Trade-off between travel distance and prioritization of high-reward sites in traplining bumblebees

1.Animals exploiting renewable resource patches are faced with complex multi-location routing problems. In many species, individuals visit foraging patches in predictable sequences called traplines. However, whether and how they optimize their routes remains poorly understood.2.In this study, we demonstrate that traplining bumblebees (Bombus terrestris) make a trade-off between minimizing travel distance and prioritizing the most rewarding feeding locations.3.Individual bees trained to forage on five artificial flowers of equal reward value selected the shortest possible route as a trapline. After introducing a single highly rewarding flower to the array, they re-adjusted their routes visiting the most rewarding flower first provided the departure distance from the shortest possible route remained small (18%). When routes optimizing the initial rate of reward intake were much longer (42%), bees prioritized short travel distances.4.Under natural conditions, in which individual flowers vary in nectar productivity and replenish continuously, it might pay bees to prioritize highly rewarding locations, both to minimize the overall number of flowers to visit and to beat competitors.5.We discuss how combined memories of location and quality of resource patches could allow bees and other traplining animals to optimize their routing decisions in heterogeneous environments.     

Travel optimization by foraging bumblebees through readjustments of traplines after discovery of new feeding locations

Animals collecting resources that replenish over time often visit patches in predictable sequences called traplines. Despite the widespread nature of this strategy, we still know little about how spatial memory develops and guides individuals toward suitable routes. Here, we investigate whether flower visitation sequences by bumblebees Bombus terrestris simply reflect the order in which flowers were discovered or whether they result from more complex navigational strategies enabling bees to optimize their foraging routes. We analyzed bee flight movements in an array of four artificial flowers maximizing interfloral distances. Starting from a single patch, we sequentially added three new patches so that if bees visited them in the order in which they originally encountered flowers, they would follow a long (suboptimal) route. Bees' tendency to visit patches in their discovery order decreased with experience. Instead, they optimized their flight distances by rearranging flower visitation sequences. This resulted in the development of a primary route (trapline) and two or three less frequently used secondary routes. Bees consistently used these routes after overnight breaks while occasionally exploring novel possibilities. We discuss how maintaining some level of route flexibility could allow traplining animals to cope with dynamic routing problems, analogous to the well-known traveling salesman problem.     

Traplining in bumblebees (Bombus impatiens): a foraging strategy’s ontogeny and the importance of spatial reference memory in short-range foraging

To test the relative importance of long-term and working spatial memories in short-range foraging in bumblebees, we compared the performance of two groups of bees. One group foraged in a stable array of six flowers for 40 foraging bouts, thereby enabling it to establish a long-term memory of the array, and adjust its spatial movements accordingly. The other group was faced with an array that changed between (but not within) foraging bouts, and thus had only access to a working memory of the flowers that had been visited. Bees in the stable array started out sampling a variety of routes, but their tendency to visit flowers in a repeatable, stable order (“traplining”) increased drastically with experience. These bees used shorter routes and converged on four popular paths. However, these routes were mainly formed through linking pairs of flowers by near-neighbour movements, rather than attempting to minimize overall travel distance. Individuals had variations to a primary sequence, where some bees used a major sequence most often, followed by a minor less used route, and others used two different routes with equal frequency. Even though bees foraging in the spatially randomized array had access to both spatial working memory and scent marks, this manipulation greatly disrupted foraging efficiency, mainly via an increase in revisitation to previously emptied flowers and substantially longer search times. Hence, a stable reference frame greatly improves foraging even for bees in relatively small arrays of flowers.     

Radar Tracking and Motion-Sensitive Cameras on Flowers Reveal the Development of Pollinator Multi-Destination Routes over Large Spatial Scales

Central place foragers, such as pollinating bees, typically develop circuits (traplines) to visit multiple foraging sites in a manner that minimizes overall travel distance. Despite being taxonomically widespread, these routing behaviours remain poorly understood due to the difficulty of tracking the foraging history of animals in the wild. Here we examine how bumblebees (Bombus terrestris) develop and optimise traplines over large spatial scales by setting up an array of five artificial flowers arranged in a regular pentagon (50 m side length) and fitted with motion-sensitive video cameras to determine the sequence of visitation. Stable traplines that linked together all the flowers in an optimal sequence were typically established after a bee made 26 foraging bouts, during which time only about 20 of the 120 possible routes were tried. Radar tracking of selected flights revealed a dramatic decrease by 80% (ca. 1500 m) of the total travel distance between the first and the last foraging bout. When a flower was removed and replaced by a more distant one, bees engaged in localised search flights, a strategy that can facilitate the discovery of a new flower and its integration into a novel optimal trapline. Based on these observations, we developed and tested an iterative improvement heuristic to capture how bees could learn and refine their routes each time a shorter route is found. Our findings suggest that complex dynamic routing problems can be solved by small-brained animals using simple learning heuristics, without the need for a cognitive map.     

