Discrimination and representation of relative numerosity in a bisection task by pigeons

We trained 4 pigeons in a numerical bisection task to discriminate between pairs of keylight flashes with a ratio of 1∶3 (2 vs. 6, 4 vs. 12, and 8 vs. 24) that were presented in a sample phase. Responses to the blue key were reinforced after a sequence of a larger number of flashes, and responses to the white key were reinforced after a sequence of a smaller number of flashes. The intervals between flashes in the sample phase were randomized to attenuate the covariation of temporal cues with flash number. Pigeons responded accurately in each of the discriminations, with typically 85%–90% correct responses. Transfer tests showed that the proportion of large responses increased with number and performance generalized to larger values outside the training ranges. Psychometric functions superposed when plotted on a relative scale, and estimates of Weber fractions were approximately constant, suggesting that variability was scalar. However, contrary to previous research in nonhumans, bisection points were located at the arithmetic, not geometric, mean. Hierarchical logistic regressions confirmed significant control over responding by number beyond that attributable to temporal cues. These results show that pigeons are able to respond accurately in a relative numerosity discrimination with successively presented visual stimuli, although the nature of the numerical representation and response rule remains unclear.     

Scalar effects in the visual discrimination of numerosity by pigeons

Pigeons trained in a conditional discrimination procedure to respond to a visual array made a left or right choice, depending on which of two numbers of elements (i.e., anchor numerosities) the array contained. They were then tested with novel arrays at these anchor numerosities, as well as at interpolated and extrapolated numerosities. Various control conditions showed that the birds’ discrimination performance was primarily based on stimulus numerosity, and not on other factors, such as brightness or area. Results from a series of tests, spanning a wide range of numerosities, conformed to scalar principles. Psychometric functions showed superposition, indicating that Weber’s law applies to numerosity discrimination. The subjective midpoint between anchor values was at the geometric mean. Variability about this bisection point increased in proportion to the numerical value of the mean.     

Discrimination of geons by pigeons: The effects of variations in surface depiction

We explored how changes in the depiction of the surface features of a simple volume (a geon) affected the pigeon’s recognition performance. Pigeons were trained to make a different keypeck response to each of four computer-rendered single-geon objects. In Experiment 1, the pigeons were tested with images of the original stimuli in which the light source was shifted from its original position, as well as with silhouettes and line drawings of these objects. All three types of stimulus variations resulted in marked drops in performance: above chance for silhouettes and light-change stimuli, but at chance for line drawings. In Experiment 2, the pigeons were tested with images of the original stimuli in which the contrast levels were either increased or decreased. These transformations resulted in very small drops in performance (except for the complete absence of contrast-a silhouette). These results indicated that the pigeons attended to the shape of the outside contour of an object and to the relative brightness of an object’s surface contours.     

Recall of three-item sequences by pigeons

Pigeons were trained to recall an arbitrary sequence on a delayed matching-to-successive-samples (DMTSS) task. Sample items were presented successively and then displayed simultaneously. Subjects were required to respond to them in the order in which they appeared. In Experiment 1, pigeons responded correctly on 75% of the trials on a two-item DMTSS task but at a chance level of accuracy on a three-item task. In Experiment 2, pigeons who learned to produce a three-item sequence prior to DMTSS training mastered a three-item DMTSS task at a 75% level of accuracy. Control groups, trained initially with the same items on nonserial tasks, performed as poorly on a three-item DMTSS task as the naive subjects of Experiment 1. It was hypothesized that pigeons that first learned to produce a three-item list were able to recall three-item samples in DMTSS because they had learned to represent three-item sequences.     

Categorical color coding by pigeons

Pigeons were trained on two independent tasks. One involved red and yellow hues, the other involved blue and green hues. For half of the birds, the two tasks were the same (i.e., both tasks were either matching-to-sample, or oddity-from-sample). For the remaining birds, the two tasks were different (i.e., one task was matching-to-sample; the other task was oddity-from-sample). Following acquisition, the pigeons were exposed to test trials on which either the correct or the incorrect comparison hue was replaced with one of the hues from the other task. On yellow-sample trials and on green-sample trials, the pigeons performed as if they had a common code for yellow and green. When there was one comparison available that was appropriate to the “yellow/green” code, performance remained high; but when either both comparisons or neither comparison was appropriate to the “yellow/green” code, performance dropped. The pigeons also tended to code red samples as green and to code blue samples as yellow. The results indicate that pigeons can categorically code colors under conditions that rule out a failure to discriminate among the colors.     

