Spatial generalization in honeybees confirms Shepard's law

Abstract

In stimulus generalization, a subject that has learned to respond to one target stimulus also responds to other similar stimuli. Shepard's law of generalization states that probability of responding decreases exponentially with psychological distance between test and target stimuli (Shepard, R.N., 1987. Toward a universal law of generalization for psychological science. Science 237, 1317–1323). In experiments on spatial generalization, honeybees were trained to find a target at a location near one principal landmark, and then tested with the target at different locations. A theoretical scale of positional mismatch between test and target locations was computed by a weighted sum of discrepancies between test and target locations in the compass direction (0.25 weight) and size (angle) of projected retinal height (0.375 weight) and width (0.375 weight) of the landmark, derived from the model of Cartwright and Collett (Cartwright, B.A., Collett, T.S., 1982. How honeybees use landmarks to guide their return to a food source. Nature 295, 560–564; Cartwright, B.A., Collett, T.S., 1983. Landmark learning in bees. J. Comp. Physiol. A 151, 521–543) of landmark use in honeybees. Based on the theoretical scale, but not on physical distance, Shepard's law fit data from four experiments, the first time it has been confirmed in an invertebrate.

Introduction

After learning to make a particular response in one stimulus situation, an organism will also make the response to different but similar stimuli, a ubiquitous phenomenon known as stimulus generalization. Experimentally, generalization is studied by first training a subject to perform a response in one stimulus situation (the S+). Unrewarded tests are then given with a range of stimuli, including the S+. One or few dimensions of the stimulus situation are varied, and the amount of responding the organism makes to each stimulus recorded. In general, the more different the test stimulus is from S+, the lower the responding (e.g. Guttman and Kalish, 1956, Shepard, 1958a, Shepard, 1958b, Shepard, 1965, Shepard, 1987, Nosofsky, 1986).

Based on mechanistic and functional considerations, (Shepard, 1958a, Shepard, 1958b, Shepard, 1965, Shepard, 1987) formulated a law of generalization. A generalization gradient should have an exponential shape as a function of the psychological distance between the test stimulus and S+. The equation for the universal law is y=exp(−kx), where y is a measure of the amount or probability of responding relative to responding at S+, k is a scaling parameter for psychological distance, and x is the psychological distance between the test stimulus and S+. The psychological scale is in general different from the physical scale along which a stimulus dimension is varied. It is also important to note the conditions under which the law is said to hold (Shepard, 1986). The stimuli tested in generalization must be clearly discriminable to the subject. A lively discussion on this issue indicates that the shape of the generalization gradient may turn out Gaussian if the subject has difficulty discriminating stimuli (Nosofsky, 1986, Shepard, 1986, Shepard, 1988, Ennis, 1988, Nosofsky, 1988). Ideally, on generalization tests, no feedback is given, so that the subject is not learning about the new stimulus, but responding on the basis what has been learned about S+.

When the stimuli are clearly discriminable, the task of generalization is to classify which stimuli belong in the same class as the S+, same when it comes to the consequences for the response in question. The functional grounds for the law is that the structure of the world, when it comes to the probability that two stimuli belong in the same class, is likely to reflect the exponential function (Shepard, 1987). Mechanistically, Shepard (1958a)conceived of the generalization process as one of spreading activation along a topographically ordered set of mental units corresponding to a psychological scale of some stimulus dimension. When an S+ is encountered, the unit corresponding to S+ is activated to some level above zero. Over time, however, the activation spreads to neighboring units, and the distribution of activation over units is assumed to take a Gaussian shape peaking at S+. The Gaussian distribution becomes flatter over time. With repeated encounters of S+, we end up with an average of numerous Gaussian distributions of different standard deviations. Such a function is likely to have an exponential shape over the set of units, and hence over the psychological scale.

Other models based on the spread of activation can produce an exponential shaped generalization gradient as well (Staddon and Reid, 1990, Cheng et al., 1997). The shapes generated by these models, however, depend on the conditions. Gradients other than the exponential function may also be generated. A model based on the sharing of features between test stimuli and S+ also generates the exponential shape, if configurations of features count as well as elements in the similarity measure (Gluck, 1991).

Shepard (1987)presented 12 data sets supporting his law of generalization. None of the data, however, were based on invertebrates, and none on varying a dimension of spatial location. Spatial generalization has been tested on one species, the pigeon, with mixed results for Shepard's law (Cheng et al., 1997). This study represents the first test of Shepard's law on an invertebrate, the honeybee.

In testing the law, the psychological scale must be derived. Multidimensional scaling is one way to do this (Shepard, 1965, Shepard, 1958b, Shepard, 1965, Shepard, 1987). A number of overlapping generalization gradients with different S+s are obtained. The spacing along the physical scale is then adjusted by multidimensional scaling to render the gradients as similar as possible when their S+s are lined up. The resulting scale is taken to be the psychological scale, and the form of their common gradient the generalization function. It is this function that Shepard (1958a), Shepard (1958b, 1965, 1987)found to be exponential in shape. In this study, I took a different approach and derived the scale of space for honeybees from the theory of how they use landmarks in search of a location (Cartwright and Collett, 1982, Cartwright and Collett, 1983, Cheng et al., 1986, Cheng et al., 1987, Collett and Baron, 1994). The scale is specified in physical terms of mismatch with no free parameters in scale adjustment. Finding exponential generalization gradients would support at once both the theory of landmark use in honeybees and Shepard's law.

Four experiments were run. In each experiment, honeybees were trained to find a bottle capful of sugar water at the same location on a table (S+). After learning the task, they were tested occasionally with the cap, now containing tap water, at a number of locations, including S+. Because the number of unrewarded tests was small compared with the number of training trials, it is reasonable to assume that behavior is based mostly on what the bees had learned about S+. Across experiments, the salience of the target that was moved was manipulated, in order to create generalization gradients of different steepnesses. All these gradients were then fitted to the theoretical scale of mismatch, as explained fully below. I expected that the more salient the target was relative to unmoved landmarks, the shallower the generalization function.