food-exchange by foragers in the hive – a means of communication among honey bees?

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Behav Ecol Sociobiol (1996) 38 : 59–64 © Springer-Verlag 1996 Walter M. Farina Food-exchange by foragers in the hive – a means of communication among honey bees? Received: 14 January 1995 / Accepted after revision: 14 August 1995 Abstract Dancing and trophallactic behaviour of forager honey bees, Apis mellifera ligustica Spinola, that returned from an automatic feeder with a regulated ow rate of 50% weight-to-weight sucrose solution (range: 0.76–7.65 μl/ min) were studied in an observa- tion hive. Behavioural parameters of dancing, such as probability, duration and dance tempo, increased with the nectar ow rate, though with very dierent response curves among bees. For trophallaxis (i.e. mouth-to- mouth exchange of food), the frequency of giving- contacts and the transfer rate of the nectar increased with the nectar ow rate. After unloading, foragers often approached other nest mates and begged for food before returning to the food source. This behaviour was less frequent at higher nectar ow rates. These results show that the protability of a food source in terms of nectar ow rate had a quantitative representation in the hive through quantitative changes in trophallactic and dancing behaviour. The role of trophallaxis as a communication channel during recruitment is discussed. Key words Apis mellifera · Foraging · Trophallaxis · Dancing behaviour · Communication Introduction Nectar is presented in owers in discrete small amounts, although it is continuously produced at very low rates (Watt et al. 1974; Núñez 1977; Vogel 1983). The rate of nectar production, henceforth dened as nectar ow rate, inuences the foraging behaviour of pollinators (for review see Vogel 1983). The honey bee has been extensively studied in this regard. By using articial feeders which provide sugar solution at controlled ow rates, i.e., feeders which qualitatively and quantitatively mimic natural sources (Núñez 1966, 1971, 1974, 1977, 1982a), it was shown that an increase in the nectar ow rate results in an increment of the nal crop load carried back to the hive (Núñez 1966). Contrarily, bees trained to collect at sources providing sugar solutions of dierent concentrations in unlimited ow rates attain maximal crop loads, remain for a shorter time at the source and the nectar ow gathered is only limited by the bee’s intake rate (Núñez 1966, 1982b; Wells and Giacchino 1968). After a successful foraging trip honeybee foragers arriving at the hive unload the collected nectar to their hive-mates and often perform dancing behaviour (von Frisch 1968). Dancing behaviour is the most extensively studied channel of information among bees. It has been observed that dance maneuvers, running speed, sound emission and thorax temperature change in dependence on the concentration of the sugar solution (Esch 1962; von Frisch 1965; Stabentheiner and Hagmüller 1991; Waddington and Kirchner 1992). Nectar collected is regurgitated from the honey sac and transferred by trophallaxis, i.e. opening the mandibles while one or more recipient bees take the oered food by protruding their proboscis and placing them between the mouth parts of the donor bee (Korst and Velthuis 1982). After unloading the nectar, for- agers often approach other nest-mates and beg for food before returning to the food source (von Frisch 1965, Núñez 1970). Von Frisch (1923) demonstrated that recipient bees can be informed about the odour of the nectar as well as other parts of the owers visited. Trophallactic food-exchange was therefore suggested as a potential explanation of the fact that experienced foragers, having temporarily stayed in the hive, resume nectar collection at a known, previously exhausted food source upon perception of such an odour carried by a This work was dedicated to Prof. Dr. Josué A. Núñez on the occa- sion of his 70th birthday W.M. Farina Departamento de Ciencias Biológicas, Universidad de Buenos Aires, Ciudad Universitaria, CP 1428 Buenos Aires, Argentina

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Page 1: Food-exchange by foragers in the hive – a means of communication among honey bees?

Behav Ecol Sociobiol (1996) 38 : 59–64 © Springer-Verlag 1996

Walter M. Farina

Food-exchange by foragers in the hive – a means of communication among honey bees?

