Distributive Control Models for Honeybee Decision Making During Foraging (1997)
Bud Vos
Colorado State University Ft. Collins, CO

Abstract
How does a whole honeybee colony discriminate, and direct activity to, different food source locations via the dynamic behavior of thousands of individuals? The answer to this question goes to the heart of self-organization theories for social insect behavior studies, yet it remains a mysterious and disputed topic. Numerous sources cast honeybee colonies as superorganismal systems that adaptively sense, plan and act to function and survive in the world. Conversely, other sources describe honeybee colonies as goal-directed, decision making, systems whos function is governed by the decentralized control, and action, of its individual entities. Colonial decision making results from this design. This paper explores and examines models of decentralized control for foraging honeybee colonies to reveal its unique and auspicious features.

To show this relation, a history of the work on honeybee colonies is first presented. Using this as a basis, the distributed control model of Seeley is dissected to understand its underlying function, constraints and variables that correlate to the colonial system. What can then be shown, is that the model Seeley proposes arises from an individual bees inherent interaction with the environment in which it finds itself - including individuals within the colony. This theme is commonly used in the design and development of distributive control models for engineering applications and we can thus show their correlation to the colonial design.

Introduction

Doubly determinate systems - a term coined in the late sixties [Grene, 1969] - can be used to describe distributed systems that exhibit decision making activity. Double determinacy refers to the organization in a system where the structure and function of the elements comprising the complex system fundamentally constrains the behavior of the elements themselves [Grene, 1969]. From a philosophical point of view, systems that exhibit this characteristic are seen in many biological examples. Particularly interesting are social insect colonies. For example, individuals of a honeybee colony are often found working for the betterment of the colony as a whole. In these cases, it has been shown that the individual works to achieve an individual-level performance which, in turn, creates a colony-level success [von Frisch 1967, Seeley 1991, Weher 1985]. As the definition of double determinacy implies, this phenomenon is not the function of a central organizing body [Hofstader, 1989] in the colony that directs each individuals operation, yet it is a function of the limited behavior and action of each individual as governed by the environment in which each individual finds itself [Simon, 1981].

From a biological model point of view, the honeybee colony has many life critical operations requiring precise modulation from the decisions and actions of its constituents. For example, the colony must undergo precise thermoregulation in different sections of the hive by modulating their activity [Watmough et al, 1995]. Further, the colony must monitor the inflow of nectar to the hive and augment its foraging activities accordingly [Seeley, 1991, 1995]. Also, the colony must monitor pollen hoarding and augment its pollen foraging activity accordingly[Page et al,1995]. All in all, the colony must operate in a changing environment where the actions of the individuals govern the survival of the whole colony. 

It has been shown that in these societies, each individual is tightly coupled with the environment and the task they are required to complete. This review focuses on the task of foraging in a honeybee colony where each individual has distinct behaviors and decision making operations as described by the model developed by Thomas Seeley. This model has been designed to give a colony-level response, via individual behavior as the foraging conditions in the environment change. It can be shown that this model is doubly determinate in nature because, as we shall see, the foragers behavior changes and limits the behavior of the complete system as the colony exploits appropriate sources of nectar during foraging activities.

Discussion
The orientation and communication among honeybees has been well known and explored by numerous individuals. It was first developed by Karl von Frisch in 1967, and has been furthered by the work of Rudiger Wehner and Samuel Rossel in 1985. These pivotal works in the field of honeybee ecology have revealed many mysteries about the orientation and communication of honeybees. However, a fundamental question that remains is: what does a honeybee communicate and orient for? In reference to foraging activities, this particular question has been pursued by Thomas Seeley's work. Seeley [1986, 1989, 1991, 1995] has conducted hundreds of experiments on foraging honeybee colonies fundamentally based upon the principle that using known orientation and communication mechanisms, how does the ability of a honeybee colony to choose among nectar sources emerge from the behaviors of thousands of bees? Seeley's experiments have focused on the individual forager activity outside and inside the hive as he conducted the environment changes (nectar concentration at foraging sites). Through his experiments, Seeley has shown that individual activity and decision making form a colony-level response to changing foraging conditions. Furthering his own work, Seeley used his experiments and observations to develop a colonial, biologically based, mathematical model of the foraging activity that captures the essence of this phenomenon from the individual point of view.

The Biological Basis of the Model
Extensive experiments and observations of actual honeybee colonies operating in the world has developed the biological basis of Seeley's model. Seeley's [1991] experiments have shown that foraging honeybees will augment their foraging strategy as environmental conditions change. This was accomplished by an experiment where Seeley monitored the number of foragers at two different nectar sources of different sucrose concentration. Seeley was able to show that when a colony was faced with two different sources of nectar, it consistently focused on the source with the highest profitability - profitability is defined as a function of nectar sweetness, accessibility, abundance and distance from the hive. Furthermore, if the nectar sources changed profitability, the colony changed its focus. Moreover, the most profitable source of nectar was not only visited by more foraging bees, but it was visited at a higher rate of returning bees than the less profitable source. Therefore, the profitable source made the foraging bees act quickly and thus returned sooner than the bees visiting the less profitable source (not considering other environmental impacts). This implies that the activity at the hive somehow impacted the foragers activity.

