Jones, C. E. and R. J. Riddle, eds. Van Nostrand Reinhold. New York, New York. Carpenter, F. L. 1988. Pollen-transfer efficiency compensates for pollinator crashes on a specialized bird-pollinated plant. Acta XIX Congressus Internationalis Ornithologici, pp. 537-548. Carpenter, F. L., M. A. Hixon, A. Hunt and R. W. Russell. 1991. Why hummingbirds have such large crops. Evol. Ecol. 5:405414. Cole, S., F. R. Hainsworth, A. C. Kamil, T. Mercier and L. L. Wolf. 1982. Spatial learning as an adaptation in hummingbirds. Science 217:655-657. Collias, N. E. and E. C. Collias. 1968. Anna's hummingbirds trained to select different colors in feeding. Condor 70:273-274. Colwell, R. K. 1989. Hummingbirds of the Juan Fernandez Islands: natural history, evolution and population status. Ibis 131:548-566. Corbet, S. A., P. G. Willmer, J. W. L. Beament, D. M. Unwin and 0. E. Prys-Jones. 1979. Post-secretory determinants of sugar concentration in nectar. Plant, Cell Environ. 2:293308. CRC Handbook of Chemistry and Physics. 1979. CRC Press. West Palm Beach, Florida. Daniel, T. L., J. G. Kingsolver and E. Meyhtifer. 1989. Mechanical determinants of nectar-feeding energetics in butterflies: muscle mechanics, feeding geometry, and functional equivalence. Oecologia 79:66-75. DeBenedictis, P. A., F. B. Gill, F. R. Hainsworth, G. H. Pyke and L. L. Wolf. 1978. Optimal meal size in hummingbirds. Am. Nat. 112:301-316. Delesalle, V. A. and S. L. Buchmann. 1991. Outcrossing hypothesis and weak preference for pistillate flowers in the monoecious cucurbit, Apodanthera undulata. Evol. Trends Plants 5:37-41.  84 Diamond, J. M., W. H. Karasov, D. Phan and F. L. Carpenter. 1986. Digestive physiology is a determinant of foraging bout frequency in hummingbirds. Nature 320:62-63. Dobkin, D. S. 1984. Flowering patterns of long-lived Heliconia inflorescences: implications for visiting and resident nectarivores. Oecologia 64:245-254. Eckhart, V. M. 1991. The effects of floral display on pollinator visitation vary among populations of Phacelis linearis (Hydrophyllaceae). Evol. Ecol. 5:370-384. Emlen, J. M. 1966. The role of time and energy in food preference. Am. Nat. 100:611-617. Epting, R. J. 1980. Functional dependence of the power for hovering flight on wing disc loading in hummingbirds. Physiol. Zool. 53:347-357. Erhardt, A. 1991a. Pollination of Dianthus superbus L. Flora 185:99-106. Erhardt, A. 1991b. Nectar sugar and amino acid preferences of Battus philenor (Lepidoptera, Papilionidae). Ecol. Entomology 16:425-434. Ewald, P. W. 1980. Energetics of resource defense: an experimental approach. Proceedings of the XVII Ornithological Congress 2:1093-1099. Ewald, P. W. 1983. Effects of resource depression on use of inexpensive and escalated aggressive behavior: experimental tests using Anna hummingbirds. Behay. Ecol. Sociobiol. 12:95-101 Ewald, P. W. and R. J. Bransfield. 1987. Territory quality and territorial behavior in two sympatric species of hummingbirds. Behay. Ecol. Sociobiol. 20:285-293. Ewald, P. W. and W. A. Williams. 1982. Function of the bill and tongue in nectar uptake by hummingbirds. Auk 99:573-576. Feinsinger, P. 1983. Variable nectar secretion in a Heliconia species pollinated by hermit hummingbirds. Biotropica 15:48-52. Feinsinger, P. 1987. Approaches to nectarivore-plant interactions in the New World. Revista Chilena de Historia Natural 60:285-319. Feinsinger, P., W. H. Busby and H. M. Tiebout III. 1988. Effects of indiscriminate foraging by tropical hummingbirds on pollination and plant reproductive success: experiments with two tropical treelets (Rubiaceae). Oecologia 76:471-474.  