Optimal foraging in bumblebees: Rule of movement between flowers within inflorescences

It is hypothesized that nectar-collecting bumblebees will be found to forage in ways that maximize their net rate of energy intake. Attention is focused, in this paper, on the manner in which these bumblebees move from one flower to another within inflorescences. Observations were made on workers of Bombus appositus, which were collecting nectar from Aconitum columbianum (monkshood). The rule of movement of the bumblebees was determined and compared, in terms of net rate of energy intake, with several possible alternative rules. Two of these alternatives gave equally high net rates of energy intake. The observed rule was very similar in nature to one of these and indistinguishable from both in terms of net rate of energy intake.     

Remote perception of floral nectar by bumblebees

Summary On both artificial flowers in the laboratory and certain plant species in the field, bumblebees often closely approached flowers and then departed without probing for nectar. In laboratory experiments where nectar rewards were associated with subtle visual or olfactory cues, bumblebees approached and avoided non-rewarding flowers. Flowers that bees entered and probed for nectar contained rewards much more frequently than predicted by chance alone. When there were no external cues associated with nectar content, bees visited rewarding flowers by chance alone, provided rewarding flowers were not spatially clumped. In the field, bumblebees approached and rejected a large proportion of dogbane flowers and red clover inflorescences. On both species, flowers or inflorescences probed by bees contained more nectar than those rejected by bees or those that I chose at random. On fireweed and monkshood, bees rarely or never approached and rejected healthy-looking flowers. Predictions generated by an optimal foraging model were tested on data from four bumblebee species foraging on red clover. The model was highly successful in qualitatively predicting the relationship between handling time and proportion of inflorescences rejected by individual bees, and the relationship between threshold nectar content for acceptance by bees and average resource availability. Thus, bees appeared to use remotely perceived cues to maximize their rates of nectar intake.     

Estimating nest locations of bumblebee <Emphasis Type="Italic">Bombus ardens</Emphasis> from flower quality and distribution

The central-place forager in a social-insect colony, e.g., the bumblebee, has been expected to maximize its net rate of energy gain to increase the success of its colony. In addition to foraging behavior, the nest location is an important factor for the success of the colony. The bumblebee’s nest location would be affected by the spatial distribution of flowers and their food quality. In this study, we constructed a model to estimate bumblebee nest sites, using the net energy intake rate at available food sites for workers foraging from the nest site. We hypothesized that the probability of colony establishment at a site in coordinates (x, y) was high as the sum of the net energy intake rate I(x, y) increased. To obtain I(x, y), nectar standing crop, sugar concentration, and foraging time were measured for ten plant species in the study site covering 6.25 km². As available flowers changed seasonally, I(x, y) was calculated for three periods: the end of April, the beginning of May, and the middle of May. To verify our hypothesis, we compared the estimations in our model with the actual nest sites of Bombus ardens found in the beginning of May and June by means of tracking bumblebees. From the results, we considered that the net energy intake rate at mid-May might represent the probability of colony establishment, because it could affect colony persistence and reproductive success.     

Optimal foraging in bumblebees: Calculation of net rate of energy intake and optimal patch choice

To test many predictions of “optimal foraging theory” it is necessary to calculate the rate of net energy intake of a foraging animal. Equations are derived for the calculation of the rate of net energy intake of a foraging bumblebee. The assumptions that form the basis of these energy equations are discussed. As examples, the rates of net energy intake are calculated for Bombus flavifrons workers foraging on neighboring patches of Aconitum columbianum and Delphinium barbeyi. If the bumblebees forage optimally, their net rates of energy intake in the two patches should be equal. The observed rates are consistent with this hypothesis. The application of an optimality approach to pollination biology is briefly discussed.     

草乌花蜜产量的梯度分布及熊蜂自下而上的访花行为

收益降低假说(declining reward hypothesis)认为熊蜂自下而上的访花顺序是对花蜜产量的直接响应,先访问下部花蜜产量高的花可以获得更多的收益;花开口方向假说认为自下而上访花是因为熊蜂更容易看见其上部的花朵。为了验证上述两个假说,我们于2008年8月在北京小龙门国家森林公园调查了红光熊蜂(Bombus ignitus)访问草乌(Aconitum kusnezoffii)直立和倒立顶生花序的访问顺序,测量了直立花序下部雌性阶段花和上部雄性阶段花花蜜的糖浓度、体积,计算了花蜜中的糖含量。结果表明,红光熊蜂在直立花序和倒立花序内均以向上运动为主,分别占总运动次数的62.77%和68.35%;直立花序下部雌性阶段花花蜜糖浓度比上部雄性阶段花低1.44%,但是花蜜体积和花蜜中的糖含量都显著高于雄性阶段的花。由于熊蜂访问倒立花序时先访问的是下部的低回报雄性阶段的花,然后再访问上部高回报的雌性阶段的花,这与收益降低假说矛盾,表明红光熊蜂自下而上访问草乌直立花序可能不是受到花蜜产量的调节。     