Invasive ant (<Emphasis Type="Italic">Anoplolepis gracilipes</Emphasis>) disrupts pollination in pumpkin

Yellow crazy ant (Anoplolepis gracilipes (F. Smith); “YCA”) is known for its aggressive predatory ability and ability to exert exploitation competition on both native and other invasive ants via floral nectar. We argue that YCA invasion can exert both interference and exploitation competition on legitimate pollinators. In pumpkin fields (Cucurbita maxima L.) of south India, YCA infested the flowers, particularly the pistillate flowers, for nectar foraging. Pumpkin is a honey bee-mediated cross-pollinated monoecious plant that produces disproportionately very few pistillate flowers. We hypothesize that YCA presence in the flowers can affect the visitation rate and foraging time of honey bees in the flowers, the fruit set in pumpkins, and can exert predatory pressure on the honey bees if the bees linger in ant-colonized flowers. Both YCA and honey bees preferred to forage on the limited pistillate flowers in the plants. After colonizing the flowers, YCA did not retreat for hours, even upon disturbance by competitors, such as honey bees. Both the visitation frequency and the foraging time of honey bees were drastically reduced in ant-colonized flowers, and none of the ant-colonized flowers developed into fruits, suggesting that the YCA exert both an ecological and evolutionary pressure on pumpkin. The ants preyed upon about 17% of the honey bees that lingered in ant-colonized flowers, and the time the bees spent foraging predicted the fate of the bees. Exploitation competition exerted by the YCA on pumpkin may have far-reaching consequences for the pollination and productivity of this cash crop.     

Trapline foraging by bumblebees: I. Persistence of flight-path geometry

By setting out arrays of potted plants of Penstemon strictus,I tested whether freely foraging bumblebee (Bombus spp. ) workerswould establish regular foraging routes that reflected the geometryof the array. They did, passing through an asymmetrical arrayin a pattern that minimized interplant flight distances. Afterthe array was changed to a symmetrical pattern, however, theexperienced bees continued to show their previous asymmetricalflight patterns. New bees without experience on the asymmetricalarray showed no asymmetry on the symmetrical array. I term thispersistence of flight-path geometry "trapline holdover, " anddiscuss its implications for the study of animals' learningand foraging behavior.     

Bees do not use nearest-neighbour rules for optimization of multi-location routes

Animals collecting patchily distributed resources are faced with complex multi-location routing problems. Rather than comparing all possible routes, they often find reasonably short solutions by simply moving to the nearest unvisited resources when foraging. Here, we report the travel optimization performance of bumble-bees (Bombus terrestris) foraging in a flight cage containing six artificial flowers arranged such that movements between nearest-neighbour locations would lead to a long suboptimal route. After extensive training (80 foraging bouts and at least 640 flower visits), bees reduced their flight distances and prioritized shortest possible routes, while almost never following nearest-neighbour solutions. We discuss possible strategies used during the establishment of stable multi-location routes (or traplines), and how these could allow bees and other animals to solve complex routing problems through experience, without necessarily requiring a sophisticated cognitive representation of space.     

