Experimental approaches to studying numerical competence in animals

The earliest attempts to find experimental evidence of numerical abilities in animals belong to Kinnaman (1902) and Porter (1904). They used similar experimental procedures. Porter (1904) tested response of house sparrows to numbers by hiding food under, say, the third container in a row, then recording which container a bird flew to first on repeated trials. Then he changed the number of the baited pot and tested the birds’ ability to redirect its choices. After extensive testing, Porter concluded that the sparrows based their choice on the relative distance of the baited container from the end of the row. Kinnaman (1902) examined two rhesus monkeys. He aligned 21 boxes and trained monkeys to choose the boxes in the requested order. One of Kinnaman’s subjects successfully mastered this task and searched bait in six positions, whereas the second subject learned to search a goal only within three last positions after many attempts. For comparison, Kinnaman trained two children to solve the same task using marbles as rewards. The eldest child of five years old demonstrated the same results as the “retarded” monkey; the younger child of three years was able to find the marbles only in the first two boxes. The similar procedure has been applied then for studying many species and brought contradictory results. For example, chimpanzees have shown great individual differences in their ability to solve such a simple task as searching for a reward in a second box from a proximal point. Some of them never solved this problem whereas raccoons, skunks, martens, and pigs did not find any difficulties in mastering this task (see: Boysen, Hallberg, 2000 for a review).

Another set of early studies of counting in animals was based on matching-to-sample paradigm. The results obtained by different species were rather modest. For example, Ladygina’s pupil Ioni, a chimpanzee, with whom we have already met many times in this book, hardly distinguished “one” and “two” stimuli during matching-to-sample procedure. It took hundreds and even thousands trials for teaching monkeys, rats and raccoons to distinguish between a card with one circle and another one with two circles. Obviously measurement capabilities of the methods applied were limited rather than numerical competence of animals.

The first real progress was made in this field by Otto Koehler (1941, 1956). He established a number of experimental paradigms and applied them for studying counting, such as simultaneous or successive stimulus presentation, as well as matching-to-sample and oddity matching procedures. The experiments were performed on a variety of animals, including squirrels, pigeons, jackdaws, a raven, an African Grey parrot, and budgerigars. These experiments had been so much appreciated that historical development of this field was subdivided in pre-and- post- Koehler developments.

Koehler concluded that animals have two basic numerical abilities. One, based on a visual-spatial sense, enables them to assess the number of items presented simultaneously in a group, while the other allows them to assess the number of events that occur successively, or spread out in time (see: Emmerton, 2001, for a detailed description). Below we will consider the main training procedures elaborated by Koehler for studying these abilities. Many of these procedures are included into modern experimental techniques.

In one series of Koehler’s experiments pigeons were trained to approach a strip of cardboard on which there were two sets of grain that differed in number. A bird had to choose the set containing a particular amount (e.g., 4 grains) and was allowed to eat this set as a reward. To prevent it eating the other set (of say 3 grains), Koehler shooed the bird away if it reached toward the incorrect group. At different stages of training, the correct set sometimes contained the larger and sometimes the smaller number of grains. The experimenter hid behind a screen, out of sight of the bird. The punishment of shooing a bird away was delivered in a standardised fashion by a mechanical device. The reactions of the birds were filmed to provide an objective record of their behaviour.

Another series of experiments were based on a matching to sample task. After looking at an array of blobs on a " sample" card, the subject had to remove the lid from one of two pots in order to find a hidden food reward. On each lid was a different array. A correct choice, which led to reward, was to remove the lid with the same number of marks as on the sample card. Jacob, a raven, was particularly successful on this task. He could match the numbers of items on the sample card and the comparison lid even when the configuration of blobs and their sizes differed (both between and within trials), so that the only common feature was their number. One of jackdaws was correct in its matching behaviour when the patterns of the blobs differed between the card and the numerically matching lid, but its choices were not statistically reliable when the blob sizes varied. In this case, as Koehler recognised, the bird’s performance did not guarantee that it was discriminating solely on the basis of the equality of numbers. Instead, it could have been comparing the overall areas of the stimulus marks on the card with those on the lids.

Other studies were aimed at birds’ ability to " act on number", as Koehler put it, i.e. to respond sequentially until a specific number of items had been obtained or events had been completed. For instance, pigeons and budgerigars were trained to eat only a given number of seeds from a much larger number they saw. So if they were required to take exactly 4 seeds their behaviour was scored as correct if they walked away after eating the fourth food item, but they were automatically shooed away if they tried to eat a fifth item. The accuracy of their performance was tested on trials in which this mild punishment was withheld.

It is of particular interest how birds behave overstepping the limits. For instance, a pigeon ate the fifth – allowed – seed and then slowly and warily sneaked to steal the sixth, then quickly gasped it and rushed away flapping the wings. Such expressive behavioural cues were later collected from many studies on a wide variety of species as “behavioural indicators” of counting in animals (Krachun, 2002).

In another experiment with pigeons, peas were delivered one at a time down a chute into a large dish. In this experiment, the time interval between deliveries was randomly varied to prevent the birds estimating the total time that had expired, rather than the number of items taken. Koehler also argued that it was the number of peas, rather than the number of pecks, or the pecking rhythm that was important since the pigeons often had to peck several times at a rolling pea before they could grasp it.

The following series of experiments expressively illustrate bird’s capacity to “act on number”. With jackdaws, the task consisted of taking the lids off boxes until a specific number of hidden food items had been retrieved. An important feature of this experiment was that on successive trials, the same number of food items was differently distributed. There were both filled and empty boxes in the row. The bird had to open boxes until it found the allowed number of food items. For instance, it had to stop after finding the fifth item irrespective of how many boxes were opened. Some birds were able to manage up to four tasks simultaneously. One subject was taught to lift black lids until two items had been found, green lids until three items had been found, red ones to find four, and white ones to find five items. Expressive behaviour of one jackdaw was of significant interest. This bird was taught to open lids until five items had been found. When found four items, it returned to the first box (that was empty now) and made a low bow in front of it. Then the bird made two bows near the second box (in which two items were found) and one bow in front of the third; after that the jackdaw returned to searching in order to find the fifth item. This interesting case enabled Koehler to suggest that birds are able to “act on six” rather than “count to six”.

From these and other studies, Koehler concluded that birds have at least a limited ability to discriminate objects or events on the basis of their numerosity and inferred that animals have some way of internally tagging the items they have seen or responded to. Koehler was careful to say that animals do not seem to count in the way that an adult human might by precisely enumerating items with a fixed series of symbolic labels (e.g. one, two, three, and four). Rather, he argued that animals learn what he called " unnamed numbers", so that four items might be represented by a series of inner marks or tags. He also noted that different species showed remarkable similarities in the limits to their ability to discriminate numerosity. However, for most species, the accuracy of performance broke down when the number of items or events they had to respond to was between 5 and 6, or 6 and 7 (Koehler, 1956).