Andreas Gumbert | Heinrich Heine University Düsseldorf (original) (raw)

Papers by Andreas Gumbert

Research paper thumbnail of Floral colour diversity in plant communities, bee colour space and a null model

Proceedings of the Royal Society B: Biological Sciences, 1999

Evolutionary biologists have long hypothesized that the diversity of £ower colours we see is in p... more Evolutionary biologists have long hypothesized that the diversity of £ower colours we see is in part a strategy to promote memorization by pollinators, pollinator constancy, and therefore, a directed and e¤cient pollen transfer between plants. However, this hypothesis has never been tested against a biologically realistic null model, nor were colours assessed in the way pollinators see them. Our intent here is to ¢ll these gaps. Throughout one year, we sampled £oral species compositions at ¢ve ecologically distinct sites near Berlin, Germany. Bee-subjective colours were quanti¢ed for all 168 species. A model of colour vision was used to predict how similar the colours of sympatric and simultaneously blooming £owers were for bees. We then compared £ower colour di¡erences in the real habitats with those of random plant communities. We did not ¢nd pronounced deviations from chance when we considered common plants. When we examined rare plants, however, we found signi¢cant divergence in two of the ¢ve plant communities. At one site, similarly coloured species were found to be more frequent than expected, and at the other two locations, £ower colours were indistinguishable from a random distribution. These results ¢t theoretical considerations that rare plants are under stronger selective pressure to secure pollination than common plants. Our study illustrates the power of linking such distinct biological traditions as community ecology and the neuroethology of bee vision.

Research paper thumbnail of A generalised mimicry system involving angiosperm flower colour, pollen and bumblebees’ innate colour preferences

Plant Systematics and Evolution, 2005

Ó Springer-Verlag 2005 colour patterns, and that these correspond to visually displayed pollen. T... more Ó Springer-Verlag 2005 colour patterns, and that these correspond to visually displayed pollen. These findings together suggest a prominent role of floral colour patterns in advertisement to and guidance of naive flower visitors.

Research paper thumbnail of Symmetry is in the eye of the ?beeholder?: innate preference for bilateral symmetry in flower-na�ve bumblebees

Naturwissenschaften, 2004

Bilateral symmetry has been considered as an indicator of phenotypic and genotypic quality suppor... more Bilateral symmetry has been considered as an indicator of phenotypic and genotypic quality supporting innate preferences for highly symmetric partners. Insect pollinators preferentially visit flowers of a particular symmetry type, thus leading to the suggestion that they have innate preferences for symmetrical flowers or flower models. Here we show that flower-naïve bumblebees (Bombus terrestris), with no experience of symmetric or asymmetric patterns and whose visual experience was accurately controlled, have innate preferences for bilateral symmetry. The presence of color cues did not influence the bees' original preference. Our results thus show that bilateral symmetry is innately preferred in the context of food search, a fact that supports the selection of symmetry in flower displays. Furthermore, such innate preferences indicate that the nervous system of naïve animals may be primed to respond to relevant sensory cues in the environment.

Research paper thumbnail of POLLINATORS' STRATEGIES IN FINDING FLOWERS

Israel Journal of Plant Sciences, 1997

Research paper thumbnail of FLOWERS THROUGH INSECT EYES

Israel Journal of Plant Sciences, 1997

Research paper thumbnail of Inflorescence Height Affects Visitation Behavior of Bees-A Case Study of an Aquatic Plant Community in Bolivia1

Biotropica, 1999

We studied the bee fauna visiting a plant community of 10 species of flowering aquatic plants in ... more We studied the bee fauna visiting a plant community of 10 species of flowering aquatic plants in an inundated savanna region in Bolivia. In total we observed 36 bee species in 17 genera at the flowers. Cluster analysis of the similarities among the plant species in terms of their visitor spectra showed a division into two groups: plants with inflorescence heights shorter than the grass height and plants with inflorescences projecting out of the surrounding vegetation. Larger bees of the genera Apis, Melipona, Bombus, and Xylocopa were observed only at flowers above the surrounding vegetation. Smaller, mainly solitary bees (e.g-, AugochLorcLa, An~yloxeLis) visited flowers in the dense vegetation near the water surface. Analyses of the pollen loads revealed that most individuals were highly flower constant. When bees carried different pollen types, it was generally pollen from flowers within a single stratum. We discuss specialization, flower constancy, competition, and different foraging strategies as possible reasons for stratum fidelity.

