Brood pheromone stimulates pollen foraging in honey bees (Apis mellifera)

Foraging and the mechanisms that regulate the quantity of food collected are important evolutionary and ecological attributes for all organisms. The decision to collect pollen by honey bee foragers depends on the number of larvae (brood), amount of stored pollen in the colony, as well as forager genotype and available resources in the environment. Here we describe how brood pheromone (whole hexane extracts of larvae) influenced honey bee pollen foraging and test the predictions of two foraging-regulation hypotheses: the indirect or brood-food mechanism and the direct mechanism of pollen-foraging regulation. Hexane extracts of larvae containing brood pheromone stimulated pollen foraging. Colonies were provided with extracts of 1000 larvae (brood pheromone), 1000 larvae (brood), or no brood or pheromone. Colonies with brood pheromone and brood had similar numbers of pollen foragers, while those colonies without brood or pheromone had significantly fewer pollen foragers. The number of pollen foragers increased more than 2.5-fold when colonies were provided with extracts of 2000 larvae as a supplement to the 1000 larvae they already had. Within 1 h of presenting colonies with brood pheromone, pollen foragers responded to the stimulus. The results from this study demonstrate some important aspects of pollen foraging in honey bee colonies: (1) pollen foragers appear to be directly affected by brood pheromone, (2) pollen foraging can be stimulated with brood pheromone in colonies provided with pollen but no larvae, and (3) pollen forager numbers increase with brood pheromone as a supplement to brood without increasing the number of larvae in the colony. These results support the direct-stimulus hypothesis for pollen foraging and do not support the indirect-inhibitor, brood-food hypothesis for pollen-foraging regulation. Received: 5 March 1998 / Accepted after revision: 29 August 1998     

Regulation of pollen foraging in honeybee colonies: effects of young brood, stored pollen, and empty space

Pollen storage in a colony of Apis mellifera is actively regulated by increasing and decreasing pollen foraging according to the “colony's needs.” It has been shown that nectar foragers indirectly gather information about the nectar supply of the colony from nestmates without estimating the amount of honey actually stored in the combs. Very little is known about how the actual colony need is perceived with respect to pollen foraging. Two factors influence the need for pollen: the quantity of pollen stored in cells and the amount of brood. To elucidate the mechanisms of perception, we changed the environment within normal-sized colonies by adding pollen or young brood and measured the pollen-foraging activity, while foragers had either direct access to them or not. Our results show that the amount of stored pollen, young brood, and empty space directly provide important stimuli that affect foraging behavior. Different mechanisms for forager perception of the change in the environment are discussed. Received: 13 June 1998 / Accepted after revision: 25 October 1998     

The effects of colony-level selection on the social organization of honey bee (Apis mellifera L.) colonies: colony-level components of pollen hoarding

Two-way selection for quantities of stored pollen resulted in the production of high and low pollen hoarding strains of honey bees (Apis mellifera L.). Strains differed in areas of stored pollen after a single generation of selection and, by the third generation, the high strain colonies stored an average 6 times more pollen than low strain colonies. Colony-level organizational components that potentially affect pollen stores were identified that varied genetically within and between these strains. Changes occurred in several of these components, in addition to changes in the selected trait. High strain colonies had a significantly higher proportion of foragers returning with loads of pollen, however, high and low strain colonies had equal total numbers of foragers Colony rates of intake of pollen and nectar were not independent. Selection resulted in an increase in the number of pollen collectors and a decrease in the number of nectar collectors in high strain colonies, while the reciprocal relationship occurred in the low strain. High and low strain colonies also demonstrated different diurnal foraging patterns as measured by the changing proportions of returning pollen foragers. High strain colonies of generation 3 contained significantly less brood than did low strain colonies, a consequence of a constraint on colony growth resulting from a fixed nest volume and large quantities of stored pollen. These components represent selectable colony-level traits on which natural selection can act and shape the social organization of honey bee coloniesCommunicated by R.F.A. Moritz     

Cuticular volatiles,attractivity of worker larvae and invasion of brood cells by Varroa mites. A comparison of Africanized and European honey bees