Hummingbird avoidance of nectar-robbed plants: spatial location or visual cues

Broad-tailed and rufous hummingbirds avoid plants and flowers that have recently been visited by nectar-robbing bees. However, the cues the hummingbirds use to make such choices are not known. To determine the proximate cues hummingbirds use to avoid visiting nectar-robbed plants, I conducted multiple field experiments and one aviary study using the nectar-robbed, hummingbird-pollinated plant Ipomopsis aggregata . In the first field experiment, free-flying hummingbirds were presented with plants in which I manipulated nectar volume and the presence of nectar-robber holes. Hummingbirds visited significantly more plants with nectar and probed more available flowers on those plants, regardless of the presence of nectar-robber holes. Thus, I hypothesized that hummingbirds may avoid robbed plants based on their spatial memory of unrewarding plants and/or visual cues that nectar absence provides. In an aviary study, I removed spatial cues by re-randomizing the position of plants after each hummingbird-foraging bout, but hummingbirds still selected plants with nectar. Nectar may provide a visual cue in I. aggregata flowers because corollas are translucent, and nectar is visible through the side of the corolla. To determine if hummingbirds use this visual cue to avoid plants with no nectar, I masked corolla translucence in a field study by painting flowers with acrylic paint. Hummingbirds still visited significantly more plants with nectar and probed more flowers on those plants, whether or not the corollas were painted. These results suggest that hummingbirds use nectar as a proximate cue to locate and avoid non-rewarding, nectar-robbed plants, even in the absence of spatial cues and simple visual cues.     

Effects of recent experience on foraging decisions by bumble bees

The temporal and spatial scales employed by foraging bees in sampling their environment and making foraging decisions should depend both on the limits of bumble bee memory and on the spatial and temporal pattern of rewards in the habitat. We analyzed data from previous experiments to determine how recent foraging experience by bumble bees affects their flight distances to subsequent flowers. A single visit to a flower as sufficient to affect the flight distance to the next flower. However, longer sequences of two or three visits had an additional effect on the subsequent flight distance of individual foragers. This suggests that bumble bees can integrate information from at least three flowers for making a subsequent foraging decision. The existence of memory for floral characteristics at least at this scale may have significance for floral selection in natural environments.     

Departure rules used by bees foraging for nectar: A field test

Summary Departure rules used by solitary long-tongued bees (Anthophora spp. andEucera spp.) collecting nectar from flowers ofAnchusa strigosa (Boraginaceae) were studied. The amount of nectar a bee receives from an individual flower was estimated by measuring the time elapsed since the previous bee visit to that flower. Measurements of nectar accumulation in experimentally emptied flowers indicated that this time interval is an accurate predictor of nectar volumes in flowers. We found that nectar rewards influence the probability of departure from individual plants, as well as distances of movements within plants. The probability of departure from individual plants was negatively related to the amount of reward received at the two lastvisited flowers. This result indicates that the bees used a probabllistic departure rule, rather than a simple threshold departure rule, and that rewards from both the current and the previously visited flower were important in determining departure points. Distances of inter-flower movements within plants were negatively related to the amount of reward received at the current flower. The overall results suggest that the pollinators ofA. strigosa make two types of departure decisions-departures from the whole plant and departures from the neighbourhood of individual flowers-and that they use different departure rules for each scale. Factors influencing the decision-making processes of the observed foraging behaviour are discussed.     

Monitoring Flower Visitation Networks and Interactions between Pairs of Bumble Bees in a Large Outdoor Flight Cage

Pollinators, such as bees, often develop multi-location routes (traplines) to exploit subsets of flower patches within larger plant populations. How individuals establish such foraging areas in the presence of other foragers is poorly explored. Here we investigated the foraging patterns of pairs of bumble bees (Bombus terrestris) released sequentially into an 880m² outdoor flight cage containing 10 feeding stations (artificial flowers). Using motion-sensitive video cameras mounted on flowers, we mapped the flower visitation networks of both foragers, quantified their interactions and compared their foraging success over an entire day. Overall, bees that were released first (residents) travelled 37% faster and collected 77% more nectar, thereby reaching a net energy intake rate 64% higher than bees released second (newcomers). However, this prior-experience advantage decreased as newcomers became familiar with the spatial configuration of the flower array. When both bees visited the same flower simultaneously, the most frequent outcome was for the resident to evict the newcomer. On the rare occasions when newcomers evicted residents, the two bees increased their frequency of return visits to that flower. These competitive interactions led to a significant (if only partial) spatial overlap between the foraging patterns of pairs of bees. While newcomers may initially use social cues (such as olfactory footprints) to exploit flowers used by residents, either because such cues indicate higher rewards and/or safety from predation, residents may attempt to preserve their monopoly over familiar resources through exploitation and interference. We discuss how these interactions may favour spatial partitioning, thereby maximising the foraging efficiency of individuals and colonies.     