85 Feinsinger, P. and R. K. Colwell. 1978. Community organization among neotropical nectar-feeding birds. Am. Zool. 18:779795. Feinsinger, P., Y. B. Linhart, L. A. Swarm, and J. A. Wolfe. 1979. Aspects of the pollination biology of three Erythrina species on Trinidad and Tobago. Annals of the Missouri Botanical Garden 66:451-471. Feinsinger, P., K. G. Murray, S. Kinsman and W. H. Busby. 1986. Floral neighborhood and pollination success in four hummingbird-pollinated cloud forest plant species. Ecology 67:449-464. Feinsinger, P., L. A. Swarm, and J. A. Wolfe. 1985. Nectarfeeding birds on Trinidad and Tobago: comparison of diverse and depauperate guilds. Ecol. Monogr. 55:1-28. Feinsinger, P. and H. M. Tiebout III. 1991. Competition among plants sharing hummingbird pollinators: laboratory experiments on a mechanism. Ecology 72:1946-1952. Feinsinger, P., H. M. Tiebout III and B. E. Young. 1991. Do tropical bird-pollinated plants exhibit density-dependent interactions? Field experiments. Ecology 72:1953-1963. Fenster, C. B. 1991. Selection on floral morphology by hummingbirds. Biotropica 23:98-101. Freeman, C. E., R. D. Worthington and M. S. Jackson. 1991. Floral nectar compositions of some south and southeast Asian species. Biotropica 23:568-574. Galetto, L. 1991. Sobre el nectar y los nectarios de algunas especies de Nicotiana (Solanaceae). Kurtziana 21:165-176. Gass, C.L. 1974. Feeding territoriality in postbreeding migratory rufous hummingbirds. PhD Thesis. University of Oregon. Eugene. Gass, C.L. 1978a. Rufous hummingbird feeding territoriality in a suboptimal habitat. Can. J. Zool. 56:1535-1539. Gass, C. L. 1978b. Experimental studies of foraging in complex laboratory environments. Am. Zool. 18:729-738. Gass, C.L. 1985. Behavioral foundations of adaptation. pp. 63107 In Perspectives in ethology, Volume 6, Bateson, P.P.G. and P.H. Klopfer eds. Plenum Press. New York. 309 pp. Gass, C.L. 1988. Inferring evolutionary history in pollination biology. Acta XIX Congressus Internationalis Ornithologici, pp. 528-536. Gass, C. L., G. Angehr, and J. Centa. 1976. Regulation of food supply by feeding territoriality in the rufous hummingbird. Can. J. Zool. 54:2046-2054.  86 Gass, C. L. and K. P. Lertzman. 1980. Capricious mountain weather: a driving variable in hummingbird territorial dynamics. Can. J. Zool. 58:1964-1968. Gass, C. L. and R. D. Montgomerie. 1981. Hummingbird foraging behavior: decision-making and energy regulation. pp. 159194 In Foraging behavior: ecological, ethological, and psychological approaches, Kamil, A. C. and T. D. Sargent eds. Garland Press. New York. Gass, C. L. and G. D. Sutherland. 1985. Responses of territorial hummingbirds to experimentally enriched patches of flowers: energetic profitability and learning. Can. J. Zool. 63:2125-2133. Gill, F. B. 1978. Proximate costs of competition for nectar. Am. Zool. 18:753-763. Gill, F. B. 1987. Ecological fitting: use of floral nectar in Heliconia stilesii Daniels by three species of hermit hummingbirds. Condor 89:779-787. Gill, F. B. 1988. Trapline foraging by hermit hummingbirds: competition for an undefended, renewable resource. Ecology 69:1933-1942. Gill, F. B., A. L. Mack, and R. T. May. 1982. Competition between hermit hummingbirds Phaethorninae