Received: 14 January 1995/Accepted after revision: 14 August 1995

Abstract Dancing and trophallactic behaviour offorager honey bees, Apis mellifera ligustica Spinola, thatreturned from an automatic feeder with a regulatedflow rate of 50% weight-to-weight sucrose solution(range: 0.76–7.65 µl/min) were studied in an observa-tion hive. Behavioural parameters of dancing, such asprobability, duration and dance tempo, increased withthe nectar flow rate, though with very different responsecurves among bees. For trophallaxis (i.e. mouth-to-mouth exchange of food), the frequency of giving-contacts and the transfer rate of the nectar increasedwith the nectar flow rate. After unloading, foragersoften approached other nest mates and begged for foodbefore returning to the food source. This behaviour wasless frequent at higher nectar flow rates. These resultsshow that the profitability of a food source in terms ofnectar flow rate had a quantitative representation inthe hive through quantitative changes in trophallacticand dancing behaviour. The role of trophallaxis asa communication channel during recruitment isdiscussed.

Key words Apis mellifera · Foraging · Trophallaxis ·Dancing behaviour · Communication

Introduction

Nectar is presented in flowers in discrete small amounts,although it is continuously produced at very low rates(Watt et al. 1974; Núñez 1977; Vogel 1983). The rateof nectar production, henceforth defined as nectar flowrate, influences the foraging behaviour of pollinators

(for review see Vogel 1983). The honey bee has beenextensively studied in this regard. By using artificialfeeders which provide sugar solution at controlled flowrates, i.e., feeders which qualitatively and quantitativelymimic natural sources (Núñez 1966, 1971, 1974, 1977,1982a), it was shown that an increase in the nectar flowrate results in an increment of the final crop loadcarried back to the hive (Núñez 1966). Contrarily, beestrained to collect at sources providing sugar solutionsof different concentrations in unlimited flow rates attainmaximal crop loads, remain for a shorter time at thesource and the nectar flow gathered is only limited bythe bee’s intake rate (Núñez 1966, 1982b; Wells andGiacchino 1968).

After a successful foraging trip honeybee foragersarriving at the hive unload the collected nectar to theirhive-mates and often perform dancing behaviour (vonFrisch 1968). Dancing behaviour is the most extensivelystudied channel of information among bees. It has beenobserved that dance maneuvers, running speed, soundemission and thorax temperature change in dependenceon the concentration of the sugar solution (Esch 1962;von Frisch 1965; Stabentheiner and Hagmüller 1991;Waddington and Kirchner 1992).

Nectar collected is regurgitated from the honey sacand transferred by trophallaxis, i.e. opening themandibles while one or more recipient bees take theoffered food by protruding their proboscis and placingthem between the mouth parts of the donor bee (Korstand Velthuis 1982). After unloading the nectar, for-agers often approach other nest-mates and beg for foodbefore returning to the food source (von Frisch 1965,Núñez 1970). Von Frisch (1923) demonstrated thatrecipient bees can be informed about the odour ofthe nectar as well as other parts of the flowers visited.Trophallactic food-exchange was therefore suggested asa potential explanation of the fact that experiencedforagers, having temporarily stayed in the hive, resumenectar collection at a known, previously exhausted foodsource upon perception of such an odour carried by a

This work was dedicated to Prof. Dr. Josué A. Núñez on the occa-sion of his 70th birthday

W.M. FarinaDepartamento de Ciencias Biológicas, Universidadde Buenos Aires, Ciudad Universitaria, CP 1428Buenos Aires, Argentina

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nest-mate without the need of information containedin the dance (von Frisch 1968).

Trophallaxis might also potentially play a role dur-ing information transfer about food source profitability.Two observations suggest that foragers could representit through some components of the food exchangebehaviour:

1. The nectar transfer rate (i.e. transferred volumeof sugar solution/contact time) during the first foodunloading depends positively on the crop load carriedby the donor bee in experimental arenas (Farina andNúñez 1991).

2. If food availability in the hive is sparse, foragersreturning from poor nectar sources display recruitingdances only after begging contacts with hive-mates(Núñez 1970).

Even where changes in foraging behaviour in rela-tion to nectar flow rate have been well studied (Núñez1966, 1971, 1982a), how it modifies recruiting behav-iour in the hive is not fully understood (Núñez 1970).In this study, the interaction between dancing andtrophallactic behaviour of individual returning foragerswas analyzed in relation to the flow rate of sugar solu-tion offered at the food source.