Flower choice by honey bees (Apis mellifera L.): sex-phase of flowers and preferences among nectar and pollen foragers

Bees foraging for nectar should choose different inflorescences from those foraging for both pollen and nectar, if inflorescences consist of differing proportions of male and female flowers, particularly if the sex phases of the flowers differ in nectar content as well as the occurrence of pollen. This study tested this prediction using worker honey bees (Apis mellifera L.) foraging on inflorescences of Lavandula stoechas. Female flowers contained about twice the volume of nectar of male flowers. As one would predict, bees foraging for nectar only chose inflorescences with disproportionately more female flowers: time spent on the inflorescence was correlated with the number of female flowers, but not with the number of male flowers. Inflorescence size was inversely correlated with the number of female flowers, and could be used as a morphological cue by these bees. Also as predicted, workers foraging for both pollen and nectar chose inflorescences with relatively greater numbers of both male and female flowers: time spent on these inflorescences was correlated with the number of male flowers, but not with the number of females flowers. A morphological cue inversely associated with such inflorescences is the size of the bract display. Choice of flowers within inflorescences was also influenced predictably, but preferences appeared to be based upon corolla size rather than directly on sex phase.     

Pollinator genetics and pollination: do honey bee colonies selected for pollen‐hoarding field better pollinators of cranberry Vaccinium macrocarpon?

1. Genetic polymorphisms of flowering plants can influence pollinator foraging but it is not known whether heritable foraging polymorphisms of pollinators influence their pollination efficacies. Honey bees Apis mellifera L. visit cranberry flowers for nectar but rarely for pollen when alternative preferred flowers grow nearby. 2. Cranberry flowers visited once by pollen‐foraging honey bees received four‐fold more stigmatic pollen than flowers visited by mere nectar‐foragers (excluding nectar thieves). Manual greenhouse pollinations with fixed numbers of pollen tetrads (0, 2, 4, 8, 16, 32) achieved maximal fruit set with just eight pollen tetrads. Pollen‐foraging honey bees yielded a calculated 63% more berries than equal numbers of non‐thieving nectar‐foragers, even though both classes of forager made stigmatic contact. 3. Colonies headed by queens of a pollen‐hoarding genotype fielded significantly more pollen‐foraging trips than standard commercial genotypes, as did hives fitted with permanently engaged pollen traps or colonies containing more larvae. Pollen‐hoarding colonies together brought back twice as many cranberry pollen loads as control colonies, which was marginally significant despite marked daily variation in the proportion of collected pollen that was cranberry. 4. Caloric supplementation of matched, paired colonies failed to enhance pollen foraging despite the meagre nectar yields of individual cranberry flowers. 5. Heritable behavioural polymorphisms of the honey bee, such as pollen‐hoarding, can enhance fruit and seed set by a floral host (e.g. cranberry), but only if more preferred pollen hosts are absent or rare. Otherwise, honey bees' broad polylecty, flight range, and daily idiosyncrasies in floral fidelity will obscure specific pollen‐foraging differences at a given floral host, even among paired colonies in a seemingly uniform agricultural setting.     

A Simple Iterative Model Accurately Captures Complex Trapline Formation by Bumblebees Across Spatial Scales and Flower Arrangements

Pollinating bees develop foraging circuits (traplines) to visit multiple flowers in a manner that minimizes overall travel distance, a task analogous to the travelling salesman problem. We report on an in-depth exploration of an iterative improvement heuristic model of bumblebee traplining previously found to accurately replicate the establishment of stable routes by bees between flowers distributed over several hectares. The critical test for a model is its predictive power for empirical data for which the model has not been specifically developed, and here the model is shown to be consistent with observations from different research groups made at several spatial scales and using multiple configurations of flowers. We refine the model to account for the spatial search strategy of bees exploring their environment, and test several previously unexplored predictions. We find that the model predicts accurately 1) the increasing propensity of bees to optimize their foraging routes with increasing spatial scale; 2) that bees cannot establish stable optimal traplines for all spatial configurations of rewarding flowers; 3) the observed trade-off between travel distance and prioritization of high-reward sites (with a slight modification of the model); 4) the temporal pattern with which bees acquire approximate solutions to travelling salesman-like problems over several dozen foraging bouts; 5) the instability of visitation schedules in some spatial configurations of flowers; 6) the observation that in some flower arrays, bees'' visitation schedules are highly individually different; 7) the searching behaviour that leads to efficient location of flowers and routes between them. Our model constitutes a robust theoretical platform to generate novel hypotheses and refine our understanding about how small-brained insects develop a representation of space and use it to navigate in complex and dynamic environments.     