Prospective and retrospective timing by pigeons

Pigeons discriminated between two pairs of durations: a short set (2.5 and 5 sec) and a long set (5 and 10 sec). The pairs were intermixed within sessions and identified by the colors on the signal and choice keys. Once the task was learned, the pigeons experienced the following three conditions seriatim: (1) The signal key was made ambiguous about the test change, but the choice keys were informative (retrospective); (2) the signal key identified the test range, but the choice keys did not (prospective); (3) probe trials were introduced in which the color of the center key signaled one test range, but the color of the choice keys signaled the other test range (inconsistent). Accuracy of choice decreased in the retrospective condition and, returned to baseline levels, was higher under the prospective condition than under the retrospective condition. In a final condition, referred to as conflict trials, the center-key color signified one test range and the choice-key colors the other range. The results from these conflict-inconsistent tests indicate that choice behavior was largely controlled by the signal-key color and not by the choice-key color. We relate these findings to different approaches to timing in animals.     

Stereotyped adjunctive pecking by caged pigeons

The behavior of 77 pigeons maintained at 80% of their free-feeding weights in open-wire battery cages was monitored 16 times a day by observers for up to 285 days. Five distinct types of stereotyped behaviors were operationally defined. One of these behaviors, “spot pecking,” clearly predominated. Forty-nine of the 77 pigeons were observed spotpecking on at least 25% of the days they were observed, and several pigeons emitted more than 50,000 spot pecks per day. This occurred in spite of the total absence of any explicit reinforcer. A series of three experiments demonstrated that the great majority of spot pecks occurred in the hours immediately after feeding, that only food-deprived birds spot pecked, and that the behavior of adjacent birds influenced the rate of acquisition of stereotypes. Difficulties with labeling spot pecking as superstitious, respondent, or mediating are discussed. It is suggested that spot pecking be classed as an “adjunctive” behavior.     

Oddity of visual patterns conceptualized by pigeons

Pigeons were trained to learn an instrumental oddity-from-sample discrimination involving visual forms. One group, the “few examples” group, dealt with 5 patterns in 40 different combinations. Another group, the “many examples” group, dealt with 20 patterns in 160 different combinations. After both groups had reached asymptotic performance and had learned to operate under partial reinforcement conditions, they were tested for transfer under extinction conditions with two different groups of 5 novel patterns, each in 40 combinations. All animals showed significant above chance transfer to both of these novel stimulus sets. Transfer performance with test stimuli of similar geometric design to training stimuli was better than performance with stimuli of markedly different design. The transfer performance of the “many examples” group was marginally better than that of the “few examples” group, even though the latter’s performance on the training stimuli was better throughout. It is concluded that pigeons can learn to employ an oddity concept and that this may be promoted by the use of many training exemplars. Furthermore, it is inferred that pigeons may normally use a mixture of strategies to solve oddity and identity problems.     

Strategic aspects of children’s numerosity judgement

A previous study (Luwel, Verschaffel, Onghena, & De Corte, 2000) revealed that 2^nd and 6^th graders use at least 3 different kinds of strategies for determining different numerosities of blocks presented in square grids: (a) an addition strategy by means of which (groups of) blocks are counted (and added), (b) a subtraction strategy in which the number of empty squares is subtracted from the total number of blocks in the grid (i.e. the anchor), and (c) an estimation strategy, whereby the number of blocks is determined in a quick but imprecise way. Although 6^th as well as 2^nd graders used the clever subtraction strategy, the majority of 2^nd graders had serious trouble with the correct determination of the anchor, resulting in huge numerosity judgement errors. Since this finding seriously complicated the testing of a number of hypotheses in that study, we replicated the above study but presented the children information about the grid size. This manipulation led to a substantial increase in the proportion of appropriate subtraction strategy users and made it possible to investigate the effect of several subject and task variables on the frequency, accuracy, and adaptiveness with which the different strategies were applied. Results are discussed in terms of the conceptual framework of Lemaire and Siegler (1995) regarding strategic change.     