Materials and methods

Procedure

The study was undertaken between February and April 1991 (i.e.at the end of the nectar flow season) in the apiary of the ArgentineBeekeeper Society (S.A.D.A.), González Catán (34°6@S), Provinceof Buenos Aires, Argentina. A two-frame observation hive (see vonFrisch 1965) with nearly 4000 Apis mellifera ligustica bees was used.Bee foragers, one at a time and marked with a spot of paint, weretrained to collect 50% weight/weight scented sucrose solution(80 µl vanilla essence per liter) from an automatic rate-feeder placedon a window sill of the laboratory, 30 m distant from the colony.At the rate-feeder, sucrose solution was injected at different flowrates of sucrose solution via a pump driven by a synchromotor (seeNúñez 1970). By varying the velocity of the synchromotor, flowrates of 0.76, 1.53, 3.06 and 7.65 µl /min of 50% w/w sucrose solu-tion were obtained. The synchromotor was switched on when atrained and marked bee arrived at the rate-feeder, and off immedi-ately after it left to return to the hive.

Experiments began early in the morning, when a trained bee was allowed to forage on the rate-feeder. Nectar flow was main-tained constant during four to eight successive foraging visits.Thereafter, while the trained bee was absent, it was changed to adifferent nectar flow. Trained bees exploited two to four differentnectar flows during the day and presented either on a decreasingor increasing program. The same bees were recorded during 1–2successive days. These experimental programs allowed us (1) tocompensate for transient responses to changes in nectar flow rateby maintaining the reward constant during four to eight visits,(2) to analyse changes in the foraging behaviour of individual beesdepending on the rewarding program offered at the rate-feeder, and(3) to control for possible effects of daily activity rhythms. A totalof 268 foraging cycles performed by five bees were tested with morethan one rewarding program in 11 observation days.

Measurements

At the rate-feeder

Feeding time, defined as the time a bee spent at the rate-feeder fromarrival until it decided to departure to the hive, was measured.By multiplying the feeding time by the nectar flow rate offeredthe crop load attained in the foraging trip was obtained. Thisestimation is based on previous work by Núñez (1966, 1974).He found no difference between foragers’ crop load calculated byweighing the animal before and after drinking and the method usedhere. It is worth mentioning that this is only valid when the nectarflow rate offered at a rate-feeder is lower than the bee’s maximalintake rate (c. 60 µl/min. for 50% w/w sucrose solutions, see Núñez1966; Pflumm 1969).

At the observation hive

The behaviour of the returning bees were recorded on audio tapesand later transcribed for statistical analysis (see Seeley 1989). Thebehavioural parameters recorded were the following:

1. Duration of dancing, defined as the time the bee spentdancing (at 30 m from the hive only round dances were performedby this strain, see von Frisch 1965), excluding the time for whichit stopped dancing if this was more than 4 s (see Waddington 1982).

2. Dance tempo, defined as the number of reversals per 15 s ofrunning on the comb (von Frisch 1965).

3. Hive time, defined as the time a bee spent into the hivebetween feeding visits.

4. Giving time, defined as the time a forager spent in each actof nectar unloading (i.e. a marked bee opens its mandibles whileone or more recipient bees contact its prementum with their pro-truded proboscis). Only contacts lasting more than 1 s were takeninto account (after Korst and Velthuis 1982).

5. Number of giving contacts, defined as the number of timesthe marked forager unloaded nectar per each stay in the hive.

6. Number of begging contacts, defined as the number of timesthe forager touched the prementum of their hive-mates with herprotruded proboscis for more than 1 s per each stay in the hive.

Statistics

Data were analysed by means of analysis of frequency (Sokal andRohlf 1981) and analysis of covariance (ANCOVA) (Winer 1971).Analysis of covariance was performed to factor out effects amongbees, since it is known that there is inter-individual variability inforaging and recruiting behaviour (Núñez 1966; Oldroyd et al.1991a, 1993; Waddington and Kirchner 1992). Since the same beesexploited a constant flow rate of sugar solution throughout four toeight successive foraging visits, measurements taken in the timeinterval when the flow rate was constant were pooled as mean ofthe samples before statistical analysis, in order to avoid pseudorepli-cations (see Hurlbert 1984).

Results

A negative dependence was found between time in-vested at the rate-feeder, defined as feeding time, andsugar solution flow [Fig. 1, empty circles; covariableof the sugar flow (log transformation): P < 0.001,ANCOVA test]. Moreover, response curves among beeswere similar, i.e. neither the intercepts nor the slopesof the linear regressions between flow rate and feeding

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time were significantly different (factor variationamong bees: NS; interaction factor slopes × bee: NS).From the feeding time, the forager’s crop load attainedat the end of the visit could be estimated (Fig. 1, filledcircles; for details see Materials and methods). Usingthis, a positive relationship between final crop load andnectar flow rate found at the rate-feeder was found.This confirms Núñez’s results (1966) in the sense thatthe higher the nectar flow rate of sugar solution offered

at the food source, the greater the volume collected byforagers.