Research paper thumbnail of Colour similarity to rewarding model plants affects pollination in a food deceptive orchid, Orchis boryi

Biological Journal of the Linnean Society, 2001

... and field observations in other species, we expected that the reproductive success of this de... more ... and field observations in other species, we expected that the reproductive success of this deceptive species should be negatively correlated to its density and frequency (Sabat & Ackerman, 1996; Smithson & Macnair, 1997; Ferdy et al., 1998 ... Pollinia export [Yo] - 41.93 22.53 ...

Research paper thumbnail of The combined effect of color and odor on flower choice behavior of bumble bees in flower mimicry systems

Behavioral Ecology, 2001

Food-deceptive flowers are pollinated by animals that expect a reward but are cheated. Such plant... more Food-deceptive flowers are pollinated by animals that expect a reward but are cheated. Such plants profit from their similarity to rewarding plants and should develop signals that hinder discrimination. We use artificial rewarding model flowers and nonrewarding mimicking flowers that present similar visual cues. We test how additional scent cues change flower choice of the mimic by bumble bees (Bombus terrestris) in two situations: (1) both flower types are simultaneously present and can be compared by the pollinator, and (2) both flower types are encountered successively in the absence of each other. We find that in situation 1, discrimination learning is greater if scents are used as cues for identifying the mimic, whether the mimic has a different scent or if it is scentless while the model is scented. In situation 2, a generalization task, a scented mimic is avoided faster than a scentless one. Discrimination of the mimic is poorest if it has the same scent as the model, thus demonstrating a potential for scent mimicry, which has not yet been proved to exist among differently rewarding flowers. Thus, the best strategy for a mimic would be to have the same scent as the model, but this strategy may not be used due to evolutionary constraints. Alternatively, if there are several potential models, then having no scent would be a better strategy than mimicking just one of the models. In situation 1 flower discrimination by color cues is enhanced in the mere presence of scent, compared to unscented controls, even if the scent does not provide a distinguishable cue itself. The results indicate that the presence of scent may enhance color discrimination by improving attention towards visual cues and/or that combined color/odor cues may lead to better memory formation and retrieval.

Research paper thumbnail of Relationship of visual and olfactory signal parameters in a food-deceptive flower mimicry system

Behavioral Ecology, 2004

Pollinators such as bees are attracted to flowers by their visual display and their scent. Althou... more Pollinators such as bees are attracted to flowers by their visual display and their scent. Although most flowers reinforce visits by providing pollen and/or nectar, there are species-notably from the orchid family-that do not but do resemble rewarding species. These mimicry relationships provide ideal opportunities for investigating the evolution of floral signals and their impact on pollinator behavior. Here, we have reanalyzed a case of specialized food mimicry between the orchid Orchis israelitica and its model, the lily Bellevalia flexuosa. Based on current knowledge of insect sensory physiology, we were able to characterize both the visual and olfactory signals of model and mimic, as well as of two phylogenetically related orchids. By using a color vision model, we mapped each species' visual signals to the perceptual space of honeybees and found an apparent shift of the mimic's visual signals towards the model. We confirm that visual mimicry is present. We analyzed the flower odors by using gas chromatography/ mass spectroscopy. We related these signals to the perceptual space of the pollinators by testing the scent extracts physiologically, using in vivo brain imaging. We found no evidence of olfactory mimicry. The results indicate that evolutionary pressure acts on the visual, but not olfactory, traits of O. israelitica toward a higher similarity to its model. Apparently, odor mismatch does not prevent a bee from landing on a flower that has the expected visual display. The results therefore argue for the dominance of visual stimuli in short-distance flower choice. The orchid may still depend on long-distance olfactory attraction originating from neighboring model plants.