and insects for nectar in a Costa Rican rain forest. Ibis 124:44-49. Gill, F. B. and L. L. Wolf. 1978. Comparative foraging efficiencies of some montane sunbirds in Kenya. Condor 80:391-400. Gill, F. B. and L. L. Wolf. 1979. Nectar loss by golden-winged sunbirds to competitors. Auk 96:448-461. Gracie, C. 1991. Observation of dual function of nectaries in Ruellia radicans (Nees) Lindau (Acanthaceae). Bull. Torrey Bot. Club 118:188-190. Green, R. F. 1980. Bayesian birds: a simple example of Oaten's stochastic model of optimal foraging. Theor. Popul. Biol. 18:244-256. Gryl, E., C. Martinez del Rio and I. Baker. 1990. Avian pollination and nectar use in Combretum fruticosum (Loefl.). Biotropica 22:266-271. Hainsworth, F. R. 1973. On the tongue of a hummingbird: its role in the rate and energetics of feeding. Comp. Biochem. Physiol. 46:65-78.  87 Hainsworth, F. R. 1974. Food quality and foraging efficiency: the efficiency of sugar assimilation by hummingbirds. J. Comp. Physiol. 88:425-431. Hainsworth, F. R. 1981. Energy regulation in hummingbirds. Am. Scientist 69:420-429. Hainsworth, F. R. 1989. 'Fast food' vs 'haute cuisine': painted ladies, Vanessa cardui (L.), select food to maximize net meal energy. Funct. Ecol. 3:701-707. Hainsworth, F. R., T. Mercier and L. L. Wolf. 1983. Floral arrangements and hummingbird feeding. Oecologia 58:225-229. Hainsworth, F. R. and L. L. Wolf. 1972a. Power of hovering flight in relation to body size in hummingbirds. Am. Nat. 106:589-596. Hainsworth, F. R. and L. L. Wolf. 1972b. Energetics of nectar extraction in a small, high altitude, tropical hummingbird, Selasphorus flammula. J. Comp. Physiol. 80:377-387. Hainsworth, F. R. and L. L. Wolf. 1976. Nectar characteristics and food selection by hummingbirds. Oecologia 25:101-114. Hainsworth, F. R. and L. L. Wolf. 1979. Feeding: an ecological approach. Advances in the Study of Behavior 9:53-96. Hainsworth, F. R. and L. L. Wolf. 1983. Models and evidence for feeding control of energy. Am. Zool. 23:261-272. Harder, L. D. 1986. Effects of nectar concentration and flower depth on flower handling efficiency of bumble bees. Oecologia. 69:309-315. Harder, L. D. and M. B. Cruzan. 1990. An evaluation of the physiological and evolutionary influences of inflorescence size and flower depth on nectar production. Funct. Ecol. 4:559-572. Heinrich, B. 1975. Energetics of pollination. Ann. Rev. Ecol. Syst. 6:139-170. Heyneman, A. 1983. Optimal sugar concentrations of floral nectars: dependence on nectar energy flux and pollinator foraging costs. Oecologia 60:198-213. Hixon, M. A. and F. L. Carpenter. 1988. Distinguishing energy maximizers from time minimizers: a comparative study of two hummingbird species. Am. Zool. 28:913-925. Hixon, M. A., F. L. Carpenter, and D. C. Paton. 1983. Territory area, flower density, and time budgeting in hummingbirds: an experimental and theoretical analysis. Am. Nat. 122:366391.  88 Houston, A. J. 1991. A note on the results of Barkan and Withiam on simultaneous choice. Am. Nat. 138:533-535. Hughes, R. N. 1979. Optimal diets under the energy maximization premise: the effects of recognition time and learning. Am. Nat. 113:209-221. Itino, T., M. Kato and M. Hotta. 