Habitat structure and animal movement: the behaviour of bumble bees in uniform and random spatial resource distributions

Foraging organisms (like bumble bees) move between resource points (like flowers) whose natural distributions vary enormously: from hyperdispersed to random to clumped. These differences in habitat structure may significantly influence the fitness of both plant and pollinator. To examine the effect of habitat structure on pollinator movement and fitness, we observed captive worker bumble bees collecting nectar from artificial flowers containing equal volumes of reward and arranged in two spatial configurations: a hexagonal array with constant distances between flowers (“constant”), and an “exploded hexagonal” array, with variable distances between flowers (“variable”). The mean nearest-neighbour distance was the same in both arrays, as was the general hexagonal appearance. The experiment therefore compares how resource dispersion, independent of nearest-neighbour distance, influences bee behaviour. Bees in the variable array showed decreased directionality, higher revisitation frequencies, and greater inter-flower flight distances than shown in the constant array. As a consequence, bees in the variable array had a 19% lower gross rate of nectar collection. Our results suggest that wild-foraging bees should prefer regularly spaced flowers (when all else, including mean nearest-neighbour distance, is equal), and that plants can decrease self-pollination by regular spacing between flowers, inflorescences, or individuals. Received: 16 January 1996 / Accepted: 30 June 1997     

A test of spatial memory and movement patterns of bumblebees at multiple spatial and temporal scales

Naive bumblebee foragers appear to use movement rules at smallspatial and temporal scales, but it is not clear whether theserules determine movement patterns as the scales increase. Onestrategy for efficient foraging used by bumblebees is near-farsearch, involving short flights when in good patches of flowersand longer flights when in poor patches. Bumblebees also demonstratethe use of a spatial memory strategy by returning repeatedlyto patches of flowers, and even following the same route betweenflowers, over periods of days. We attempted to determine atwhat spatial scales bumblebees use spatial memory while foragingwithin a patch and after how many flower visits spatial memoryoutweighs near-far search. Bumblebees in the laboratory foragedon a 4 x 4 array of artificial flowers with distances rangingfrom 10 to 80 cm between flowers in two simple spatial patterns.The proportion of visits to flowers containing a sucrose rewardwas monitored for either 100 or 400 flower visits in two separateexperiments, after which the locations of the rewarding andnonrewarding flowers were interchanged, producing a mirror image.A drop in accuracy after the mirror image switch would indicatethat the bees had memorized the location of rewarding flowers.Mirror image tests, and comparisons to a simulation model ofnear-far search based on actual flight distances, indicate thatnaive bumblebees used near-far search on flowers 10 cm apartbut increasingly used spatial memory as experience and spatialseparation increased. Bumblebees thus have multiple tacticsavailable to forage efficiently in different environments.     

Foraging by Male and Female Solitary Bees with Implications for Pollination

Both male and female solitary bees visit flowers for rewards. Sex related differences in foraging efficiency may also affect their probability to act as pollinators. In some major genera of solitary bees, males can be identified from a distance enabling a comparative foraging-behavior study. We have simultaneously examined nectar foraging of males and females of three bee species on five plant species in northern Israel. Males and females harvested equal nectar amounts but males spent less time in each flower increasing their foraging efficiency at this scale. The overall average visit frequencies of females and males was 27.2 and 21.6 visits per flower per minute respectively. Females flew shorter distances increasing their visit frequency, relative foraging efficiency and their probability to pollinate. The proportion of conspecific pollen was higher on females, indicating higher floral constancy and pollination probability. The longer flights of males increase their probability to cross-pollinate. Our results indicate that female solitary bees are more efficient foragers; females seem also to be more efficient pollinators but males contribute more to long-distance pollen flow.     

