Artificial Life Laboratory, Graz, Austria

 [Picture © Robert Brodschneider, Brood nest of a honeybee observation hive]

Background
Collective behaviour is a term that describes the behaviour of a meta-organism like a swarm similar to the behaviour of an individual. It is determined by the behaviour of interacting individuals, but yields capabilities that none of the individuals can achieve on its own. This emergent phenomenon is known for many species of social organisms with a wide spectrum of organizational complexity, from simple slime mould to sophisticated animals like mammals or birds. One of the best studied species that exhibit swarm intelligent behaviour are honeybees.

Honeybees
Honeybees (Apis mellifera ssp.) are eusocial animals that live in colonies of up to some 10,000 individuals. The population consists of a queen and a small number of males, which together constitute the fertile stock of the colony and a large number of sterile workers. The latter exhibit a pronounced division of labour among age dependent casts (age polyethism). The homeostasis of the hive and, as a consequence, the survival of the colony is solely dependent upon these worker casts.

Brood nest of a honeybee observation hive. In the center of the brood nest comb are the cells with open (Bo) and capped (Bv) brood. The brood is surrounded by pollen (Po) and honey (Ho). The bees regulate the temparature in the center of the brood nest in a very narrow range from approx. 34 °C to 36 °C (93,2 °F to 96.8 °F). This stable thermal environment is crucial for the proper development of the larvae and freshly emerged bees.

The honeybees' aggregation behaviour is a prominent example for collective behaviour. They form aggregations (clusters) at different occasions. A reduced set of worker bees survive the winters in cold and temperate climates by forming a tightly packed winter cluster in the hive which allows them to conserve body temperature and to protect their queen, which remains encapsulated at the center of the cluster. Reproductive swarms, which consist of a queen and a large portion of a spawning colony's worker bees, repeatedly form large clusters while searching for a new nesting site. Aggregations regularly occur in the hive, especially among freshly emerged worker bees in the brood nest. Honeybees are able to precisely perceive temperature with the help of their antennae and they have an age dependent preference for specific temperatures. The young bees in the brood nest have a preference for approximately 36 °C (96.8 °F). This preference has been determined in the 1950s by Herbert Heran, who exposed honeybees of different casts to a simple and steep linear thermal gradient and evaluated the positions they preferred. In these experiments, the bees quickly moved to the position of their preferred temperature and stayed there. Five decades after Heran's experiments, we oberved honeybees in a more complex, two-dimensional thermal gradient and found that, in contrast to Heran's report, only larger groups of bees, but not single bees or small groups, were consistently able to find an area of preferred temperature. This stunning observation lead us to initiate this project, in which we determined the individual behavioural background of the bees' swarm-intelligent temperature-induced aggregation behaviour, which in turn allowed us to develop algorithms to facilitate swarm intelligent behaviour in groups of robots.

Temperature arena set-up. Our temperature arena consists of the arena floor (a), equipped with temperature sensors and covered with wax. The thermal gradient is generated with heat lamps (b). We use infrared light (c), which is invisible for bees and record the experiments with an IR-sensitive camera (d).

The project
In order to investigate the behaviour of honeybees in a two-dimensional thermal gradient, we constructed a circular arena (d = 60 cm or 90 cm), which we equipped with two infrared heat lamps and a wax floor fitted with 61 temperature sensors. We used one or both heat lamps to establish a deliberate, automatically controlled thermal gradient in the arena. Infrared lighting, which is invisible to bees, allowed us to observe and record them under dark conditions via an IR-sensitive camera. We opted to conduct our experiments with young honeybee workers (Apis mellifera ssp.), less than one day after their hatching, because they still lack the endothermic capabilities of older bees which enable the latter to actively regulate their body temperature. Thus, young bees are dependent upon an environment that suits their thermal needs, which in turn catalyzes their disposition to move to an optimal area within the thermal gradient.

In each experiment, we observed and recorded a single bee or groups of up to 128 bees as they were moving through the arena. The bees were exposed to different thermal gradients that dropped from the optimum temperature of 36 °C (96.8 °F) to a variable minimum (pessimum) temperature. We recorded them and then automatically analyzed the recordings in order to evaluate the sequence of positions (trajectory) for single bees. Recordings with groups of bees were analyzed manually in order to evaluate the size and positions of aggregations in different time intervals. For future analyses, we will be able to resort to an improved tracking algorithm which performs well on small and medium sized groups of bees (watch video). This will allow us do explore the bees' swarm behaviour at a deeper level.

Results
It is remarkable that single bees showed diverse behaviours under comparable environmental conditions. According to their varying locomotion behaviours, we classify the bees into four categories. Besides the small faction of Goal Finders, which are able to directly find the area of preferred temperature, we distinguish between Random Walkers, Wall Followers and Immobile Bees, none of which are able to find the optimum (see diagram or watch video). The bees do not natively belong to a specific class and do not strictly adhere to it so that a momentary classification cannot be regarded as an innate trait of an individual. Based on the trajectories of single bees we determined a number of behavioural parameters (e.g. moving speed, turning angles, resting times) in dependence of local temperature, gradient steepness and position in the arena. We could show that some of the behavioural parameters are indeed dependent on the bees’ local temperature. For instance, bees stop more frequently and rest longer in areas whose temperature is closer to the bees' optimum temperature. This explains the ability of groups of bees to quickly aggregate and then stay at the optimum area. The increased resting time of individual bees in the optimum leads to an increased probability of two bees colliding and then resting there together for a longer period than an individual bee would. Like in a snowball effect, a larger aggregation will grow quickly around this "cluster seed".