1991. Pollination ecology of the two wild bananas, Musa acuminata subsp. halabanensis and M. salaccensis: chiropterophily and ornithophily. Biotropica 23:151-158. Jennersten, 0. and M. M. Kwak. 1991. Competition for bumblebee visitation between Melampyrum pratense and Viscaria vulgaris with healthy and Usti/ago-infected flowers. Oecologia 86:88-98. Johnsgard, P. A. 1983. The hummingbirds of North America. Smithsonian Institution Press. Washington, D.C. Kacelnik, A. 1984. Central place foraging in starlings (Sturnus vulgaris). I. Patch residence time. J. Anim. Ecol. 53:283299. Karasov, W. H., D. Phan, J. M. Diamond and F. L. Carpenter. 1986. Food passage and intestinal nutrient absorption in hummingbirds. Auk. 103:453-464. Kingsolver, J. G. and T. L. Daniel. 1979. On the mechanics and energetics of nectar feeding in butterflies. J. theor. Biol. 76:167-179. Kingsolver, J. G. and T. L. Daniel. 1983. Mechanical determinants of nectar feeding strategy in hummingbirds: energetics, tongue morphology, and licking behavior. Oecologia 60:214-226. Klinkhamer, P. G. L. and T. J. de Jong. 1990. Effects of plant size, plant density and sex differential nectar reward on pollinator visitation in the protandrous Echium vulgare (Boraginaceae). Oikos 57:399-405. Kodric-Brown, A. and J. H. Brown. 1978. Influence of economics, interspecific competition, and sexual dimorphism on territoriality of migrant rufous hummingbirds. Ecology 59:285-296. Kuban, J. F. 1977. The ecological organization of hummingbirds in the Chisos Mountains, Big Bend National Park, Texas. M.A. thesis. University of Texas. Arlington. Laverty, T. M. 1980. The flower-visiting behavior of bumble bees: floral complexity and learning. Can. J. Zool. 58:1324-1335. Lawrence, G. H. M. 1955. An introduction to plant taxonomy. The Macmillan Company. New York.  89 Lima, S. L. 1991. Energy, predators and the behaiour of feeding hummingbirds. Evol. Ecol. 5:220-230. MacArthur, R. H. and E. R. Pianka. 1966. On optimal use of a patchy environment. Am. Nat. 100:603-609. Martinez del Rio, C. 1990a. Sugar preferences in hummingbirds: the influence of subtle chemical differences on food choice. Condor 92:1022-1030. Martinez del Rio, C. 1990b. Dietary, phylogenetic, and ecological correlates of intestinal sucrase and maltase activity in birds. Physiol. Zool. 63:987-1011. Martini, M., A. Schmid and D. Hess. 1990. Antibiotics, sugars, and amino acids in nectar of Rhododendron and Piptanthus species from Nepal). Bot. Acta 103:343-348. May, P. G. 1985. Nectar uptake rates and optimal nectar concentrations of two butterfly species. Oecologia 66:381386. May, P. G. 1988. Determinants of foraging profitability in two nectarivorous butterflies. Ecol. Ent. 13:171-184. Michaud, J. P. 1990. Observations on nectar secretion in fireweed, Epilobium angustifolium L. (Onagraceae). J. Apic. Res. 29:132-137. Miller, R. S. and R. E. Miller. 1971. Feeding activity and color preference of ruby-throated hummingbirds. Condor 73:309-313. Mitchell, R. J. and D. C. Paton. 1990. Effects of nectar volume and concentration on sugar intake rates of Australian honeyeaters (Meliphagidae). Oecologia 83:238-246. Mitchell, W. A. 1989. Informational constraints on optimally foraging hummingbirds. Oikos 55:145-154. Mohr, N. A. and S. C. Jay. 1990. Nectar production of selected cultivars of Brassica campestris L. and Brassica napus L. J. Apic. Res. 29:95-100. Monneuse, M.-O., F. Bellisle and J. Louis-Sylvestre. 1991. Impact of sex and age on sensory evaluation of sugar and fat in dairy products. Physiol. and Behay. 