Behavioural differences between male and female carpenter bees in nectar robbing and its effect on reproductive success in Glechoma longituba (Lamiaceae)

Male and female nectar robbers may show significantly different behaviour on host plants and thus have different impacts on reproductive fitness of the plants. A 4-year study in natural populations of Glechoma longituba has shown that male carpenter bees (Xylocopa sinensis) are responsible for most of the nectar robbing from these flowers, while female bees account for little nectar robbing, demonstrating distinct behavioural differentiation between male and female bees in visiting flowers. The smaller male bee spends less time visiting a single flower than the larger female bee, consequently, the male bee is capable of visiting more flowers per unit time and has a higher foraging efficiency. Moreover, the robbing behaviour of female carpenter bees is more destructive and affects flower structures (ovules and nectaries) and floral life-span more than that of the male bee. According to the energy trade-off hypothesis, the net energy gain for male bees during nectar robbing greatly surpasses energy payout (17.72 versus 2.43 J), while the female bee net energy gain is barely adequate to meet energy payout per unit time (3.78 versus 2.39 J). The differences in net energy gain for male and female bees per unit time in nectar robbing are the likely cause of observed behavioural differences between the sexes. The differences in food resource preference between male and female bees constitute an optimal resource allocation pattern that enables the visitors to utilise floral resources more efficiently.     

Effects of nectar robbing on nectar dynamics and bumblebee foraging strategies in Linaria vulgaris (Scrophulariaceae)

Differences in morphology among bumblebee species sharing a nectar resource may lead to variation in foraging behaviour and efficiency. Less efficient bumblebees might opportunistically switch foraging strategies from legitimate visitation to secondary robbing when hole-biting primary robbers are present. We observed various aspects of pollination and nectar robbing ecology of Linaria vulgaris in the Colorado Rocky Mountains, with emphasis on the role of bumblebee proboscis length. Bees can extract nectar from a nectar spur legitimately, by entering the front of the flower, or illegitimately, by biting or reusing holes in the spur. Although L. vulgaris flowers are apparently adapted for pollination by long-tongued bees, short-tongued bees visited them legitimately for trace amounts of nectar but switched to secondary robbing in the presence of primary robbers. Longer-tongued bees removed more nectar in less time than did shorter-tongued bees, and were less likely to switch to secondary robbing even when ∼100% of flowers had been pierced. As the proportion of robbed flowers in the population increased, the relative number of legitimate visits decreased while the relative number of robbing visits increased. Robbing decreased nectar standing crop and increased the proportion of empty flowers per inflorescence. Despite these potentially detrimental effects of robbers, differences in inflorescence use among robbers and pollinators, and the placement of holes made by primary robbers, may mitigate negative effects of nectar robbing in L. vulgaris . We discuss some of the reasons that L. vulgaris pollination ecology and growth form might temper the potentially negative effect of nectar robbing.     

Trapline foraging by pollinators: its ontogeny, economics and possible consequences for plants

Background

Trapline foraging (repeated sequential visits to a series of feeding locations) has been often observed in pollinators collecting nectar or pollen from flowers. Although field studies on bumble-bees and hummingbirds have clarified fundamental aspects of this behaviour, trapline foraging still poses several difficult questions from the perspectives of both animals and plants. These questions include whether and how traplining improves foraging performance, how animals develop traplines with accumulating foraging experience, and how traplining affects pollen flow or plant reproduction.

Scope

First, we review our previous work performed by using computer simulations and indoor flight-cage experiments with bumble-bees foraging from arrays of automated feeders. Our findings include the following: (1) traplining benefits foragers that are competing for resources that replenish in a decelerating way, (2) traplining is a learned behaviour that develops over a period of hours and (3) the establishment of traplines could be hampered by spatial configuration of plants such as zigzags. Second, using a simulation model linking pollinator movement and pollen transfer, we consider how service by pollinators with different foraging patterns (searchers or trapliners) would affect pollen flow. Traplining increases mating distance and mate diversity, and reduces ‘iterogamy’ (self-pollination caused by return visits) at the population level. Furthermore, increased visitation rates can have opposite effects on the reproductive success of a plant, depending on whether the visitors are traplining or searching. Finally, we discuss possible consequences of traplining for plants in the light of new experimental work and modelling.

Conclusions

We suggest that trapline foraging by pollinators increases variation among plant populations in genetic diversity, inbreeding depression and contributions of floral traits to plant fitness, which should in turn affect the rates and directions of floral evolution. More theoretical and empirical studies are needed to clarify possible outcomes of such a neglected side of pollination.Key words: Artificial flower, Bombus, competition, floral evolution, foraging experience, iterogamy, model, pollen flow, pollinator movement, renewing resource, spatial memory, trapline foraging