Stimulus stringing by pigeons: Conditional strings

Pigeons were trained to produce one serial list in the presence of a green background cue and another serial list in the presence of a red background cue when the items for both serial lists were presented on each trial. This demonstrated a combination of serial learning and conditional discrimination learning not previously shown in pigeons. Specifically, when presented with four geometric forms, A B C D, in random locations of a five-key display, the pigeons learned to peck A B C when the background was green and A B D when the background was red. Accuracy on the conditional string ranged from 73% to 85%. Transfer tests using different locations of the stimuli on the keys showed positive transfer, thus ruling out learning of specific locations as the basis of the accurate performance. Above-chance performance was maintained when the conditional colors were presented only on the key that did not contain one of the serial stimuli. The results are interpreted in terms of a chaining model that postulates that the sequential selections were controlled by cues produced by both onset of the trial and prior selections within the trial.     

Time-of-day discrimination by pigeons,Columba livia

Pigeons were trained to discriminate between four keys. One provided food in the mornings, another provided food in the afternoons, and two never provided food. Three experiments were performed to determine whether pigeons could track food availability over a 24-h period. All the subjects appeared to demonstrate time-place associative learning. A fourth experiment was designed to investigate the mechanisms underlying the timing behavior. Lights-on time was shifted back by 6 h, and no decrease in performance was found during the first session following the phase shift. This suggests that a circadian type of timing mechanism with a self-sustaining oscillator mediates time-place learning over a period of 24 h. Further support for this notion was found in a fifth experiment, in which the subjects were tested in constant dim light. In that experiment, the subjects’ continued correct responding provides additional support for a self-sustaining circadian timer.     

Categorical discrimination of objects and pictures by pigeons

With a three-choice instrumental discrimination procedure, pigeons were taught to distinguish small spherical objects from nonspherical objects. Spherical objects were defined as positive, nonspherical objects as negative. A device allowing an automatic presentation of the stimuli was employed. The subjects actually pecked the objects, and grain rewards were presented directly beside the correct objects. Acquisition was rapid, with the birds reaching a criterion of 80% correct choices within less than 150 trials. There was evidence that more than 200 objects were remembered individually over 3 months. Pigeons transferred the discrimination of spherical/nonspherical objects to novel objects. The criteria by which the birds judged the sphericity of objects seemed to be similar to those applied by humans. They could apply the categorization in a relational manner and generalize it to apply to photographs and drawings of objects. The categorization competence was retained for at least 3 months.     

Value transfer in concurrent-schedule discriminations by pigeons

When pigeons are trained on a discrete-trial simultaneous discrimination, some of the value associated with the positive stimulus appears to transfer to the negative stimulus (Zentall & Sherburne, 1994). Pigeons preferred a negative stimulus that had been discriminated from an always-positive stimulus (S+) over a negative stimulus that had been discriminated from a sometimes-positive stimulus (S±). A very different finding (suggestive of transitivity of preference or contrast) was reported by Belke (1992). On concurrent probe tests of stimuli associated with equal variable interval (VI) schedules but originally trained in alternative concurrent pairs (one with a richer schedule, the other with a poorer schedule—VI 20 sec vs. VI 40 sec and VI 40 sec vs. VI 80 sec), the stimulus originally paired with the poorer schedule was preferred. But Belke’s results may have been obtained because the pigeons had been trained to peck the VI 40 sec paired with the poorer schedule and they had been trained not to peck the VI 40 sec paired with the richer schedule. In the present experiment, we avoided this bias by training pigeons on two concurrent schedules in which the tested stimuli both had been associated with the poorer schedule of the pair [A(VI 20 sec) vs. B(VI 80 sec) and C(VI 40 sec) vs. D(VI 80 sec)]. Evidence for value transfer was demonstrated when on probe trials pigeons preferred B over D.     

Pigeons’ serial ordering of numerosity with visual arrays

Pigeons were trained in a conditional discrimination paradigm to differentiate successively presented visual arrays according to the relative number of their elements. Transfer tests with novel stimuli demonstrated that they discriminated the categories of “many” (6 or 7) from “few” (1 or 2) items. In further tests, other new stimuli were introduced that consisted not only of these training numerosities, but also of the intervening ones (3, 4, and 5). Variations in the birds’ discrimination performance corresponded to the order of stimuli on a numerosity dimension. This serial ordering was maintained when other factors such as brightness, size, shape, area, and contour of the elements were systematically controlled across tests. Smaller numerosities were somewhat better discriminated than those at the higher end of this test range.     