Bombus terrestris in a mass‐flowering pollinator‐dependent crop: A mutualistic relationship?

Bumblebees (Bombus spp.) rely on an abundant and diverse selection of floral resources to meet their nutritional requirements. In farmed landscapes, mass‐flowering crops can provide an important forage resource for bumblebees, with increased visitation from bumblebees into mass‐flowering crops having an additional benefit to growers who require pollination services. This study explores the mutualistic relationship between Bombus terrestris L. (buff‐tailed bumblebee), a common species in European farmland, and the mass‐flowering crop courgette (Cucurbita pepo L.) to see how effective B. terrestris is at pollinating courgette and in return how courgette may affect B. terrestris colony dynamics. By combining empirical data on nectar and pollen availability with model simulations using the novel bumblebee model Bumble‐BEEHAVE, we were able to quantify and simulate for the first time, the importance of courgette as a mass‐flowering forage resource for bumblebees. Courgette provides vast quantities of nectar to ensure a high visitation rate, which combined with abundant pollen grains, enables B. terrestris to have a high pollination potential. While B. terrestris showed a strong fidelity to courgette flowers for nectar, courgette pollen was not found in any pollen loads from returning foragers. Nonetheless, model simulations showed that early season courgette (nectar) increased the number of hibernating queens, colonies, and adult workers in the modeled landscapes. Synthesis and applications. Courgette has the potential to improve bumblebee population dynamics; however, the lack of evidence of the bees collecting courgette pollen in this study suggests that bees can only benefit from this transient nectar source if alternative floral resources, particularly pollen, are also available to fulfill bees’ nutritional requirements in space and time. Therefore, providing additional forage resources could simultaneously improve pollination services and bumblebee populations.     

The effect of sugar solution type,sugar concentration and viscosity on the imbibition and energy intake rate of bumblebees

Nectar is an essential resource for bumblebees and many other flower-visiting insects. The main constituents of nectar are sugars, which vary in both composition and concentration between plant species. We assessed the influence of sugar concentration, sugar solution viscosity and sugar solution composition on the imbibition and energy intake rate of bumblebees, Bombus impatiens Cresson (Hymenoptera: Apidae). To do this, we measured their rate of solution intake for 49 different sugar solution treatments, which varied in both sugar composition and concentration. In general, the imbibition rates of bumblebees were found to increase with increasing sugar concentration, probably due to their preference for high sugar concentrations, up to a concentration of 27% (w/w), at which point solutions reached a threshold viscosity of approximately 1.5–1.6 mPa.s. Above this threshold, the increasing viscosity of the solutions physically inhibited the imbibition rates of bees, and imbibition rate began to decrease as the concentration increased. Nevertheless, bumblebee energy intake rate increased with increasing concentration up to about 42–56%. Although we found that sugar solution composition had an impact on both imbibition and energy intake rate, its effect was not as straightforward as that of sugar concentration and viscosity.     

Abundance,body size,and morphology of bumblebees in an area where an exotic species, <Emphasis Type="Italic">Bombus terrestris</Emphasis>, has colonized in Japan

An exotic bumblebee species, Bombus terrestris, has colonized in Japan and becomes dominant in some local communities. We examined the effects of land use and bumblebee abundance on the number and body size of bumblebees collected using window traps in a lowland area in the southern Ishikari district, Hokkaido. In 2004, we collected 922 bumblebees of six species using 70 traps at 17 sites. A statistical model fitted to the data demonstrated that dispersion from commercial B. terrestris colonies used in greenhouses positively affected the number of B. terrestris caught by each trap. This exotic species was abundant in sites where paddy fields were prevalent, but three native species, B. hypocrita, B. ardens, and B. diversus, were abundant in sites where farms and woodlands were widespread. The local abundance of B. terrestris was not associated negatively with the number and body size of native bumblebees. Thus, we did not find any competitive interactions between exotic and native bumblebees although habitat conditions seem to be common determinants of the bumblebee populations. A morphological analysis showed that B. terrestris had intermediate tongue length between B. hypocrita and B. ardens.     