Summary. Africanized honey bees (AHBs) of Brazil and Mexico have proven to be tolerant to Varroa destructor mites. In contrast, European honey bees (EHBs: Apis mellifera carnica) at the same tropical study site are highly intolerant to these ectoparasites. A lower attractiveness of Varroa-tolerant AHB larvae has been hypothesised to be an important trait in reducing the susceptibitlity of AHBs to these mites. Thus, selection for EHB brood that is less attractive to mites is thought to be one possibility for limiting mite population growth and thus increase the tolerance of EHBs to the mite.?In Ribeir?o Preto, Brazil, European A. m. carnica bees and AHBs were tested with respect to their rate of brood infestation and brood attractiveness to Varroa mites. For the comparison of brood infestation rates, we introduced combs with pieces of EHB and AHB brood into honey bee colonies (18 repetitions). The relative infestation rate of EHB brood was significantly higher compared to AHB brood.?The preference behaviour of single Varroa mites was tested in a laboratory bioassay where either living host stages were offered or host extracts were presented on dummies. By these tests we could confirm the preference of Varroa females for certain developmental host stages and for their corresponding extracts. In contrast to the within-colony results, Varroa mites in the laboratory bioassay showed a slight preference for AHB compared to EHB larvae.?The gas chromatographic analysis revealed differences in the chemical spectrum of extracts obtained from different larvae. In accord with the results of the bioassays, we could detect stage-specific odour differences in larval cuticular compounds, including methyl esters and hydrocarbons that have been described as kairomones. None of these substances, however, revealed significant race-specific differences. Therefore, the quantity and composition of certain cuticular compounds seem to be responsible only for the recognition of a suitable host stage by Varroa females. The different infestation rates in the colonies, however, seem to be caused neither by race-specific differences in attractiveness of bee larvae nor by an extended attractive period of EHB larvae: both AHB and EHB larvae become attractive approximately 21 h before capping of the brood cell, and thus have the same window of time when they can be parasitised.?Therefore differential Varroa-infestation rates are not related to larval attraction but probably are determined by other race-specific and colony-related factors. Received 11 June 2001; accepted 19 November 2001.     

Effects of protein-constrained brood food on honey bee (<Emphasis Type="Italic">Apis mellifera</Emphasis> L.) pollen foraging and colony growth

Pollen is the sole source of protein for honey bees, most importantly used to rear young. Honey bees are adept at regulating pollen stores in the colonies based on the needs of the colony. Mechanisms for regulation of pollen foraging in honey bee are complex and remain controversial. In this study, we used a novel approach to test the two competing hypothesis of pollen foraging regulation. We manipulated nurse bee biosynthesis of brood food using a protease inhibitor that interferes with midgut protein digestion, significantly decreasing the amount of protein extractable from hypopharyngeal glands. Experimental colonies were given equal amounts of protease inhibitor-treated and untreated pollen. Colonies receiving protease inhibitor treatment had significantly lower hypopharyngeal gland protein content than controls. There was no significant difference in the ratio of pollen to nonpollen foragers between the treatments. Pollen load weights were also not significantly different between treatments. Our results supported the pollen foraging effort predictions generated from the direct independent effects of pollen on the regulation of pollen foraging and did not support the prediction that nurse bees regulate pollen foraging through amount of hypopharyngeal gland protein biosynthesis.     

Colony state and regulation of pollen foraging in the honey bee,Apis mellifera L.

Summary To place social insect foraging behavior within an evolutionary context, it is necessary to establish relationships between individual foraging decisions and parameters influencing colony fitness. To address this problem, we examined interactions between individual foraging behavior and pollen storage levels in the honey bee, Apis mellifera L. Colonies responded to low pollen storage conditions by increasing pollen intake rates 54% relative to high pollen storage conditions, demonstrating a direct relationship between pollen storage levels and foraging effort. Approximately 80% of the difference in pollen intake rates was accounted for by variation in individual foraging effort, via changes in foraging activity and individual pollen load size. An additional 20% resulted from changes in the proportion of the foraging population collecting pollen. Under both high and low pollen storage treatments, colonies returned pollen storage levels to pre-experimental levels within 16 days, suggesting that honey bees regulate pollen storage levels around a homeostatic set point. We also found a direct relationship between pollen storage levels and colony brood production, demonstrating the potential for cumulative changes in individual foraging decisions to affect colony fitness. Offprint requests to: J.H. Fewell at the current address     