Association of conditioned stimuli during serial conditioning by pigeons

CS2-CS1-US autoshaping was given to hungry pigeons and evidence of CS2-CS1 association was sought. Pigeons pecked that key of a two-key compound CS2 located where the upcoming CS1 key light was to occur. Such CS2-CS1 association was: (1) quickly acquired, (2) quite durable, and (3) stronger with simultaneous than with successive discrimination tasks.     

Processing of conflicting and redundant stimulus information by pigeons

Selective attention in processing of visual information by pigeons, trained on alternating sessions with two colors (red and green) and two forms (a diamond and an X shape) differentially associated with a left—right key choice task, was examined. A color and a form were presented together on probe trials during sessions in which, on other trials, only one of the dimensions, color or form, was shown. The dimension in effect on the surrounding trials had no influence on choice when the information provided by the two dimensions on probe trials was in conflict—color correct for one choice and form for the other. When both color and form redundantly cued the correct choice, there was no increase in accuracy in comparison with that associated with one dimension. Following separate training on the color and form discriminations, pigeons appeared to base their choices on color on some trials, on form on other trials, but not on both simultaneously. These findings are discussed in terms of an exemplar model of information processing.     

Spontaneous focusing on numerosity and the arithmetic advantage

Children show individual differences in their tendency to focus on the numerical aspects of their environment. These individual differences in ‘Spontaneous Focusing on Numerosity’ (SFON) have been shown to predict both current numerical skills and later mathematics success. Here we investigated possible factors which may explain the positive relationship between SFON and symbolic number development. Children aged 4–5 years (N = 130) completed a battery of tasks designed to assess SFON and a range of mathematical skills. Results showed that SFON was positively associated with children's symbolic numerical processing skills and their performance on a standardised test of arithmetic. Hierarchical regression analyses demonstrated that the relationship between SFON and symbolic mathematics achievement can be explained, in part, by individual differences in children's nonsymbolic numerical processing skills and their ability to map between nonsymbolic and symbolic representations of number.     

A bottlenose dolphin discriminates visual stimuli differing in numerosity

A bottlenose dolphin was trained to discriminate two simultaneously presented stimuli differing in numerosity (defined by the number of constituent elements). After responding correctly to stimuli consisting of three-dimensional objects, the dolphin transferred to two-dimensional stimuli. Initially, a variety of stimulus parameters covaried with the numerosity feature. By systematically controlling for these stimulus parameters, it was demonstrated that some of these attributes, such as element configuration and overall brightness, affected the animal’s discrimination performance. However, after all the confounding parameters were under control, the dolphin was able to discriminate the stimuli exclusively on the basis of the numerosity feature. The animal then achieved a successful transfer to novel numerosities, both intervening numerosities and numerosities outside the former range. These findings provide substantial evidence that the dolphin could base his behavior on the numerosity of a set independently of its other attributes and that he represented ordinal relations among numerosities.     

The nature of the response in simon discriminations by pigeons

Spence (1952) postulated that under some conditions, responding in simple discriminations is controlled by compounds or patterns consisting of the nominal discriminative cue, plus its spatial position. Stimulus control by such compounds was said to develop when no single cue or element was systematically reinforced more than any other. This analysis has been applied to good effect in understanding some peculiar accuracy results obtained from pigeons performing Simon discrimination tasks. This article describes how Spence's cue-position analysis provides a better account of pigeons' performance in this task than do nominal cue-only and configurational views of the functional discriminative stimuli. Adding a value transfer assumption improves the ability of the cue-position hypothesis to account for the accuracy data.     

Matching-to-sample performance by pigeons trained with visual-duration compound samples

Pigeons were trained on duration matching-to-sample in which each of four combinations of signal type (red or white light) and duration (2 or 10 see) was mapped onto a different choice stimulus. Probe trials in Experiments 1 and 2 involved a successive presentation of two duration samples. In each experiment, birds tended to summate two durations when the same signal was presented twice, but not when two different signals appeared. These results contrast with those reported by Spetch and Sinha (1989), who found a summation effect with both same-signal and different-signal compounds. In Experiment 3, pigeons chose among two alternatives which were both associated with the duration of the sample but of which only one was also associated with the signal type of the sample. Pigeons systematically chose the stimulus that matched both sample duration and signal type. The implications of these findings are discussed in terms of transfer of training and coding of event duration.