Honey bees use the sun as a reference point in navigation and communication. Experiments have shown that bees have internal representation of the sun's movement through the sky and suggest that this representation is innate, but is tailored by experience. Attempts to model this representation have not been entirely successful.
Consider a normal worker bee foraging for food. If the bee does not know where to find food, she will take a somewhat irregular path away from the hive until she finds a suitable food source which may be up to 10 km distant. She will then fly a straight line path back to the hive and make a peculiar ``dance'' on the vertical combs in the hive. Shortly after this dance, many bees will fly a straight path to the source the original bee found and will repeat the process themselves. This behavior interests zoologists because it implies that bees have notions of location and communication that might not be expected in such simple organisms. [The principal flaw with this paper is that too many of the topic sentences are at the end of the paragraph. The reader has to guess repeatedly where the author is going.]
Research into this pattern shows that the bees navigate relative to the sun. Since the sun is so far from t he earth, over short time, the bee cannot see the sun's motion, even if the bee moves. (Humans often see a similar effect when driving; distant objects seem to move less than the signs near the road.) The bee can, therefore, use the sun as a fixed point and orient itself by maintaining a fixed angle between its line of flight and the line to the sun.
The sun, however, plays a greater role in the food gathering cycle. The dance language, which bees use to communicate, is also based on the location of the sun. When bees return from a food source, they perform a ``waggle dance'' on the vertical comb nearest the entrance to the hive. The dancing bee makes a short, straight run while waggling its abdomen, then circles back and repeats the action several times. The bee orients its dance so that the angle between the direction of the straight run and the ray opposite gravity is the same as the angle between the food source and the position of the sun  (see Figure 1). In this scheme, dancing straight up means ``fly toward the sun,'' and dancing straight down means ``fly away from the sun.'' Given this angle, other bees can orient themselves to the sun and locate the food source.
|Figure 1: Waggle dance orientation. The waggle dance is performed on a vertical section of comb in the hive. In (a) the straight portion of the dance is opposite gravity, indicating that other bees should ``fly into the sun.'' In (b) the dance is oriented at a right angle to gravity, indicating that other bees should ``fly with the sun to their left.''|
The sun's movement across the sky varies by location on the earth, season, and time of day. In the Northern Hemisphere, the sun appears to rise in the northeast and set in the northwest, but conversely, in the Southern Hemisphere, the sun rises in the southeast and sets in the southwest. This is a direct consequence of the earth's tilted axis. Even in the same hemisphere, the closer the observer is to the pole, the more of the sky the sun's path includes. Even more subtle is that the angular change in the sun's position is greater at midday than at sunrise and sunset. The function that describes the sun's position with time at a given latitude is called the local ephemeris function.
Given that bees do use the sun for navigation and communication, they must have a working sense of the ephemeris function. Bees usually only eke a few flights outside the hive before foraging, so if they learn the ephemeris, they must do it quickly. There are also experiments which limit the times of day that bees can see the sun and indicate that bees ``know'' where the sun is even at hours when they have never seen it. These facts combined with experimental data suggest that bees have an innate sense of the sun's motion which can be represented by a step function as shown in Figure 2. Moreover, zoologists observing flying bees throughout the day know that the bee's dances show a smooth transition through midday on overcast days when the bees cannot see the sun. This seems to imply that, with experience, the bees can refine this innate sense so that it accurately represents their particular ephemeris function.
From an evolutionary perspective, an innate, but adaptable sense of the ephemeris function makes sense. Since the sun plays such a crucial role in bee navigation, there is a selective advantage to having the basic features of the ephemeris function genetically encoded. At the same time however, the variations in the ephemeris over time and location almost requires adaptability so that today's bees can navigate under solar conditions that are different from those which their ancestors experienced.
|Figure 2: The ephemeris function. The vertical axis represents the compass direction of the sun, where 0°360° is north. Local solar time is defined to be 12 when the sun is highest in the sky. The heavy line, (a), represents the step function innate to bees. For comparison, (b) is a sample ephemeris from the Northern Hemisphere and (c) is a sample from the Southern Hemisphere.|
One interesting and current research goal is to model observed bee behavior on an understood physical system. If, for example, a computer chip was built that simulated the bees' patterns, there would be a sense that the bees' behavior, or at least the modeled portion, was well understood. At the same time, a good model should no be so complicated that the processes that drive it could not drive the bee. So, returning to the example, if the computer chip has comparable computing power to that of the human brain, it would not be a good model since bees do not have mental facilities of that magnitude.
Zoologists have modeled the behavior on a neural net.  The neural net takes several inputs at once and can light any grid square on axes like those shown in Figure 2. When functioning properly, the system should take a time input and light the square on the grid that falls on the ephemeris function line on the graph. The system works by varying the strength of the connections between input and output ``nodes''. When there is a strong connection between a given input node and a given output node, activating that input will activate the output; conversely, if there is a weak connection, activating the input node will not activate the output. It is possible to set the connection strengths so that the neural net will simulate the sun tracking capabilities of the bees.
While this neural net is successful in modeling, it lacks biological realism. Obviously no one sets the connections between the bees' nerve cells manually. They must "learn" it on their own. In this regard the neural net is only partially successful. The neural net will correct the strength of its connections in a manner that simulates learning if sample data is sent through and then the correct response is forced backward through the net, from output to input. The response of the network will converge to the correct answer after several such training sessions. On the one hand, this seems like a success for the network since it "learned" the pattern it needs, but further consideration shows that it was only able to do so because an outside agent, the experimenter, knew the correct answer, and forced a comparison with the given output. As a biological model, this is somewhat unsatisfying because it requires the animal to know the answer before she has learned it.
 von Frisch, Karl, Bees: Their Vision, Chemical Senses, and Language, Revised Edition (Cornell University Press, Ithaca, New York, 1971), p. 93.  von Frisch, Karl, The Dance Language and Orientation of Bees, translated by Leigh E. Chadwick (The Belknap Press of Harvard Press, Cambridge, Massachusetts, 1967), pp. 57-58.  Dickinson, Jeffrey, and Fred Dyer, "How insects learn about the sun's course; alternative modeling approaches," Animals to Animals: 4 Proceedings of SAB96, 193-203 (1996).  Dyer, Fred C., and Jeffrey A. Dickinson, "Sun-Compass Learning in Insects: Representation in a Simple Mind," Current Directions in Psychological Science 5, 67-71 (1996).  Adapted from Figure 4, Dyer and Dickinson, 1996.  Dyer and Dickinson, 1996.