The change in the number of foragers to the source gives way that there must be the notion of the abandonment or recruitment to each source by other foraging bees. In this sense, foraging bees must recruit bees that are uncommitted to a particular source and those that are committed must choose whether or not to continue foraging at a particular source. There must be a individual decision in each forager based on a number of variables. Noticing these activities and relationships, Seeley developed the following model describing the process of a foraging honeybee.

control models
Figure 1 - Foraging Model (Reproduced from Seeley 1991)

This model has three primary parts. The first is a hive section (at the top) where foraging honeybees unload their collected nectar to a food storer bee. The second is a Dance Floor (located in the middle) where honeybees utilize their communication skills to recruit other honeybees to a particular source or choose to follow another forager to another source. The third section is the nectar source (located at the bottom). The model begins with a pool of foragers that are uncommitted to either source (A or B). These bees are considered follower bees. A particular follower bee begins the day at the dance floor and may choose to be recruited to either source. After visiting the source, this bee returns to the hive and unloads its load of nectar to a storer bee. At this point the bee has some decisions to make - denoted by the diamonds in the process model. The bee can return to the dance floor in search of a more profitable source to visit, it may return to the dance floor to recruit other follower bees, or it may mearly return to the source directly without further abandonment or recruitment. These behaviors are the complete repertoire of the foraging honeybee as observed by Seeley.

This process requires a foraging honeybee to make critical decisions about the profitability of a particular source of nectar and the current condition of the nectar inflow to the hive as a whole. If for instance the hive as a whole had a current low nectar inflow rate, a highly profitable source is desirable. Conversely, if the current inflow rate of nectar is high, a highly profitable source may not be required or even desirable for the hive because the hive must maintain a regulated nectar inflow rate. We find that in these cases the individual decision and behavioral mechanisms are crucial to the overall hive function and survival. Note, that this model does neglect many other environmental factors and simplifies the model to a basic level of understanding where we can observe the bee behavior based on simple rules.

The key to this model is that it develops fundamental, quantifiable, measures of the bees success from which it makes simple decisions that will augment the colony performance as a whole. Further described are the hypothetical processes used by honeybees to augment their behaviors as they move through the different phases of the model. These measures are the assessment of the profitability of the nectar source and the nutritional status of the colony as a whole. These assessments change the behavior of the honeybee. Although important to verification of this model, the mathematical basis of the model is not described here, for further information see Seeley, 1991.

Assessment of Profitability
As shown by Seeley's model, the foraging honeybee must asses the profitability of each source it encounters. The measure of profitability is a function of many factors including nectar sweetness, nectar abundance, nectar accessibility, and distance from the hive [Seeley, 1991, Stabentheiner, 1996]. As hypothesized by Seeley, the honeybee itself must asses this quality and use it to determine whether to abandon a source, or recruit others. Seeley's hypothesis points to three possibilities. First, each forager could visit each source and compare it to the previously visited sources. This would require a forager to visit each source which seems impractical considering the distances between sources has been found to cover areas up to 100 km2. Second, each forager could rely on comparisons of nectar quality made by the food storer bees inside the hive which taste each nectar as it is delivered to the hive. According to this hypothesis, the taste of a foragers nectar would be a testament to its goodness and would be communicated through increased or decreased antennaeation [Seeley, 1991]. However, this does not consider the distance required to travel to the source - an important quantity due to the fact that it has an impact upon the energy required to acquire the nectar. The third possibility is that the foraging honeybee individually calculates the profitability of the source, independently of other sources, and uses this information to augment its behavior. The first hypothesis seems unreasonable. However, to distinguish between the second and third hypotheses, Seeley designed a series of experiments. The experiments were designed to show that the food storer bees did not change their activity and attention to the foragers based on the nectar source distance from the hive. It was shown that the food storer bees didn't account for distance in any way. By a process of elimination, Seeley showed that each individual bee must measure the profitability of each source it visits and determine if it is highly profitable. Seeley suggests this could be accomplished by an energy expended versus energy acquired calculations, but has not completed experiments to show this is the case. Once a foraging bee determines the profitability, the foraging honeybee must asses the colony nectar status to before its actions on the dance floor.