(a) Random Walker	(b) Wall Follower
(c) Goal Finder	(d) Immobile Bee

Behavioural classes among young honeybees. The trajectories of four bees are shown, representing the distinct classes of locomotion behaviours. The solid and dashed green lines indicate the arena wall and the wall zone (the zone up to 3 cm inwards from the wall), respectively. The dashed red line indicates the zone of the thermal optimum in experiments with simple gradients. The light blue marks indicate the bee's starting position (triangle) and its position at the end of the experiment (circle). The experiment duration was 20 min, the bees' positions were evaluated with a resolution of 1 second. Random Walkers (a) move throughout the arena, have a bias towards the optimum but don‘t stay there. Wall Follower (b) move mostly within the wall zone. Goal Finder (c) quickly move to the optimum and stay there. Immobile Bees (d) hardly move at all.

The knowledge about the parameters of individual locomotion behaviour enabled us to describe the behavioural classes by the specific behavioural traits associated with them and to establish an algorithm for automatic classification. Additionally, we used these parameters to create a multi agent (bottom-up) model to simulate individual bees and groups in a virtual arena. While this simulation is able to reproduce the behaviour of single bees quite well, the behaviour of groups of bees can only be partially reproduced with this simulation (watch video). This finding once more reveals the swarm intelligent component of the bees' swarm behaviour, which is not apparent in the behaviour of single bees.

Besides the simulation, we also derived a bio-inspired navigation algorithm for robots from the bees' aggregation behaviour. This BEECLUST algorithm, which allows a swarm to find a light spot in an arena, was implemented in a model and in real robots. Similar to bees aggregating at a spot of their preferred temperature, the BEECLUST driven robots aggregate at light spots by modulating their  resting time in accordance with the local brightness (watch video1, video2). However, a light gradient is physically different from a thermal gradient in propagation, homogeneity and perceptibility. In order to reproduce the bees' behaviour more realistically, we constructed a robot with temperature sensors at the tip of two antennae similar to the anatomy of honeybees and implemented the BEECLUST algorithm. A small swarm of these prototype robots performed well in an arena with a thermal gradient (watch video).

In addition to single bees we investigated groups of up to 128 bees as they moved through the thermal gradient in the arena. We found that these groups quickly form aggregations in the area of the thermal optimum (watch video), provided the group size exceeds a certain threshold. These aggregations usually involve the majority of the group. The steeper the thermal gradient (i.e., the greater the range between optimum and lowest temperature in the arena), the faster the aggregations are formed and the more individuals they comprise. Once formed, the aggregation itself persists as long as the thermal gradient remains stable, despite a continuous, balanced stream of single individuals away from and towards the cluster.

In a complex thermal gradient, which consists not only of a thermal optimum (36 °C, 96.8 °F) and pessimum (the coolest area, i.e. ambient temperature), but also includes a (local) sub-optimum (e.g. 32 °C, 89.6 °F), the majority of the bees reliably aggregate at the optimum area. Only a small faction of them are attracted by the thermal sub-optimum. If the heat source sustaining the optimum temperature is turned off and the optimum area starts to cool down towards the pessimum temperature, the former sub-optimum becomes the global optimum. After a relatively long latency, the aggregation at the former optimum starts to dissolve and most of the bees reaggregate at the former sub-optimum (watch video). Therefore, aggregations are in a dynamic equilibrium, stable in stable environments but adaptive to environmental changes.

We also investigated the influence of social interaction on the bees' aggregation behaviour. We established a complex thermal gradient (optimum and sub-optimum) and a simple social gradient (a few bees in a cage at the sub-optimum) in the arena and observed a small number of freely roaming bees as they navigated through the arena. In this scenario the bees have to trade off between environmental quality (optimal temperature) and their tendency to aggregate. We found that social interaction is more important to bees than optimal temperature and that the social gradient outweighs the thermal gradient. A group will rather aggregate at a cooler area next to caged bees than at the optimum spot next to an empty cage (watch video). This also explains the long latency between the cooling down of the original optimum after shutting down the heat source and the dissipation of the aggregation at this area. We could also observe symmetry breaking in larger groups of bees (watch video), a phenomenon related to their strong social interactions.

We tested the robustness of the bees' swarm behaviour by observing groups contaminated with individuals that are unable to perceive temperature. We found that the presence of temperature insensitive individuals did not have a negative impact on the swarm's capability to find the optimum area in a thermal gradient if the number of impaired individuals did not exceede a certain threshold.