Research paper thumbnail of Foraging dynamics of bumble bees: correlates of movements within and between plant species

Behavioral Ecology, 1997

What rules determine whether bumble bee* continue exploiting plants of the species just visited o... more What rules determine whether bumble bee* continue exploiting plants of the species just visited or switch to another species? To tackle this question, we recorded handling times and flight times from bees foraging in a natural meadow containing five plant species. Inter-and ultra-specific plant distances were quantified. The bee-subjective colors of the five species were determined; two of these species had similar colors and structures, while three species were distinct from all others. The following rules were identified: (1) The decision to switch species was correlated with previous flower handling time, which we assume is a function of the reward amount received at the flower. After short handling times, the probability of switching to another species increased, whereas it decreased after long handling times. This difference became even greater if the bee had had a run of several short or several long handling times. (2) Constant flights (those between flowers of the same species) and transition flights (those between flowers of different species) followed stereotyped temporal patterns independent of the distances between flowers. Constant flights within five plant species consistently had median durations of about 2 seconds, whereas median transition times between species took 3-6 seconds. (3) This temporal rule broke down, however, if the flowers of two species had similar colors, in which case transition flights had equal dynamics as constant flights. (4) Bees switched more frequently from rare than from common species but even more frequently between similar species. We conclude that the bees' choices were determined by a set of rules that guided them to stay with the current plant species as long as flowers were rewarding and available within close distance but to switch to another species if flowers offered low rewards or were not encountered at close range. Kty words: bumble bees, Bombus, flower color, flower constancy, foraging, pollination ecology, switching. (Behav Ecol 8:239-249 (1997)] TTWaging bees have to make economic choices among a JL multitude of different flower species with different signals and rewards (Giurfa et aL, 1995; Greggers and Menzel, 1993; Waddington and Heinrich, 1981; Waser, 1983). The principles by which bees forage among plants of a single species have been the subjects of numerous studies. A well-established rule is, for example, that bees leave patches or individual plants and tend to fly longer distances when several of the previous rewards were low (Dukas and Real, 1993; Giurfa and Nunez, 1992; Pyke, 1978; Thomson et aL, 1982; Zimmerman, 1983). Bumble bees, however, often visit several distinct flower types during single foraging flights (Bennett, 1883; Clements and Long, 1923; Grant, 1950; Waser, 1986). Bees' decisions to stay constant on their current plant species or switch to another are not well understood. According to Heinrich (1979), visitation of different flower species can be categorized into two types: majoring (systematic exploitation of flowers of only a single type) and minoring (exploratory visits to other types). A minor can become a major when the bee finds its flowers more rewarding than its current specialty. However, bumble bees are often observed to forage systematically from flowers of several species during single bouts (Bennett, 1883; Free, 1970; Grant, 1950; Thomson, 1981; Waddington, 1983), and so the majoring-minoring dichotomy cannot fully explain how bees make choices in a mixed floral array. Laboratory studies using artificial flowers have primarily in-vestigated the overall distribution of choices between targets of different color (e.g., Chittka et al., 1992; Waser, 1986), or different nectar amounts and variances (e.g., Banschbach and Waddington 1994; Heinrich, 1976; Real, 1991; Thomson etaL, 1982), but not the question of what induces a switch between floral types. Only a few studies have analyzed the sequential dynamics of choices made by bees foraging from mixed foodsource types (e.g., Greggers and Menzel, 1993), although the importance of considering visitation sequences in addition to frequencies was recognized long ago (e.g., Waddington, 1983).

Research paper thumbnail of Male bumble bee pheromonal components in the scent of deceit pollinated orchids; unrecognized pollinator cues?

Arthropod-Plant Interactions, 2007

Research paper thumbnail of Two spatial memories for honeybee navigation

Proceedings of the Royal Society B: Biological Sciences, 2000

Insect navigation is thought to be based on an egocentric reference system which relates vector i... more Insect navigation is thought to be based on an egocentric reference system which relates vector information derived from path integration to views of landmarks experienced en route and at the goal. Here we show that honeybees also possess an allocentric form of spatial memory which allows localization of multiple places relative to the intended goal, the hive. The egocentric route memory, which is called the specialized route memory (SRM) here, initially dominates navigation when an animal is ¢rst trained to a feeding site and then released at an unexpected site and this is why it is the only reference system detected so far in experiments with bees. However, the SRM can be replaced by an allocentric spatial memory called the general landscape memory (GLM). The GLM is directly accessible to the honeybee (and to the experimenter) if no SRM exists, for example, if bees were not trained along a route before testing. Under these conditions bees return to the hive from all directions around the hive at a speed comparable to that of an equally long £ight along a trained route. The £exible use of the GLM indicates that bees may store relational information on places, connections between landmarks and the hive and/or views of landmarks from di¡erent directions and, thus, the GLM may have a graph structure, at least with respect to one goal, i.e. the hive.