Regulation of honey bee division of labor by colony age demography

The age at which worker honey bees begin foraging varies under different colony conditions. Previous studies have shown that juvenile hormone (JH) mediates this behavioral plasticity, and that worker-worker interactions influence both JH titers and age at first foraging. These results also indicated that the age at first foraging is delayed in the presence of foragers, suggesting that colony age demography directly influences temporal division of labor. We tested this hypothesis by determining whether behavioral or physiological development can be accelerated, delayed, or reversed by altering colony age structure. In three out of three trials, earlier onset of foraging was induced in colonies depleted of foragers compared to colonies depleted of an equal number of bees across all age classes. In two out of three trials, delayed onset of foraging was induced in colonies in which foragers were confined compared to colonies with free-flying foragers. Finally, in three out of three trials, both endocrine and exocrine changes associated with reversion from foraging to brood care were induced in colonies composed of all old bees and devoid of brood; JH titers decreased and hypopharyngeal glands regenerated. These results demonstrate that plasticity in age-related division of labor in honey bee colonies is at least partially controlled by social factors. The implications of these results are discussed for the recently developed ‘‘activator-inhibitor” model for honey bee behavioral development. Received: 8 November 1995/Accepted after revision: 10 May 1996     

The effects of young brood on the foraging behavior of two strains of honey bees (<Emphasis Type="Italic">Apis mellifera</Emphasis>)

Honey bee foragers specialize on collecting pollen and nectar. Pollen foraging behavior is modulated by at least two stimuli within the nest: the presence of brood pheromone and young larvae and the quantity of stored pollen. Genetic variation in pollen foraging behavior has been demonstrated repeatedly. We used selected high and low pollen-hoarding strains of bees that differ dramatically in the quantity of pollen collected to determine if the observed differences in foraging could be explained by differential responses to brood stimuli. Workers from the high and low pollen-hoarding strains and wild-type bees were co-fostered in colonies with either brood or no brood. As expected based on previous studies, returning high pollen-hoarding foragers collected heavier pollen loads and lighter nectar loads than low pollen-hoarding bees. Effects of brood treatment were also observed; bees exposed to brood collected heavier pollen loads and initiated foraging earlier than those from broodless colonies. More specifically, brood treatment resulted in increased pollen foraging in high pollen-hoarding bees but did not affect pollen foraging in low pollen-hoarding bees, suggesting that high pollen-hoarding bees are more sensitive to the presence of brood. However, response to brood stimuli does not sufficiently explain the differences in foraging behavior between the strains since these differences persisted even in the absence of brood.     

Collective decision-making in honey bees: how colonies choose among nectar sources

Summary A honey bee colony can skillfully choose among nectar sources. It will selectively exploit the most profitable source in an array and will rapidly shift its foraging efforts following changes in the array. How does this colony-level ability emerge from the behavior of individual bees? The answer lies in understanding how bees modulate their colony's rates of recruitment and abandonment for nectar sources in accordance with the profitability of each source. A forager modulates its behavior in relation to nectar source profitability: as profitability increases, the tempo of foraging increases, the intensity of dancing increases, and the probability of abandoning the source decreases. How does a forager assess the profitability of its nectar source? Bees accomplish this without making comparisons among nectar sources. Neither do the foragers compare different nectar sources to determine the relative profitability of any one source, nor do the food storers compare different nectar loads and indicate the relative profitability of each load to the foragers. Instead, each forager knows only about its particular nectar source and independently calculates the absolute profitability of its source. Even though each of a colony's foragers operates with extremely limited information about the colony's food sources, together they will generate a coherent colonylevel response to different food sources in which better ones are heavily exploited and poorer ones are abandoned. This is shown by a computer simulation of nectar-source selection by a colony in which foragers behave as described above. Nectar-source selection by honey bee colonies is a process of natural selection among alternative nectar sources as foragers from more profitable sources survive (continue visiting their source) longer and reproduce (recruit other foragers) better than do foragers from less profitable sources. Hence this colonial decision-making is based on decentralized control. We suggest that honey bee colonies possess decentralized decision-making because it combines effectiveness with simplicity of communication and computation within a colony. Offprint requests to: T.D. Seeley     

Manuscript in preparation for <Emphasis Type="Italic">Behavioral Ecology and Sociobiology</Emphasis> Bumble bee pollen foraging regulation: role of pollen quality,storage levels,and odor