Optimal foraging: Random movement by pollen collecting bumblebees

Summary Two bumblebee species, Bombus bifarius and B. flavifrons, forage randomly with respect to direction when gathering pollen on Potentilla gracilis. Bees avoid revisiting flowers by being able to differentiate recently visited from unvisited flowers. This recognition occurs while bees are flying over open flowers and appears to be a response to the amount of available pollen within flowers. Random foraging with respect to direction is the optimal strategy when the probability of flower revisitation is low. Bumblebees appear to be moving preferentially between nearest neighbors, again as predicted by foraging theory. This behavior causes the establishment of pollen patches in the P. gracilis population. Unlike other pollinators studied in similar situations, bumblebees on P. gracilis do not forage utilizing an area-restricted searching behavior. Because floral reward quality can be assessed at low cost by bees foraging on P. gracilis, their tendency to move to nearby flowers even after encountering a poor quality blossom apparently yields a higher rate of net energy intake than does area-restricted searching. The data indicate that bumblebees exhibit great plasticity in foraging behavior and that they are able to forage efficiently under a wide range of environmental conditions.     

Scaling of nectar foraging in orchid bees

Morphology influences the rate at which foraging bees visit nectar flowers, the quantity of nectar they must consume to fuel their activities, and, consequently, the profitability of flower species. Because feeding time is a major determinant of visitation rate, I used a biomechanical model to examine how energy intake rate (E) varies with sucrose concentration, body mass (M), and proboscis length in orchid bees (Apidae: Euglossini). Under geometric scaling, the optimal sugar concentration (Smax) should be largely independent of body size, and E proportional to M1.0. In a comparative study of 30 orchid bee species ranging from 50 to 800 mg, Smax fell between 35% and 40% w/w, but E proportional to M0.54, significantly less than model predictions. Proboscis length and radius scale geometrically with body mass, but proboscis length exhibits substantial size-independent variation, particularly in small bees. One cost of a long proboscis is a reduction in both E and Smax in accordance with the scaling model. This finding highlights a difference between the lapping mechanism used by bumblebees and the suction mechanism used by orchid bees. A field study confirms that orchid bees harvest nectars with between 34% and 42% sucrose, independent of body size.     

Nectar uptake rates and optimal nectar concentrations of two butterfly species

Summary The relationship between sucrose concentration of nectar and volume uptake rate by the butterflies Agraulis vanillae (Nymphalidae) and Phoebis sennae (Pieridae) was examined. Recent theoretical models simulating feeding energetics of nectarivores have assumed that this volume uptake rate is produced by a constant but undetermined pressure drop (the difference between pressure at the proximal and distal ends of the feeding channel) at all nectar concentrations. These models predict that nectar of 20–25% sucrose maximizes the rate of energy intake and should thus be preferred by nectarivores. Data collected for Agraulis and Phoebis falsify this pressure drop assumption; both species produce greater pressure drops with increasing nectar concentration. In addition, males of both species produce greater suction pressure and uptake rates than females. This results in greater rates of energy intake for males of both species. The volume uptake rates produced by each species differ from those predicted by the models. This produces a maximal rate of energy intake at 35–40% sucrose rather than 20–25%. The empirically determined relationship between energy intake rate and nectar concentration esembles that predicted for discontinuous nectar feeders such as hummingbirds more closely than the relationship predicted for continuous suction feeders, suggesting that other basic assumptions about the feeding mechanism of butterflies should be critically examined.     

Optimal foraging in bumblebees: Hunting by expectation

The foraging behaviour literature contains three hypotheses concerned with hunting by expectation. These suggest possible rules animals use to decide when to leave particular feeding sites and search in other places for food. Predictions of the three hypotheses were tested experimentally by varying the quality of plants (amount and distribution of nectar) encountered by bumblebees (Bombus appositus). Results support only a rate expectation hypothesis. Bees left multiflowered plants when the amount of nectar found in the first flower was below a threshold volume. Bees stayed on plants if they received greater than the threshold volume. This threshold nectar volume is close to the amount predicted if a bee forages to maximize its rate of net energy intake.     