Research paper thumbnail of Floral colour diversity in plant communities, bee colour space and a null model

Proceedings of the Royal Society B: Biological Sciences, 1999

Evolutionary biologists have long hypothesized that the diversity of £ower colours we see is in p... more Evolutionary biologists have long hypothesized that the diversity of £ower colours we see is in part a strategy to promote memorization by pollinators, pollinator constancy, and therefore, a directed and e¤cient pollen transfer between plants. However, this hypothesis has never been tested against a biologically realistic null model, nor were colours assessed in the way pollinators see them. Our intent here is to ¢ll these gaps. Throughout one year, we sampled £oral species compositions at ¢ve ecologically distinct sites near Berlin, Germany. Bee-subjective colours were quanti¢ed for all 168 species. A model of colour vision was used to predict how similar the colours of sympatric and simultaneously blooming £owers were for bees. We then compared £ower colour di¡erences in the real habitats with those of random plant communities. We did not ¢nd pronounced deviations from chance when we considered common plants. When we examined rare plants, however, we found signi¢cant divergence in two of the ¢ve plant communities. At one site, similarly coloured species were found to be more frequent than expected, and at the other two locations, £ower colours were indistinguishable from a random distribution. These results ¢t theoretical considerations that rare plants are under stronger selective pressure to secure pollination than common plants. Our study illustrates the power of linking such distinct biological traditions as community ecology and the neuroethology of bee vision.

Research paper thumbnail of A generalised mimicry system involving angiosperm flower colour, pollen and bumblebees’ innate colour preferences

Plant Systematics and Evolution, 2005

Ó Springer-Verlag 2005 colour patterns, and that these correspond to visually displayed pollen. T... more Ó Springer-Verlag 2005 colour patterns, and that these correspond to visually displayed pollen. These findings together suggest a prominent role of floral colour patterns in advertisement to and guidance of naive flower visitors.

Research paper thumbnail of Symmetry is in the eye of the ?beeholder?: innate preference for bilateral symmetry in flower-na�ve bumblebees

Naturwissenschaften, 2004

Bilateral symmetry has been considered as an indicator of phenotypic and genotypic quality suppor... more Bilateral symmetry has been considered as an indicator of phenotypic and genotypic quality supporting innate preferences for highly symmetric partners. Insect pollinators preferentially visit flowers of a particular symmetry type, thus leading to the suggestion that they have innate preferences for symmetrical flowers or flower models. Here we show that flower-naïve bumblebees (Bombus terrestris), with no experience of symmetric or asymmetric patterns and whose visual experience was accurately controlled, have innate preferences for bilateral symmetry. The presence of color cues did not influence the bees' original preference. Our results thus show that bilateral symmetry is innately preferred in the context of food search, a fact that supports the selection of symmetry in flower displays. Furthermore, such innate preferences indicate that the nervous system of naïve animals may be primed to respond to relevant sensory cues in the environment.

Research paper thumbnail of POLLINATORS' STRATEGIES IN FINDING FLOWERS

Israel Journal of Plant Sciences, 1997

Research paper thumbnail of FLOWERS THROUGH INSECT EYES

Israel Journal of Plant Sciences, 1997

Research paper thumbnail of Inflorescence Height Affects Visitation Behavior of Bees-A Case Study of an Aquatic Plant Community in Bolivia1

Biotropica, 1999

We studied the bee fauna visiting a plant community of 10 species of flowering aquatic plants in ... more We studied the bee fauna visiting a plant community of 10 species of flowering aquatic plants in an inundated savanna region in Bolivia. In total we observed 36 bee species in 17 genera at the flowers. Cluster analysis of the similarities among the plant species in terms of their visitor spectra showed a division into two groups: plants with inflorescence heights shorter than the grass height and plants with inflorescences projecting out of the surrounding vegetation. Larger bees of the genera Apis, Melipona, Bombus, and Xylocopa were observed only at flowers above the surrounding vegetation. Smaller, mainly solitary bees (e.g-, AugochLorcLa, An~yloxeLis) visited flowers in the dense vegetation near the water surface. Analyses of the pollen loads revealed that most individuals were highly flower constant. When bees carried different pollen types, it was generally pollen from flowers within a single stratum. We discuss specialization, flower constancy, competition, and different foraging strategies as possible reasons for stratum fidelity.