Assessing the Colonies Nectar Status
Not only is the source profitability of interest to the honeybees, but the colonies nutritional status is as well. For example, it has been observed that when a colonies food status is favorable, it only exploits highly profitable sources of food. However, when the food situation is poorer, the colony will exploit most food sources, regardless of the profitability, to quickly acquire nectar [Seeley, 1989, Farnia, 1996]. Therefore, the nutritional status of the colony as a whole is important to the individual decision making mechanism shown by Seeley's model. In this situation, it has been hypothesized that information about the colonial status is communicated by trophallaxis between the forager and the storer bees [Farina, 1996]. This hypothesis is based on an experimental analysis of the length and frequency of probascis contact during unloading of nectar at different strains of nutritional status in different colonies. The results of Farnia's work showed that the returning foragers must directly acquire information about the actual feeding state of the colony by informational contact with the food storer bees. This was done by showing that bees returning from low nectar profitability sources tended to beg from other bees for nectar after contact with the food storer bee when the hive was running low on its food source. This is hypothesized as a method to determine where others have been by the pollen odor of a previously visited profitable source. As a result, this particular forager would tend to dance less, and have a higher trophallaxis among the hive mates to determine where to go when they returned with a low profitable source and the hive was in need of food. In this sense, the individual and its contact with the food storer gave a quantitative measure of the nutritional status of the hive to the forager who tries to augment its own behavior quickly.

Another theory developed by Seeley, shows that the nutritional status of the hive is revealed through the length of time required for a returning forager to unloaded its nectar [Seeley, 1989]. Through his experiments, Seeley shows that the length of time to be serviced by a food storer increases as the hive becomes full of honey. Moreover, as the rate of nectar inflow increases, the food storer bee becomes busier and busier, and therefore it is more difficult for a forager to find a food storer bee. Both limiting factors for the hives inflow of nectar. One of the most interesting experiments removed food storer bees from the hive to watch the effect of a longer time to be unloaded from the foragers perspective. In this case, the foragers lowered their recruitment levels assuming the hive was becoming full of nectar. This and other experiments provided proof that the foragers must assess the nutritional status of the colony by a direct relationship to the length of time to be unloaded by food storers. 

Each of these hypothesis point to the fact that each individual acquires information about the nutritional status of the hive and react accordingly. Although somewhat different in perspective, each hypothesis could be used by the foraging bees in making decisions that are reflected on the dance floor.

The Dance Floor
The dance floor area is of particular interest because it contains the interesting dynamics of Seeley's model through the interaction and informational exchange between different foraging honeybees. Using the Waggle Dance [von Frisch, 1967] each foraging bee communicates the location of different sources of nectar. However, as shown by Seeley, von Frisch, and numerous other sources, there must be a deterministic behavior that drives the waggle dance and other properties associated with it, such as thoracic temperature [Stabentheiner, 1996] and the condition of the comb forming the dance floor [Tautz, 1996]. It is on the dance floor that, according to Seeley's model, the decision making process is completed in each individual forager. Therefore, the foraging bee must contain certain levels of cognition and understanding of the visual, auditory, and vibrational queues received once on the dance floor. Fortunately, the decision to be made is a simple one for the forager -- continue on to the source, dance and recruit, or abandon the source altogether. If the forager chooses to continue to the source again, they will often not stop at the dance floor and continue on their travel. However, if the queues are appropriate to request additional foragers, i.e. a profitable source is found and the hive needs food, the foraging bee will go to the dance floor and dance to communicate the orientation of a perceived profitable source. Often, this is done by particular dance cycle [von Frisch, 1967]. Furthermore, it has been recently shown that the profitability can be correlated to the thoracic temperature during dancing - another que from which the follower bees determine whether or not to follow the dancing forager. Furthermore, if the source is perceived unprofitable or undesirable, then the foraging bee returns to the dance floor to become a follower bee to be recruited to another source. Therefore, the dance floor become a very important area where profitability and nutritional status information is transferred and integrated both from the recruiting bees standpoint and the follower bees standpoint.

Conclusion
Overall, we find that each bee acts individually in each area for Seeley's model. From assessment of the profitability of a nectar source, to the understanding of the nutritional status of the hive and the following actions on the dance floor, all the research shows that each individual is acting only as an individual. However, each individuals actions influences the actions of the other individuals as they make decisions of their own. The result is a colony level response to changing conditions in the environment perceives and acted upon by the individual. Functionally, this process seems to be a simple when reduced to Seeley's model where it is revealed that the system governing the action in the hive is based on very particular and crucial queues that the constituents of the foraging bees are tuned to. In this sense, Seeley's model is very interesting because it to contains these properties.

Furthermore, Seeley's model ensures that each individual is closely matched to the environment in which it functions, and only perceives the information crucial to it. Thus, the action and perception of each individual constrains the behavior of the individuals so as to create a colony level system that seems to respond to environmental change. This is a great example of a model for a doubly determinate system created through biological inspiration and mathematical synthesis - an exciting synthesis.

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