The regulation of protein collection through pollen foraging plays an important role in pollination and in the life of bee colonies that adjust their foraging to natural variation in pollen protein quality and temporal availability. Bumble bees occupy a wide range of habitats from the Nearctic to the Tropics in which they play an important role as pollinators. However, little is known about how a bumble bee colony regulates pollen collection. We manipulated protein quality and colony pollen stores in lab-reared colonies of the native North American bumble bee, Bombus impatiens. We debut evidence that bumble bee colony foraging levels and pollen storage behavior are tuned to the protein quality (range tested: 17–30% protein by dry mass) of pollen collected by foragers and to the amount of stored pollen inside the colony. Pollen foraging levels (number of bees exiting the nest) significantly increased by 55%, and the frequency with which foragers stored pollen in pots significantly increased by 233% for pollen with higher compared to lower protein quality. The number of foragers exiting the nest significantly decreased (by 28%) when we added one pollen load equivalent each 5 min to already high intranidal pollen stores. In addition, pollen odor pumped into the nest is sufficient to increase the number of exiting foragers by 27%. Foragers directly inspected pollen pots at a constant rate over 24 h, presumably to assess pollen levels. Thus, pollen stores can act as an information center regulating colony-level foraging according to pollen protein quality and colony need. An erratum to this article can be found at     

Genetic determination of nectar foraging,pollen foraging,and nest-site scouting in honey bee colonies

Summary Allozyme analyses of honey bee workers revealed significant differences in the intracolonial subfamily composition of groups of nectar foragers, pollen foragers, and nest-site scouts. These differences demonstrate that colony genetic structure influences the division of labor among older foraging-age bees just as it does for younger workers. The maintenance of genetic variability for the behavior of individual workers and its possible effects on the organization of colonies are discussed.     

Directional change in a suite of foraging behaviors in tropical and temperate evolved honey bees (<Emphasis Type="Italic">Apis mellifera</Emphasis> L.)

The concept of a suite of foraging behaviors was introduced as a set of traits showing associative directional change as a characterization of adaptive evolution. I report how naturally selected differential sucrose response thresholds directionally affected a suite of honey bee foraging behaviors. Africanized and European honey bees were tested for their proboscis extension response thresholds to ascending sucrose concentrations, reared in common European colonies and, captured returning from their earliest observed foraging flight. Race constrained sucrose response threshold such that Africanized bees had significantly lower sucrose response thresholds. A Cox proportional hazards regression model of honey bee race and sucrose response threshold indicated that Africanized bees were 29% (P<0.01) more at risk to forage over the 30-day experimental period. Sucrose response threshold organized age of first foraging such that each unit decrease in sucrose response threshold increased risk to forage by 14.3% (P<0.0001). Africanized bees were more likely to return as pollen and water foragers than European foragers. Africanized foragers returned with nectar that was significantly less concentrated than European foragers. A comparative analysis of artificial and naturally selected populations with differential sucrose response thresholds and the common suite of directional change in foraging behaviors is discussed. A suite of foraging behaviors changed with a change in sucrose response threshold that appeared as a product of functional ecological adaptation.Communicated by R.F.A. Moritz     

Limited flexibility in the temporal caste system of the honey bee

Caste theory predicts that social insect colonies are organized into stable groups of workers specialized on particular task sets. Alternative concepts of organization of work suggest that colonies are composed of extremely flexible workers able to perform any task as demand necessitates. I explored the flexibility of workers in temporal castes of the honey bee Apis mellifera by determining the ability of colonies to reorganize labor after a major demographic disturbance. I evaluated the flexibility of temporal castes by comparing the foraging rates of colonies having just lost their foragers with colonies having also lost their foragers but having been given a week to reorganize. The population sizes and contents of the colonies in each group were equalized and foraging rates were recorded for one week. Colonies given a weeks initial recovery time after the loss of their foragers were found to forage at significantly higher rates than those colonies given no initial recovery time. This result was consistent for nectar and pollen foraging. These results suggest that honeybee workers lack sufficient flexibility to reorganize labor without compromising foraging. This finding is consistent with the caste concept model of organization of work in insect societies.     