Research paper thumbnail of Colour similarity to rewarding model plants affects pollination in a food deceptive orchid, Orchis boryi

Biological Journal of the Linnean Society, 2001

... and field observations in other species, we expected that the reproductive success of this de... more ... and field observations in other species, we expected that the reproductive success of this deceptive species should be negatively correlated to its density and frequency (Sabat & Ackerman, 1996; Smithson & Macnair, 1997; Ferdy et al., 1998 ... Pollinia export [Yo] - 41.93 22.53 ...

Research paper thumbnail of The combined effect of color and odor on flower choice behavior of bumble bees in flower mimicry systems

Behavioral Ecology, 2001

Food-deceptive flowers are pollinated by animals that expect a reward but are cheated. Such plant... more Food-deceptive flowers are pollinated by animals that expect a reward but are cheated. Such plants profit from their similarity to rewarding plants and should develop signals that hinder discrimination. We use artificial rewarding model flowers and nonrewarding mimicking flowers that present similar visual cues. We test how additional scent cues change flower choice of the mimic by bumble bees (Bombus terrestris) in two situations: (1) both flower types are simultaneously present and can be compared by the pollinator, and (2) both flower types are encountered successively in the absence of each other. We find that in situation 1, discrimination learning is greater if scents are used as cues for identifying the mimic, whether the mimic has a different scent or if it is scentless while the model is scented. In situation 2, a generalization task, a scented mimic is avoided faster than a scentless one. Discrimination of the mimic is poorest if it has the same scent as the model, thus demonstrating a potential for scent mimicry, which has not yet been proved to exist among differently rewarding flowers. Thus, the best strategy for a mimic would be to have the same scent as the model, but this strategy may not be used due to evolutionary constraints. Alternatively, if there are several potential models, then having no scent would be a better strategy than mimicking just one of the models. In situation 1 flower discrimination by color cues is enhanced in the mere presence of scent, compared to unscented controls, even if the scent does not provide a distinguishable cue itself. The results indicate that the presence of scent may enhance color discrimination by improving attention towards visual cues and/or that combined color/odor cues may lead to better memory formation and retrieval.

Research paper thumbnail of Relationship of visual and olfactory signal parameters in a food-deceptive flower mimicry system

Behavioral Ecology, 2004

Pollinators such as bees are attracted to flowers by their visual display and their scent. Althou... more Pollinators such as bees are attracted to flowers by their visual display and their scent. Although most flowers reinforce visits by providing pollen and/or nectar, there are species-notably from the orchid family-that do not but do resemble rewarding species. These mimicry relationships provide ideal opportunities for investigating the evolution of floral signals and their impact on pollinator behavior. Here, we have reanalyzed a case of specialized food mimicry between the orchid Orchis israelitica and its model, the lily Bellevalia flexuosa. Based on current knowledge of insect sensory physiology, we were able to characterize both the visual and olfactory signals of model and mimic, as well as of two phylogenetically related orchids. By using a color vision model, we mapped each species' visual signals to the perceptual space of honeybees and found an apparent shift of the mimic's visual signals towards the model. We confirm that visual mimicry is present. We analyzed the flower odors by using gas chromatography/ mass spectroscopy. We related these signals to the perceptual space of the pollinators by testing the scent extracts physiologically, using in vivo brain imaging. We found no evidence of olfactory mimicry. The results indicate that evolutionary pressure acts on the visual, but not olfactory, traits of O. israelitica toward a higher similarity to its model. Apparently, odor mismatch does not prevent a bee from landing on a flower that has the expected visual display. The results therefore argue for the dominance of visual stimuli in short-distance flower choice. The orchid may still depend on long-distance olfactory attraction originating from neighboring model plants.