Media

A short glossary of terms

Aggregation behaviour: A manifestation of collective behaviour that leads to a concentration of individuals at a specific - usually beneficial - spot. In a thermal gradient, young honeybees aggregate at their preferred temperature of approximately 36 °C (96.8 °F).
Antennae: In honeybees a pair of sensing organs extending from the head and used, among other purposes, to perceive temperature. The bees' ability to determine the direction of a thermal gradient depends on the discrimination sensitivity and the distance of the antennae.
Behavioural class: The locomotion behaviour of single young honeybees in a thermal gradient can be categorized into four behavioural classes. Random Walkers perform a biased random walk with a preference for the optimal area but without standing still for a considerable time. Wall Followers move along the wall of the arena most of the time with occasional random walks but without a clear preference for the optimal area. Immobile bees hardly move at all. Goal Finders move towards the optimum more or less immediately and stay there. This is the only behavioural class which is associated with single bees finding the optimum.
Bio-inspiration: Inspiration of solutions to technological problems, drawn from the solutions that evolution of living organisms has found for comparable problems. These solutions are (intermediate) results of iterated optimization processes that in some cases last for millions of years. They are often characterized by a remarkable elegance and efficiency. Bio-inspiration leads to a reproduction of biological mechanisms, but not necessarily to a reproduction of the biological implementation (i.e. embodiment).
Cluster: In honeybees a three-dimensional aggregation of individuals, usually with the queen at the center. Clusters of thousands of individuals are formed during swarming events, and winter clusters of several hundred individuals allow the bees to conserve body temperature and thus survive periods of cold temperatures. Because of the similarity of the fundamental rules governing three dimensional clusters and the two dimensional, queenless aggregations that occur in our experiments, we use both terms synonymously.
Clustering behaviour: see Aggregation behaviour
Emergence: The temperature induced aggregation behaviour of young honeybees in a two dimensional thermal gradient can be considered as an emergent effect. Only groups of bees can reliably find an optimal area in this set-up while single bees, whose individual behaviour is the basis of the collective behaviour, fail at this task.
Endothermy: The ability of an organism to actively increase its body temperature. Bees achieve this by activating their antagonistic flight muscles.
Eusociality: The highest level of social organization, characterized by the presence of different castes with different specialization. Often, the majority of the individuals belong to a sterile caste. Therefore, reproduction is limited to only a few individuals. In the honeybee colony the only reproductive individuals are the queen and a few drones, while the thousands of workers are sterile.
Honeybees: A textbook example for eusocial organisms. A honeybee colony is usually made up of several thousand individuals, most of them workers. During their short lives, the workers pass through a number of different castes (age polyethism), which are associated with different tasks in the hive. In our experiments we use freshly hatched (less than one day old) western honeybees (Apis mellifera ssp.), which are not yet able to fly and cannot actively control their body temperature.
Locomotion behaviour: A sub-set of individual behaviour which contributes to the collective aggregation behaviour. In this project we analyzed several aspects of the locomotion behaviour of single bees and their correlation to the local temperature and to the slope of the thermal gradient. Specifically we determined the relationship between temperature and walking speed, stopping probability, resting time and turning angle. The resting time strongly depends on the local temperature and has its longest duration at the bees' optimum temperature.
Multi-agent model: A model for the simulation of several agents which interact with one another and with the environment in discrete time steps. The resultant (or emergent) system is determined by the few simple rules that govern the agents' interactions (bottom-up simulation) rather than by a centralized control mechanism (top-down simulation). We used a bottom-up model to simulate single bees and swarms with a parameterization that was derived from observations of real bees.
Social animals: Several species from different phyla exhibit sociality on different levels, the highest of which being eusociality (see Eusociality). The best known representatives of eusocial animals are honeybees, ants, termites and several other insect species. On lower levels of sociality, cooperation between individuals is less stringent and in some cases only temporal.
Social gradient: A gradient of social attractiveness based on groups of immobilized individuals (e.g. caged bees), with group sizes growing along the gradient's slope (larger groups are more attractive than smaller ones).
Swarm: In biology a temporal aggregation of conspecific individuals, usually moving in a coordinated manner. For honeybees the term usually refers to reproductive swarms which consist of up to several thousand individuals. In contrast to this interpretation, in artificial life any group of interacting agents is considered a swarm. In our experiments, we apply this looser definition to honeybees and robots and describe groups of at least two individuals as swarms. Swarms typically exhibit collective behaviour, often with emergent effects (swarm intelligence).
Symmetry breaking: The determination of a system to exclusively adopt one of several equally probable options. In biology the phenomenon is known - for example - for ant trails, where foraging ants often exhibit increasing preference for one of several existing trails to a food source and eventually start using this trail exclusively while discarding the alternatives.
Thermal gradient: In our experiments a two dimensional gradient in the temperature distribution on the surface of the arena, reaching from a deliberate minimum temperature to the optimum temperature and, if applicable, beyond. The steepness of the gradient is determined by the temperature range and the distance between the spots with minimum and maximum temperature. The steepness of the gradient has a positive impact on the optimum finding performance of single bees and swarms. In our experiments, the thermal gradient is established with the help of infra-red heat lamps. Finding an optimum spot in a two-dimensional thermal gradient is far more challenging than finding it in a one-dimensional gradient, which was originally used to determine the temperature preference of honeybees.