Effects of intracolony variability in behavioral development on plasticity of division of labor in honey bee colonies

There is a genetic component to plasticity in age polyethism in honey bee colonies, such that workers of some genotypes become precocious foragers more readily than do workers of other genotypes, in colonies lacking older bees. Using colonies composed of workers from two identifiable genotype groups, we determined that intracolony differences in the likelihood of becoming a precocious forager are a consequence of differences in rates of behavioral development that are also evident under conditions leading to normal development. An alternative hypothesis, that differences in the likelihood of becoming a precocious forager are due to differences in general sensitivity to altered colony conditions, was not supported. In three out of three trials, workers from the genotype group that was more likely to exhibit precocious foraging in single cohort colonies also foraged at relatively younger ages in colonies in which workers exhibited normal behavioral development. In contrast, in three out of three trials, workers from the genotype group that was more likely to exhibit precocious foraging in single-cohort colonies did not show disproportionately more overaged nursing in colonies in which workers exhibited delayed development. These results indicate that genotypic differences in plasticity in age-related division of labor are based on genotypic differences in rates of behavioral development.     

The sociality of Xylocopa pubescens: does a helper really help?

Summary Solitary and social nests of the facultatively social carpenter bee Xyclopa pubescens can be found simultaneously during the major part of the breeding season. Social nests contain a reproductively dominant forager and either her adult offspring or a formerly reproductive, guarding female. The costs and benefits to the dominant animal of allowing a defeated female to remain as a guard in the nest were analysed in terms of brood loss and brood gain. The costs included the probability that the guard would regain reproductively dominant status. The most important benefits were the protection that a guard provided against pollen robbery by conspecifics and the longer foraging time available to a forager when her nest was protected. The balance between costs and benefits depended on the severity of ecological constraints. During certain periods of intense competition for pollen or nests, the benefits clearly outweighed the costs.Correspondence to: K. Hogendoorn     

Intra-colonial foraging specialism by honey bees (Apis mellifera) (Hymenoptera:Apidae)

Summary Colonies of honey bees with two identifiable subfamilies were established. Returning foragers were captured and killed at two different sampling times. The mean volume and per cent soluble solids of crop contents were determined for each subfamily, as was the mean weight of the pollen pellets. No significant differences in nectar volume or concentration were detected between subfamilies within colonies. However, in a few colonies, significant subfamily by sampling-time interactions were present, suggesting that in these colonies subfamilies differed in their nectar and pollen collecting behavior at different times of day. The plant genera worked by pollen foragers were also determined. In four of six colonies, bees of different subfamilies were found to be majoring on different plant species (Fig. 1). Implications of this intra-colonial variance in foraging behavior for colony fitness are discussed. Offprint requests to: B.P. Oldroyd     

Genotypic differences in brood rearing in honey bee colonies: context-specific?

Summary Three experiments were performed to determine whether brood care in honey bee colonies is influenced by colony genetic structure and by social context. In experiment 1, there were significant genotypic biases in the relative likelihood of rearing queens or workers, based on observations of individually labeled workers of known age belonging to two visually distinguishable subfamilies. In experiment 2, no genotypic biases in the relative likelihood of rearing drones or workers was detected, in the same colonies that were used in experiment 1. In experiment 3, there again were significant genotypic differences in the likelihood of rearing queens or workers, based on electrophoretic analyses of workers from a set of colonies with allozyme subfamily markers. There also was an overall significant trend for colonies to show greater subfamily differences in queen rearing when the queens were sisters (half- and super-sisters) rather than unrelated, but these differences were not consistent from trial to trial for some colonies. Results of experiments 1 and 3 demonstrate genotypic differences in queen rearing, which has been reported previously based on more limited behavioral observations. Results from all three experiments suggest that genotypic differences in brood care are influenced by social context and may be more pronounced when workers have a theoretical opportunity to practice nepotism. Finally, we failed to detect persistent interindividual differences in bees from either subfamily in the tendency to rear queen brood, using two different statistical tests. This indicates that the probability of queen rearing was influenced by genotypic differences but not by the effect of prior queen-rearing experience. These results suggest that subfamilies within a colony can specialize on a particular task, such as queen rearing, without individual workers performing that task for extended periods of time.     