Returning foragers spent more time in the hive fordecreasing nectar flow rates at the source [Fig. 2,covariable of the sugar flow (log transformation):P < 0.05, ANCOVA test]. As with the feeding time, nodifference among bees was observed (factor variationamong bees: NS; interaction factor slopes × bee: NS).That means that, as nectar flow rate at the food sourcedecreased, both the time invested at the feeder and thetime spent thereafter in the hive increased.

Regarding dancing behaviour, probability, durationof dancing and dance tempo increased with the flowrate exploited, but with very different individualresponse curves (Fig. 3A, heterogeneity G-test; 3B andC, factor of interaction between slopes and bees:P < 0.01, ANCOVA test).

Trophallactic contacts of returning foragers werequantified as frequency of giving and begging contacts,i.e. contacts per minute spent in the hive. Thus, it waspossible to compare trophallactic behaviour performedby bees arriving from feeders offering different nectarflow rates for different lengths of time spent in the hive(Fig. 2).

The frequency of giving contacts, number of givingcontacts per minute, significantly increased with thenectar flow rate at the food source [Fig. 4; covariableof the sugar flow (log transformation): P < 0.001,ANCOVA test].

Marked bees had experience at the tray-feeder thatis placed near the hive, i.e. at 30 m. Under these con-ditions, it is known that bees carry little in their cropswhen returning from the hive to a close feeding site(Beutler 1950; Scholze et al. 1964; Núñez 1966).Therefore, it is assumed that when returning from therate-feeder foragers entirely transfer the collected loadin the hive. With this in mind, from data on forager’scrop load (µl) and giving time in the hive (s), the meantransfer rate (µl /s) of the bee was estimated per visit,i.e. the mean velocity at which the donor foragerunloaded the sugar solution to the recipient hive-mates.The estimated transfer rate increased significantlywith sugar flow rate [Fig. 5; covariable of sugar flow(log transformation): P < 0.01, ANCOVA test], andpresented no difference among bees [for intercepts(factor among bees: NS) as well as for slopes (interac-tion factor: NS, ANCOVA test)].

After unloading the carried nectar, foragers oftenapproach other nest-mates and beg for food beforeleaving the hive (Núñez 1970). Begging behaviour wasquantified in the same bees that had previouslyperformed giving behavior. In contrast to giving behav-iour, the frequency of begging-contacts (begging con-tacts per minute) decreased with increasing flow rateof sugar solution [Fig. 6; covariable of the sugar flow(log transformation): P < 0.001, ANCOVA test], andpresented no interindividual difference (factor amongbees: NS, interaction factor: NS; ANCOVA test).

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Fig. 1 The time invested by the trained foragers at the rate-feeder,defined as feeding time (means ± SE, empty circles), in relation tothe flow rate of 50% w/w sucrose solution. Number of observa-tions in parentheses. The corresponding one-way ANCOVA is:F(1, 19) = 14.32, P < 0.001 (covariable of the log sugar solutionflow); F(4, 19) = 0.76, NS (factor variation among bees); F(4, 15)= 0.55, NS (interaction factor between slopes and bees). Multiplyingthe feeding time by the flow rate delivered at the source could beestimated the final crop load attained by foragers (means, filled circles)

Fig. 2 The time spent by trained foragers in the hive between eachvisit to the rate-feeder, defined as hive time (means ± SE), in rela-tion to the flow rate of 50% w/w sucrose solution. Number of obser-vations in parentheses. The corresponding one-way ANCOVA is:F(1, 19) = 6.05, P < 0.05 (covariable of the log sugar solution flow);F(4, 19) = 1.66, NS (factor variation among bees); F(4, 15) = 0.60,NS (interaction factor between slopes and bees)

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Discussion

This work shows that returning foragers modify boththeir dancing and trophallactic behaviour dependingon the sugar solution flow of the food source they areexploiting.