Research paper thumbnail of Foraging dynamics of bumble bees: correlates of movements within and between plant species

Behavioral Ecology, 1997

What rules determine whether bumble bee* continue exploiting plants of the species just visited o... more What rules determine whether bumble bee* continue exploiting plants of the species just visited or switch to another species? To tackle this question, we recorded handling times and flight times from bees foraging in a natural meadow containing five plant species. Inter-and ultra-specific plant distances were quantified. The bee-subjective colors of the five species were determined; two of these species had similar colors and structures, while three species were distinct from all others. The following rules were identified: (1) The decision to switch species was correlated with previous flower handling time, which we assume is a function of the reward amount received at the flower. After short handling times, the probability of switching to another species increased, whereas it decreased after long handling times. This difference became even greater if the bee had had a run of several short or several long handling times. (2) Constant flights (those between flowers of the same species) and transition flights (those between flowers of different species) followed stereotyped temporal patterns independent of the distances between flowers. Constant flights within five plant species consistently had median durations of about 2 seconds, whereas median transition times between species took 3-6 seconds. (3) This temporal rule broke down, however, if the flowers of two species had similar colors, in which case transition flights had equal dynamics as constant flights. (4) Bees switched more frequently from rare than from common species but even more frequently between similar species. We conclude that the bees' choices were determined by a set of rules that guided them to stay with the current plant species as long as flowers were rewarding and available within close distance but to switch to another species if flowers offered low rewards or were not encountered at close range. Kty words: bumble bees, Bombus, flower color, flower constancy, foraging, pollination ecology, switching. (Behav Ecol 8:239-249 (1997)] TTWaging bees have to make economic choices among a JL multitude of different flower species with different signals and rewards (Giurfa et aL, 1995; Greggers and Menzel, 1993; Waddington and Heinrich, 1981; Waser, 1983). The principles by which bees forage among plants of a single species have been the subjects of numerous studies. A well-established rule is, for example, that bees leave patches or individual plants and tend to fly longer distances when several of the previous rewards were low (Dukas and Real, 1993; Giurfa and Nunez, 1992; Pyke, 1978; Thomson et aL, 1982; Zimmerman, 1983). Bumble bees, however, often visit several distinct flower types during single foraging flights (Bennett, 1883; Clements and Long, 1923; Grant, 1950; Waser, 1986). Bees' decisions to stay constant on their current plant species or switch to another are not well understood. According to Heinrich (1979), visitation of different flower species can be categorized into two types: majoring (systematic exploitation of flowers of only a single type) and minoring (exploratory visits to other types). A minor can become a major when the bee finds its flowers more rewarding than its current specialty. However, bumble bees are often observed to forage systematically from flowers of several species during single bouts (Bennett, 1883; Free, 1970; Grant, 1950; Thomson, 1981; Waddington, 1983), and so the majoring-minoring dichotomy cannot fully explain how bees make choices in a mixed floral array. Laboratory studies using artificial flowers have primarily in-vestigated the overall distribution of choices between targets of different color (e.g., Chittka et al., 1992; Waser, 1986), or different nectar amounts and variances (e.g., Banschbach and Waddington 1994; Heinrich, 1976; Real, 1991; Thomson etaL, 1982), but not the question of what induces a switch between floral types. Only a few studies have analyzed the sequential dynamics of choices made by bees foraging from mixed foodsource types (e.g., Greggers and Menzel, 1993), although the importance of considering visitation sequences in addition to frequencies was recognized long ago (e.g., Waddington, 1983).

Research paper thumbnail of Male bumble bee pheromonal components in the scent of deceit pollinated orchids; unrecognized pollinator cues?

Arthropod-Plant Interactions, 2007

Research paper thumbnail of Two spatial memories for honeybee navigation

Proceedings of the Royal Society B: Biological Sciences, 2000

Insect navigation is thought to be based on an egocentric reference system which relates vector i... more Insect navigation is thought to be based on an egocentric reference system which relates vector information derived from path integration to views of landmarks experienced en route and at the goal. Here we show that honeybees also possess an allocentric form of spatial memory which allows localization of multiple places relative to the intended goal, the hive. The egocentric route memory, which is called the specialized route memory (SRM) here, initially dominates navigation when an animal is ¢rst trained to a feeding site and then released at an unexpected site and this is why it is the only reference system detected so far in experiments with bees. However, the SRM can be replaced by an allocentric spatial memory called the general landscape memory (GLM). The GLM is directly accessible to the honeybee (and to the experimenter) if no SRM exists, for example, if bees were not trained along a route before testing. Under these conditions bees return to the hive from all directions around the hive at a speed comparable to that of an equally long £ight along a trained route. The £exible use of the GLM indicates that bees may store relational information on places, connections between landmarks and the hive and/or views of landmarks from di¡erent directions and, thus, the GLM may have a graph structure, at least with respect to one goal, i.e. the hive.