Optimal foraging in bumblebees and coevolution with their plants

Summary The aims of this paper were to consider the coevolution between bumblebee movement patterns within plants and various properties of the plants such as the spatial distribution of their flowers, and to determine the extent to which the bumblebees and the plants can be considered to be maximally adaptive or optimal. Attention was restricted to plants which have flowers arranged on vertical inflorescences and to the bumblebees which visit these plants.It was found that the bumblebees tend to commence foraging at the bottom of each infloresence, that they tend to move from one flower to the closest vertically higher flower, that they miss flowers as they move upwards and that they tend to leave each inflorescence before reaching the top. It was also found for the four common plant species considered that nectar abundance per flower decreases with flower height on an inflorescence, that the flowers with receptive stigmas are restricted to the bottoms of the inflorescences while the flowers shedding pollen occur above them, and that the flowers are arranged approximately in spirals on the inflorescences.The pattern of movements of the bumblebees and the various properties of the plants appear to represent coevolved adaptations. Furthermore the bumblebees' movement patterns appear to be optimal in the sense that they result in the maximum net rate of energy gain to the bumblebees. Further studies are necessary, however, to determine whether or not the plants can be considered to be optimal.An exception to the above scheme is provided by a plant which is quite uncommon in the study area. This plant also has flowers on vertical inflorescences and appears to be pollinated by bumblebees. However, while the pattern of movements of the bumblebees on this plant species are extremely similar to those on the four common species, this plant species exhibits quite different properties from the other four. Two possible explanations for this exception are presented.     

On the mechanics and energetics of nectar feeding in butterflies.

A mechanistic model describing the mechanics and energetics of nectar-feeding in butterflies is developed. The butterflies Collas eurytheme and Danaus plexippus are used to illustrate the model. Simulation results indicate that there are mechanical limitations upon the range of nectar sugar concentrations and nectar extraction times available to butterflies. There is a unique optimum for net rate of energy gain at 20–25% nectar sugar concentration which is independent of the metabolic rate and of proboscis shape and size over the ranges found in butterflies. The optimal nectar extraction rate depends upon the size and shape of the proboscis. These results are discussed in relation to the design of nectar feeding structures, optimal foraging strategy, and the evolution of insect pollination.     

Why hummingbirds have such large crops

Summary Male Anna's Hummingbirds (Calypte anna) defend territories that contain a predictable food source, floral nectar. For such a hummingbird, the meal size that maximizes long-term net energy intake is less than the maximal crop volume. Smaller meals must be consumed more frequently, but larger meals increase body mass and therefore flight cost. Individuals without territories or with inadequate territories do not have easy access to nectar and intrude on territories owned by otherC. anna, where they may be chased at nay time. It was predicted that these intruders should minimize the number of potentially risky intrusions necessary for maintenance by ingesting as much nectar as possible whenever they manage to feed without being chased (usually when owners are temporarily absent). Therefore, relative to uninterrupted feeding by owners, uninterrupted intruders should feed longer and take larger meals. Field observations supported these predictions. Intruders apparently filled their crops in all seasons, whereas owners ingested smaller amounts (0.21–0.22 ml) and fed for lengths of time consistent with the prediction of an optimization model (0.21 ml). Thus, owners may energetically optimize meal size whereas intruders fill their crops whenever they are not chased. Under most conditions, hummingbirds only fill their crops one-tenth to one-third full, leading to the question why hummingbirds have such large crops. This study demonstrates that a large crop volume may be of survival value when an individual lacks a territory or has inadequate access to resources and must poach on others' territories.     

Bumblebee death associated with Tilia x europaea L

For more than six decades, bumblebee death, which mainly occurs in August, has been assumed to be associated with intake of presumed toxic nectar from linden trees (Tilia spp.), a hypothesis which has been sustained by observations of a significant number of dead bumblebees under these trees during their flowering season. Several theories exist in current literature to account for these observations. The nectar has been assumed to contain compound(s) toxic to the bumblebees including the monosaccharide mannose, which cannot be metabolized by bumblebees. The presence of toxic compounds such as the alkaloid nicotine or pesticides of anthropogenic origin has also been indicated. However, none of the above suggested compounds have hitherto been properly characterized from the nectar. In the current paper we report on characterization of the composition of nectar of linden trees, under which a significant number of dead bumblebees were observed. The structure determinations were performed by selective 1D TOCSY NMR and extensive applications of 2D NMR spectroscopy. The nectar of the linden flowers was readily available in significant amounts during the entire period when dead bumblebees were observed under these trees. The nectar only contained non-toxic sugars such as α-glucopyranose, β-glucopyranose, sucrose, fructose and minor amounts of xylose. The nectar did not contain mannose, nor alkaloids or pesticides. Initial toxicity studies using brine shrimp lethality assay showed that the nectar did not exhibit any toxic effects even at concentrations higher than 1 mg/ml dry weight, providing disproving evidence against the assumption of the nectar's toxic character.     