Dancing behaviour quantified in this paper (i.e.probability, duration of dancing and dance tempo)showed, even if great differences among bees wereobserved (Fig. 3A–C), a positive dependence on nec-tar flow rate. These differences suggest high variabilityin the population regarding the thresholds for dancing.

This can be explained as a result of changes in hive orenvironmental factors (Núñez 1970; Seeley 1986, 1989,1994) or genetic differences among foragers’ patrilinegroups (Oldroyd et al. 1991b).

Forager bees’ unloading behaviour was dependenton the flow rate of the sucrose solution at the foodsource. With the nectar flow rate increased the croploads carried (Fig. 1, filled circles) and the number ofgiving-contacts (Fig. 4). As bees unloaded nectardiscontinuously, larger loads last for a higher numberof exchange contacts. Although one can hardly expectthat hive-mates perceive the donor’s frequency ofunloading and gain information from that, it could playan indirect informative role when competing foodsources are exploited simultaneously. When a forager

Fig. 4 Frequency of giving-contacts performed by returning for-agers expressed in contacts per minute in the hive, means ± SE, inrelation to the flow rates of 50% w/w sucrose solution delivered atthe food source. Number of observations in parentheses. The cor-responding one-way ANCOVA is: F(1,19) = 55.36, P < 0.001(covariable of the log sugar solution flow); F(3,19) = 9.48, P < 0.01(factor variation among bees); F(3,16) = 0.97, NS (interactionfactor between slopes and bees)

Fig. 3 A Probability of dancing by each trained forager in relationto the nectar flow rate. The heterogeneity G-test for each individ-ual is: for bee BB, GH = 21.153, df = 3, P < 0.001; G, GH = 1.556,df = 1, NS; GG, GH = 72.675, df = 3, P < 0.001; WW, GH = 4.831,df = 1, NS; YY, GH = 14.611, df = 1, P < 0.05. B Duration ofdancing (means ± SE) in relation to the nectar flow rate. Thecorresponding one-way ANCOVA is: F(1, 19) = 71.47, P < 0.001(covariable of the log sugar solution flow); F(4, 19) = 14.75,P < 0.01 (factor variation among bees); F(4, 15) = 3.13, P < 0.01(interaction factor between slopes and bees). Since significantdifferences between the dance duration and sugar-solution flow wereobtained among bees (interaction factor) individual curves are pre-sented. Bees that did not dance were assigned a duration of zero.C Dance tempo expressed in number of cycles per 15 s of dancing(means ± SE) in relation to the flow rate. The correspondingone-way ANCOVA is: F(1, 16) = 14.38, P < 0.01 (covariable of thelog sugar solution flow); F(2, 16) = 0.54, NS (factor variation amongbees); F(2, 14) = 6.81, P < 0.01 (interaction factor between slopesand bees). Since significant differences between the dance tempoand the sugar solution flow were obtained among beesindividual curves are presented

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flies back to the hive after a successful foraging trip, ittransfers information about nectar odour and taste ofthe visited flowers, even if it does not dance (von Frisch1923, 1968). If the source profitability increases throughan increase of the nectar flow rate, the forager couldstimulate, by performing a higher frequency of nectar-sharing, a great number of experienced hive-mates toresume their visits to a known, previously exhaustednectar source (von Frisch 1965). On the other hand, alow frequency of giving-contacts would reduce theprobability that recipients would come in trophallactic

contact with carriers arriving from a relatively poorlyprofitable food source.

Thus, from an informational point of view, the for-agers’ frequency of giving can affect the probability thathive-mates will come in contact with the collectednectar, since trophallaxis itself is a channel of “direct”information about some properties of the food sourcesuch as odour, sugar concentration and nectar flow rate(Ribbands 1955; von Frisch 1923, 1965; Seeley 1989;Farina and Núñez 1991, 1993). Information about thenectar flow rate could be given by the transfer rateduring nectar unloading (Fig. 5). Returning foragershave been observed to modulate the nectar transfervelocity not only in the natural informational context(i.e. in the hive, Fig. 5), but also under controlledconditions (i.e. in an experimental arena; Farina andNúñez 1991). On account of these observations itis postulated that the nectar transfer rate of eachcontact will code the profitability of a food source toeach recipient.

