Numerocity discrimination and estimation in animals

Animals estimate numbers. Numerosity discrimination requires only relative or ordinal judgments. For instance, a bird must show that it perceives one stimulus as having " more" items compared with the other that has " less", or one consists of " many" elements while the other has " few". However, with these relative judgments the animal does not necessarily have to recognize the precise number of elements in a stimulus.

Thomas and Chase (1980) claimed that they ruled out the hypothesis of subitizing in squirrel monkeys based on the fact that the subjects accurately distinguished numerosities of 7 from 8. It was later proposed (Thomas et al., 1999) that the monkeys may have performed some kind of prototype matching that involved building prototypes from experience with different stimuli and then identifying novel stimuli by how closely they correspond to those prototypes. In other words, the monkeys constructed specific “number-prototypes” basing on their individual experience and used them to match with novel quantitative stimuli.

There is a growing body of evidence for effective functioning of the number estimation system in non-human animals. Let us consider here two examples concerning birds. Emmerton et al. (1997) used a conditional discrimination procedure to study pigeon’s ability for estimation. First, a bird had to peck at a visual array that was shown on a centre key. If the array contained " many" items (6 or 7) then the pigeon had to peck at one of the side keys (e.g. the right-hand red-lit one) to obtain a food reward. If instead the centre array contained “few" items (1 or 2) then the correct response was to choose the other side key (e.g. the left-hand green-lit one). Incorrect choices led to a timeout period of waiting several seconds in the dark (“punishment”). As it was elaborated in Koehler’s procedures described above, several tests were conducted in this experiment to make sure that the birds really discriminated the numbers of items in the arrays, rather than detecting some other confounds. A variety of these arrays containing 1, 2, 6 or 7 items were shown until the birds had learned to discriminate accurately between " many" and " few" items. Then they were tested not only with new versions of the " many" and " few" stimuli, but also with arrays consisting of the intermediate numbers 3, 4 and 5. These numbers were completely novel to them. Most of the " many" choices were made when the centre test-array contained 6 or 7 elements, and the least choices when the array consisted of 1 or 2 items. In this respect the birds treated novel arrays as they had the familiar training stimuli. When the intermediate numbers were shown, the birds’ choices were distributed in an orderly fashion. Compared to their responses with arrays of 6 or 7 items, they made slightly fewer choices of the " many" key when the test-array contained 5 items, fewer when it had 4 items in it, and fewer still when there were 3 items. This distribution of choices indicates that pigeons can serially order numerical quantities.

In Smirnova et al’s (2000) experiments four crows were trained to choose the greater array of elements in the range 1-12. All birds demonstrated high accuracy of comparison. They chose the greater arrays in 75.3+2.4% including under the minimum difference between the compared arrays (Fig. VI-11). Researchers conclude that upper limit of the range, within which the crows are able to compare namely numerical attributes of arrays are close to 20.

In experiments of Kilian et al. (2003) a bottlenose dolphin was required to estimate numbers of visual stimuli and to choose a set containing more items versus less items. The dolphin was asked to discriminate simultaneously presented numbers of visual stimuli, basing on two-choice discrimination. For each trial, two floating hoops with a defined number of objects were hung from the hooks at the side of the dolphin’s tank. The dolphin remained at the opposite wall, holding his head out of the water. A short whistle blow was the starting signal for the dolphin to swim toward the stimuli. Noah made his choice by touching one object of one of the arrays with the tip of his snout. During the first phase, only the numerosities 2 vs. 5 were presented. With the first stimuli used, a number of parameters, such as type, size, and configuration of stimulus elements, varied with the number feature. After responding correctly to stimuli consisting of three-dimensional objects, the dolphin transferred to two-dimensional stimuli. New number pairings were presented in catch (non-reinforced) trials. All possible pairings were tested such as 3 vs. 5, 2 vs. 3, 4.vs. 5, and so on. The high performance with numerosity pairings provides substantial evidence that the dolphin represented ordinal relations.

Animals judge proportions It is a natural suggestion that animals have some ideas about quantity of things in dependence of their dimensions. For instance, food quantities differ not just as a result of the number of edible items available but also because of their sizes, volumes, weights, etc. Woodruff and Premack (1981) examined how chimpanzees understand relations between proportions and volumes basing on one of Piaget’s tests. Subjects were presented with beakers filled with water for 25%, 50%, 75% и 100%, and with paper circles that were correspondingly shaded for 25-100%. The task was to match proportions and volumes, that is, to cover a quarter-filled beaker with a quarter-shaded circle. In psychological experiments children master this task quite well at four. One adult and four juvenile subjects were tested and the adult coped with the task quite well.

Pigeons were also shown to be able to estimate differences in proportions. Emmerton (2001) trained pigeons to discriminate differences in colour proportions within horizontal bars composed of continuous blocks of colour. They were then tested under a variety of conditions to see if they still responded accurately to differences in the relative quantity of colour when the stimulus displays were altered. Initially, the pigeons learned to discriminate between a red and a green horizontal bar when these two stimuli were presented simultaneously on a computer monitor. The “correct” colour was counterbalanced across birds. Responses were sensed by a touch screen, and a peck to the correct colour led to a food reward. Then the proportion of the two colours was varied in both stimuli. If a bird chose the bar with the greater proportion of the ‘correct’ colour (e.g. red in the following stimulus examples), it was rewarded. If it chose the bar with the complementary lesser proportion of “correct” colour a timeout period (“punishment”) followed. If the proportion of red to green was equal in both bars, one of the stimuli was arbitrarily programmed to be the correct one but the bird had to guess which one it was. The accuracy with which the birds discriminated the paired bars was correlated with the colour proportions in the bars. When there was no difference in proportion, their performance was at chance level. The new experiment used stimuli consisting of continuous areas of colour. In this case, proportion was no longer equated with the relative numerosity of component items but the results of both experiments were very similar: as the difference in the proportion of coloured areas or discrete items decreased so did the accuracy of the birds’ discrimination. In one part of the study, the birds were presented not with paired horizontal bars but with arrays of small red and green rectangles.