50:1111-1117. Montgomerie, R. D. 1979. Energetics of foraging and competition in some Mexican hummingbirds. PhD thesis. McGill Univ. Montgomerie, R. D. 1984. Nectar extraction by hummingbirds: response to different floral characters. Oecologia 63:229236. Montgomerie, R. D., J. McA. Eadie, and L. D. Harder. 1984. What do foraging hummingbirds maximize? Oecologia 63:357-363.  90 Murray, M. G. 1991. Maximizing energy retention in grazing ruminants. J. Anim. Ecol. 60:1029-1045. Nilsson, L. A. 1988. The evolution of flowers with deep corolla tubes. Nature 334:147-149. Norton, M. E., P. Arcese, and P. W. Ewald. 1982. Effect of intrusion pressure on territory size in black-chinned hummingbirds (Archilochus alexandri). Auk 99:761-764. Orians, G. H. 1981. Foraging behavior and the evolution of discriminatory abilities. pp. 389-405 In Foraging behavior: ecological, ethological, and psychological approaches, Kamil, A.C. and T.D. Sargent eds. Garland Press. New York. Paton, D. C. and B. G. Collins. 1989. Bills and tongues of nectar-feeding birds: A review of morphology, function and performance, with intercontinental comparisons. Aust. J. Ecol. 14:473-506. Pearson, 0. P. 1950. The metabolism of hummingbirds. Condor 54:145-152. Pimm, S. L. 1978. An experimental approach to the effects of predictability on community structure. Am. Zool. 18:797808. Pimm, S. L., M. L. Rosenzweig and W. Mitchell. 1985. Competition and food selection: field tests of a theory. Ecology 66:798-807. Pivnick, K. A. and J. N. McNeil. 1985. Effects of nectar concentration on butterfly feeding: measured feeding rates for Thymelicus lineola (Lepidoptera: Hesperiidae) and a general feeding model for adult Lepidoptera. Oecologia 66:226-237. Pleasants, J. M. and N. M. Waser. 1985. Bumblebee foraging at a "hummingbird" flower: reward economics and floral choice. Am. Midl. Nat. 114:283-291. Plowright, R. C. 1981. Nectar production in the boreal forest lily Clintonia borealis. Can. J. Bot. 59: 156-160. Plowright, R. C. 1987. Corolla depth and nectar concentration: an experimental study. Can. J. Bot. 65:1011-1013. Possingham, H. P. 1989. The distribution and abundance of resources encountered by a forager. Am. Nat. 133:42-60. Powers, D. R. 1991. Diurnal variation in mass, metabolic rate, and respiratory quotient in Anna's and Costa's hummingbirds. Physiol. Zool. 64:850-870.  91 Powers, D. R. and K. A. Nagy. 1988. Field metabolic rate and food consumption by free-living Anna's hummingbirds (Calypte anna). Physiol. Zool. 61:500-506. Pyke, G. H. 1978a. Optimal foraging in hummingbirds: testing the marginal value theorem. Am. Zool. 18:739-752. Pyke, G. H. 1978b. Optimal foraging in bumblebees and coevolution with their plants. Oecologia 36:281-293. Pyke, G. H. 1980. Optimal foraging in bumblebees: calculation of net rate of energy intake and optimal patch choice. Theor. Popul. Biol. 17:232-246. Pyke, G. H. 1981. Optimal nectar production in a hummingbird pollinated plant. Theor. Popul. Biol. 20:326-343. Pyke, G. H. 1984. Optimal foraging theory: A critical review. Ann. Rev. Ecol. Syst. 15:523-575. Pyke, G. H. and N. M. Waser. 1981. The production of dilute nectars by hummingbird and honeyeater flowers. Biotropica 13:260-270. Raven, P. H. 1972. Why are bird-visited flowers predominantly red? Evolution 26:674. Real, L. A. and B. J. Rathcke. 1991. Individual variation in nectar production and its effect on fitness in Kalmia latifolia. Ecology 72:149-155. Sazima, M. and I. Sazima. 