Since trophallaxis is a bi-directional process it isnecessary to consider not only the giving behaviour ofa focal bee but also its begging behaviour. Foragersalso behave as recipients after unloading the carriednectar. When returning from the food source with alow nectar flow rate, the frequency of begging-contactsafter unloading increased (Fig. 6). Through begging-contacts, returning bees can receive nectar (or only tasteit) or encounter non-offering bees. Thus, by compar-ing what they actually receive with what they get,foragers could gain information about the relativeprofitability of its nectar source. Moreover, the nega-tive relationship observed between the frequency ofbegging-contacts and the nectar flow rate shows thatthe possible function of the begging behaviour toobtain fuel for the forthcoming foraging trip cannot besustained (von Frisch 1965), because: (1) the distanceto the rate-feeder was constant (i.e. 30 m from the hive),and (2) the sugar needed to return to a close feedingplace can be covered by tissue reserves (Núñez 1966,1970, 1974).

Seeley et al. (1991) excluded the possibility that for-agers can directly compare information about differentnectar sources, stating that each forager would onlyknow about its particular nectar source. Returning beescan therefore indirectly assess their relative profitabilitywhile unloading nectar, i.e. through the search time toinitiate the nectar unloading (Seeley 1986). Contrarily,if it is assumed that through each mouth-to-mouthcontact a quantity of information is transferred,returning foragers can directly acquire informationabout the actual feeding-state of the colony whenbehaving as receiver bees. Thus, bees arriving from poornectar sources extended their stay in the hive (Fig. 2),in which they begged for food intensively (Fig. 6).

Previous studies showed that responsiveness in un-loading nectar and the delay in initiating the first foodtransfer depended on the donor’s crop load and the

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Fig. 5 Estimated mean transfer rate during unloading (µl/s) as afunction of the sugar solution at the rate-feeder, mean ± SE.Number of observations in parentheses. The corresponding one-wayANCOVA is: F (1, 18) = 5.67, P < 0.01 (covariable of the log sugarsolution flow); F (3, 18) = 0.69, NS (factor variation among bees);F (3, 15) = 0.74, NS (interaction factor between slopes and bees)

Fig. 6 Frequency of begging-contacts performed by the returningforagers which previously unloaded the carried nectar, expressedin contacts per minute in the hive (means ± SE), in relation to thenectar. Number of observations in parenthesis. The correspondingone way ANCOVA is: F(1, 20) = 20.42, P < 0.001 (covariable ofthe log. sugar solution flow); F(4, 20) = 1.94, NS (factor variationamong bees); F(4, 16) = 0.86, NS (interaction factor between slopesand bees)

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time invested in nectar collection (Farina and Núñez1991, 1993). Moreover, satiated donor bees were fre-quently observed spontaneously offering a drop of solu-tion, even when no begging occurred (Núñez 1970). The present results show that returning foragers bothincreased their frequency of giving-contacts (Fig. 4)and decreased their frequency of begging-contacts(Fig. 6) when they carried greater volumes. Both resultssuggest that foragers can initiate the trophallactic con-tacts, unloading as well as begging-contacts, depend-ing on the profitability of the nectar source they areexploiting.

It is thus concluded that profitability of a food sourcein terms of flow rate of nectar finds a quantitativerepresentation in the hive through quantitative changesin both trophallactic and dancing behaviour. However,trophallactic behaviour was less variable amongindividuals and depended more on the nectar flow ratethan dancing behaviour, and could thus be an efficientchannel for information exchange about nectar sourceprofitability. Previous work showed increasing recruit-ment for feeders with higher nectar flow rate (Núñez1971), but the relative effects of trophallaxis or danc-ing (or both) on recruitment cannot be distinguished.It remains open whether and how bees integrate anduse this information during decision making.

Acknowledgments I am deeply indebted to Prof. Dr. Josué Núñezfor his permanent encouragement, fruitful discussions and valuablecomments on the manuscript, and also to N. Balderrama (Maracay,Venezuela), M. Giurfa, R. Josens, L. Moffatt, F. Roces and twoanonymous referees for valuable comments and suggestions. I thankLuciano Moffatt, for much help with the experiments describedhere, and who steadfastly tended the feeder during the experiments.The Argentine Beekeeper Society (S.A.D.A.) provided facilities andtechnical assistance. This study was partially supported by a grantfrom CONICET (PID-3672/92) to Prof. Dr. J.A. Núñez and a grantfrom the University of Buenos Aires (EX 114) to the author.

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Communicated by R.F.A. Moritz