农药暴露的机制模型：蜜蜂毒理学的重要缺失

杀虫剂在最近的蜜蜂数量减少中所扮演的角色是有争议的，部分原因是实地研究常常无法检测到实验室研究所预测的效果。这种不一致性突出了蜜蜂毒理学研究领域的一个关键空白：对蜜蜂在它们的环境中杀虫剂暴露的模式和过程知之甚少。本文作者提出蜜蜂暴露杀虫剂的2个关键过程：1)工蜂采集花蜜的过程中收集农药；2)工蜂带回的农药在蜂巢中的再分配。工蜂收集农药的过程必须被理解为环境污染和蜜蜂觅食活动之间的时空交集。这意味着农药暴露是分配的，而不是离散的，觅食工蜂的一个子集可能会获得有害剂量的农药，而群体暴露将会显得安全。蜂箱中农药的分布是一个复杂的过程，主要是由群体成员之间食物转移的相互作用而产生，而这一过程中花粉和花蜜之间有重要的区别。因此应该优先将关于蜜蜂生物学的大量文献用于发展更严谨的蜂蜜农药暴露机制模型。与效应机制模型结合，暴露机制模型具有整合蜜蜂毒理学领域的潜力，以促进风险评估和基础研究。
精选自Sponsler, D. B. and Johnson, R. M. (2017), Mechanistic modeling of pesticide exposure: The missing keystone of honey bee toxicology. Environmental Toxicology and Chemistry, 36: 871–881. doi: 10.1002/etc.3661
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Effects of colony food shortage on behavioral development in honey bees

Three experiments were conducted to explore the effects of severe food shortage on the control of two important and interrelated aspects of temporal division of labor in colonies of the honey bee (Apis mellifera): the size and age distribution of a colony's foraging force. The experiments were conducted with single-cohort colonies, composed entirely of young bees, allowing us to quickly distinguish the development of new (precocious) foragers from increases in activity of bees already competent to forage. In experiment 1, colony food shortage caused an acceleration of behavioral development; a significantly greater proportion of bees from starved colonies than from fed colonies became precocious foragers, and at significantly younger ages. Temporal aspects of this starvation effect were further explored in experiment 2 by feeding colonies that we initially starved, and starving colonies that we initially fed. There was a significant decrease in the number of new foragers in starved colonies that were fed, detected 1 day after feeding. There also was a significant increase in the number of new foragers in fed colonies that were starved, but only after a 2-day lag. These results suggest that colony nutritional status does affect long-term behavioral development, rather than only modulate the activity of bees already competent to forage. In experiment 3, we uncoupled the nutritional status of a colony from that of the individual colony members. The behavior of fed individuals in starved colonies was indistinguishable from that of bees in fed colonies, but significantly different from that of bees in starved colonies, in terms of both the number and age distribution of foragers. These results demonstrate that effects of starvation on temporal polyethism are not mediated by the most obvious possible worker-nest interaction: a direct interaction with colony food stores. This is consistent with previous findings suggesting the importance of worker-worker interactions in the regulation of temporal polyethism in honey bees as well as other social insects. Received: 17 April 1997 / Accepted after revision: 26 December 1997     

Worker allocation in insect societies: coordination of nectar foragers and nectar receivers in honey bee (Apis mellifera) colonies

Nectar collection in the honey-bee is partitioned. Foragers collect nectar and take it to the nest, where they transfer it to receiver bees who then store it in cells. Because nectar is a fluctuating and unpredictable resource, changes in worker allocation are required to balance the work capacities of foragers and receivers so that the resource is exploited efficiently. Honey bee colonies use a complex system of signals and other feedback mechanisms to coordinate the relative and total work capacities of the two groups of workers involved. We present a functional evaluation of each of the component mechanisms used by honey bees – waggle dance, tremble dance, stop signal, shaking signal and abandonment – and analyse how their interplay leads to group-level regulation. We contrast the actual regulatory system of the honey bee with theory. The tremble dance conforms to predicted best use of information, where the group in excess applies negative feedback to itself and positive feedback to the group in shortage, but this is not true of the waggle dance. Reasons for this and other discrepancies are discussed. We also suggest reasons why honey bees use a combination of recruitment plus abandonment and not switching between subtasks, which is another mechanism for balancing the work capacities of foragers and receivers. We propose that the waggle and tremble dances are the primary regulation mechanisms, and that the stop and shaking signals are secondary mechanisms, which fine-tune the system. Fine-tuning is needed because of the inherent unreliability of the cues, queueing delays, which foragers use to make recruitment decisions. Received: 15 December 1998 / Received in revised form: 6 March 1999 / Accepted: 12 March 1999