1990. Hummingbird pollination in two species of Vellozia (Liliiflorae: Velloziaceae) in Southeastern Brazil. Bot. Acta 103:83-86. Schmid-Hempel, P., A. Kacelnik and A. I. Houston. 1985. Honeybees maximize efficiency by not filling their crop. Behay. Ecol. Sociobiol. 17:61-66. Schoener, T. W. 1971. Theory of feeding strategies. Ann. Rev. Ecol. Syst. 2:369-404. Schuchmann, K.-L. and F. Abersfelder. 1986. Energieregulation and Zeitkoordination der Nahrungsaufnahme einer andinen Kolibriart, Aglaeactis cupripennis. Journal fur Ornithologie 127:205-215. Sih, A. 1980. Optimal behavior: can foragers balance two conflicting demands? Science 210:1041-1043. Simon, H. A. 1973. The organization of complex systems. pp. 327 In Hierarchy theory, Pattee, H.H. ed. George Braziller. New York. Snow, D. W. and B. K. Snow. 1980. Relationships between hummingbirds and flowers in the Andes of Colombia. Bull. Br. Mus. Nat. Hist. (Zool.) 38:105-139.  92 Southwick, E. E. 1984. Photosynthate allocation to floral nectar: a neglected energy investment. Ecology 65:17751779. Stephens, D. W. and J. R. Krebs. 1986. Foraging theory. Princeton University Press. Princeton. 247 pp. Stephens, D. W., J. F. Lynch, A. E. Sorensen and C. Gordon. 1986. Preference and profitability: theory and experiment. Am. Nat. 127:533-553. Stiles, F. G. 1976. Taste preferences, color, and flower choice in hummingbirds. Condor 78:10-26. Stromberg, S. and P. B. Johnsen. 1990. Hummingbird sweetness preferences: taste or viscosity? Condor 92:606-612. Suarez, R. K., J. R. B. Lighton, C. D. Moyes, G. S. Brown, C. L. Gass, and P. W. Hochachka. 1990. Fuel selection in rufous hummingbirds: ecological implications of metabolic biochemistry. Proc. Natl. Acad. Sci. USA 87:9207-9210. Sutherland, S. and R. K. Vickery, Jr. 1988. Trade-offs between sexual and asexual reproduction in the genus Mimulus. Oecologia 76:330-335. Tamm, S. 1985. Breeding territory quality and agonistic behavior: effects of energy availability and intruder pressure in hummingbirds. Behay. Ecol. Sociobiol. 16:203207. Tamm, S. 1987. Tracking varying environments: sampling by hummingbirds. Anim. Behay. 35:1725-1734. Tamm, S. 1989. Importance of energy costs in central place foraging by hummingbirds. Ecology 70:195-205. Tamm, S. and C. L. Gass. 1986. Energy intake rates and nectar concentration preferences by hummingbirds. Oecologia 70:2023. Temeles, E. J. and W. M. Roberts. In review. Effect of sexual dimorphism in bill length on foraging behavior: an experimental analysis of hummingbirds. Templeton, A. R. and L. R. Lawlor. 1981. The fallacy of averages in ecological optimization theory. Am. Nat. 117:390-393. Tiebout, H. M., III. 1989. Tests of a model of food passage rates in hummingbirds. Auk 106:203-208. Tiebout, H. M., III. 1991. Daytime energy management by tropical hummingbirds: responses to foraging constraint. Ecology 72:839-851.  93 Trombulak, S. C. 1990. Assessment of territory value by a tropical hummingbird (Amazilia saucerottei). Biotropica 22:9-15. Van Riper, W. 1958. Hummingbird feeding preferences. Auk 75:100-101. Waser, N. M. 1978. Competition for hummingbird pollination and sequential flowering in two Colorado wildflowers. Ecology 59:934-944. Waser, N. M. and M. V. Price. 1981. Pollinator choice and stabilizing selection for flower color in Delphinium nelsonii. Evolution 35:376-390. Waser, N. M. 1986. Flower constancy: definition, cause, and measurement. Am. Nat. 127:593-603. Waser, N. M. and M. V. Price. 