Optimal Foraging and Predator–Prey Dynamics

A system consisting of a population of predators and two types of prey is considered. The dynamics of the system is described by differential equations with controls. The controls model how predators forage on each of the two types of prey. The choice of these controls is based on the standard assumption in the theory of optimal foraging which requires that each predator maximizes the net rate of energy intake during foraging. Since this choice depends on the densities of populations involved, this allows us to link the optimal behavior of an individual with the dynamics of the whole system. Simple qualitative analysis and some simulations show the qualitative behavior of such a system. The effect of the optimal diet choice on the stability of the system is discussed.     

Size variation and foraging rate in bumblebees (Bombus terrestris)

Summary: Size polymorphism is an important life history trait in bumblebees with strong impact on individual behavior and colony organization. Within a colony larger workers tend to serve as foragers, while smaller workers fulfill in-hive tasks. It is often assumed that size-dependent division of labor relates to differences in task performance. In this study we examined size-dependent interindividual variability in foraging, i.e. whether foraging behavior and foraging capability of bumblebee workers are affected by their size. We observed two freely foraging Bombus terrestris colonies and measured i) trip number, ii) trip time, iii) proportion of nectar trips, and iv) nectar foraging rate of different sized foragers. In all observation periods large foragers exhibited a significantly higher foraging rate than small foragers. None of the other three foraging parameters was affected by worker size. Thus, large foragers contributed disproportionately more to the current nectar influx of their colony. We provide a detailed discussion of the possible proximate mechanisms underlying the differences in foraging rate.     

The costs of carnivory

Mammalian carnivores fall into two broad dietary groups: smaller carnivores (<20 kg) that feed on very small prey (invertebrates and small vertebrates) and larger carnivores (>20 kg) that specialize in feeding on large vertebrates. We develop a model that predicts the mass-related energy budgets and limits of carnivore size within these groups. We show that the transition from small to large prey can be predicted by the maximization of net energy gain; larger carnivores achieve a higher net gain rate by concentrating on large prey. However, because it requires more energy to pursue and subdue large prey, this leads to a 2-fold step increase in energy expenditure, as well as increased intake. Across all species, energy expenditure and intake both follow a three-fourths scaling with body mass. However, when each dietary group is considered individually they both display a shallower scaling. This suggests that carnivores at the upper limits of each group are constrained by intake and adopt energy conserving strategies to counter this. Given predictions of expenditure and estimates of intake, we predict a maximum carnivore mass of approximately a ton, consistent with the largest extinct species. Our approach provides a framework for understanding carnivore energetics, size, and extinction dynamics.     

Mechanical determinants of nectar-feeding energetics in butterflies: muscle mechanics,feeding geometry,and functional equivalence

Summary We develop a mechanistic model for nectar feeding in butterflies that integrates the two basic components of the feeding process: the fluid dynamics of nectar flow through the food canal and the contractile mechanics of the muscular, cibarial pump. We use the model to predict the relation between rate of energy intake during feeding and nectar concentration. We then identify nectar concentations that maximize energy intake rates (the optimal concentrations). We illustrate the model using measurements of the food canal and cibarium of Pieris butterflies. The model predicts an overall optimal range of nectar concentration of 31–39% sucrose for butterflies, which is in agreement with previously reported laboratory values. The model also predicts an interaction among the geometries of the food canal, the cibarial cavity, and the cibarial muscles, that allows us to identify the combinations of food canal, cibarium, and muscle dimensions that yield the highest rates of energy intake. Nectar-feeding is functionally equivalent in butterflies and hummingbirds: two physically different feeding mechanisms can yield identical energy intake rates. This equivalence results from a mathematical and physical similarity between quasi-steady-state fluid flow in hummingbrid tongues and the force-velocity characteristics of contracting cibarial muscle in butterflies.