1991. Reproductive costs of selfpollination in Ipomopsis aggregata (Polemoniaceae): are ovules usurped? Am. J. Bot. 78:1036-1043. Weathers, W. W. and F. G. Stiles. 1989. Energetics and water balance in free-living tropical hummingbirds. Condor 91:324-331. Weiss, M. R. 1991. Floral colour changes as cues for pollinators. Nature 354:227-229. Weymouth, R. D., R. C. Lasiewski, and A. J. Berger. 1964. The tongue apparatus in hummingbirds. Acta anat. 58:252-270. Whitham, T. G. 1977. Coevolution of foraging in Bombus and nectar dispensing in Chilopsis: a last dreg theory. Science 197:593-596. Wolf, L. L. 1975. Energy intake and expenditures in a nectarfeeding sunbird. Ecology 56:92-104. Wolf, L. L. and F. B. Gill. 1980. Resource gradients and community organization of nectarivorous birds. Acta XVII Congressus Internationalis Ornithologici, pp. 1105-1113. Wolf, L. L. and F. R. Hainsworth. 1971. Time and energy budgets of territorial hummingbirds. Ecology 52:980-988. Wolf, L. L. and F. R. Hainsworth. 1983. Economics of foraging strategies in sunbirds and hummingbirds. pp. 223-264 In Behavioral energetics: the cost of survival in vertebrates, Aspey, E. P. and S. I. Lustic eds. Ohio State University Press. Columbus. Wolf, L. L. and F. R. Hainsworth. 1986. Information and hummingbird foraging at individual inflorescences of Ipomopsis aggregata. Oikos 46:15-22.  94 Wolf, L. L., F. R. Hainsworth, and F. B. Gill. 1975. Foraging efficiencies and time budgets in nectar-feeding birds. Ecology 56:117-128. Wolf, L. L., F. R. Hainsworth, and F. G. Stiles. 1972. Energetics of foraging: rate and efficiency of nectar extraction by hummingbirds. Science 176:1351-1352. Wolf, L. L. and F. G. Stiles. 1989. Adaptations for the 'Failsafe' pollination of specialized ornithophilous flowers. Am. Midl. Nat. 121:1-10. Wolf, L. L., and J. S. Wolf. 1976. Mating system and reproductive biology of malachite sunbirds. Condor 78:2739. Wunderle, J. M., Jr. and J. S. Martinez. 1987. Spatial learning in the nectarivorous bananaquit: juveniles versus adults. Anim. Behay. 35:652-658. Zar, J. H. 1984. Biostatistical analysis. 2nd ed. PrenticeHall. New Jersey. 718 pp. Zimmerman, M. 1983. Plant reproduction and optimal foraging: experimental nectar manipulations in Delphinium nelsonii. Oikos 41:57-63.  95 APPENDIX 1 GLOSSARY OF TERMS USED IN CHAPTER 1 CF = constant licking frequency across concentration CV = constant load volume per lick across concentration  = energy constant of sucrose = 16500 ^(j*g-1) E^= energy intake rate^ f^= licking frequency^  (W) (Hz)  1^= distance of fluid flow into tongue groove^(m) 1 g = tongue groove length ^  (m)  n^= number of licks to load nectar pool r^= 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 ^ V^= volume intake rate^  (s) (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 S 2 + 0.012 S - 6.892]^(kg*ml*s-1)  =  surface tension coefficient = 7.18 10 -2 + 7.11 10 S^ -  8^=  contact angle = 0^  (N*m-1) (°)  96 APPENDIX 2 SAMPLE SIZES IN FIGURES 11 AND 12 Table 5. Sample sizes in volume and energy intake rate graphs (Figures 11 and 12). Feeding visits Foraging bouts Sucrose concentration (%) 65^25 35^45^55 25 35^45^55 65 Bird 4  10  254  396  428  641  9  254  394  427  633  Bird 5  163  215  273  495  539  162  214  273  495  538  Bird 27  32  238  374  474  610  31  236  372  474  608  Bird 38  127  245  313  516  589  126  243  310  515  587  


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items