Hank Davis

Numerical competence in animals: Definitional issues, current evidence, and a new research agenda

Numerical competence is one of the many aspects of animal cognition that have enjoyed a resurgence of interest during the past decade. Evidence for numerical abilities in animals has followed a tortuous path to respectability, however, from Clever Hans, the counting horse, to modern experimental studies. Recent surveys of the literaturereveal theoretical as well as definitional confusion arising from inconsistent terminology for numerical processes and procedures. The term “counting” has been applied to situations having little to do with its meaning in the human literature. We propose a consistent vocabulary and theoretical framework for evaluating numerical competence. Relative numerousness judgments, subitizing, counting, and estimation may be the essential processes by which animals perform numerical discriminations. Ordinality, cardinality, and transitivity also play an important role in these processes. Our schema is applied to a variety of recent experimental situations. Some evidence of transfer is essential in demonstrating higher-order ability such as counting or “sense of number.” Those instances of numerical competence in which all viable alternatives to counting (e.g., subitizing) have been precluded, but no evidence of transfer has been demonstrated might be described as “protocounting.” To show that animals are capable of “true” counting future research will have to demonstrate generality across situations.

Transitive inference in rats (Rattus norvegicus).

Although Piagetian theory proposes that the ability to make transitive inferences is confined to humans above age 7, recent evidence has suggested that this logical ability may be more broad based. In nonverbal tests, transitive inference has been demonstrated in preschool children and 2 species of nonhuman primates. In these experiments, I demonstrate evidence of transitive inference in rats (Rattus norvegicus). I used an ordered series of 5 olfactory stimuli (A < B < C < D < E) from which correct inferences were made about the novel B versus D pair. Control procedures indicated that performance did not depend on the recency with which the correct answer was rewarded during training and may be disrupted by the addition of logically inconsistent premises (F > E and A > F). The possibility that logical transitivity may reflect a form of spatial paralogic rather than formal deductions from a syllogistic-verbal system is discussed.

Discrimination of the number three by a raccoon (Procyon lotor)

This paper reports the establishment of a discrimination based upon the number three in a male raccoon. Following a 6-month training period, the subject was able to select a clear Plexiglas cube containing 3 objects (grapes or small metal bells) from an array of cubes containing 1, 2, 3, 4, and 5 items. The results confirm previous reports of “intelligence” in the raccoon, and extend the number of species in which sensitivity to number has been demonstrated (see review by Davis & Memmott, 1982).

Why humans value sensational news: An evolutionary perspective

Abstract Although it draws nearly universal disdain, sensational news continues to attract a wide audience for reasons that are not fully understood. We examined sensational front-page newspaper stories from eight countries, published between 1700 and 2001. The 736 stories that we collected were sorted thematically, and 12 categories emerged. An analysis of the frequency of stories within these categories demonstrates relative stability in their ranking over time and place, suggesting that the content of sensational news is not socially constructed. The categories that emerged correspond to major themes in evolutionary psychology (e.g., altruism, cheater detection, reputation, treatment of offspring). We propose that, like gossip, sensational news stories may trigger an evolved tendency to attend to categories of information that increased reproductive fitness in the Environment of Evolutionary Adaptedness (EEA).

Autocontingencies: Rats count to three to predict safety from shock

Following training on a variable-interval food-reinforcement schedule, rats were exposed to three unsignaled shocks during each 30-min session. Although leverpressing was initially suppressed, responding was significantly accelerated following offset of the third shock, regardless of when in the session it occurred. Control sessions in which only two shocks were programmed, one early and one late, did not yield baseline acceleration. Evidence of “counting to three” was less obvious in subjects simultaneously exposed to a temporal autocontingency, that is, for which each shock also predicted a minimum 3-min safety period. The addition of a signal prior to each shock eliminated evidence of counting behavior altogether. We conclude that rats may be taught to count, but such behavior is highly unnatural and may be blocked or overshadowed by more salient sources of information.

Numerical discrimination by rats using sequential auditory stimuli

Three rats were trained under a discrimination procedure in which responding was reinforced only following the repeated presentation of three bursts of white noise (S+). S− consisted of presentations of either two or four bursts of noise. All animals responded significantly more in the presence of S+ and, in two cases, showed lower response rates to both “2” and “4” stimuli. Responding by the third animal revealed differentiation between S+ and the stimulus “2,” but no reliable suppression to stimulus “4.” The present instances of discriminative control by the stimulus “3” replicate Fernandes and Church’s (1982) demonstration of control by sequential auditory stimuli in the rat. Moreover, because the present procedure involves adjacent S− values both greater as well as less than S+, these results extend our knowledge of the rat’s abilities with sequential auditory stimuli: Rats are capable of making intermediate numerical discriminations based upon something other than a simple many-versus-few dichotomy.

Human-based social interaction can reward a rat’s behavior

Rats were trained to leverpress in a conventional operant test chamber; however, their behavior was rewarded solely by social interaction with a human being. This training was successful for half the subjects tested; success was confined to animals for which social interaction had occurred prior to training. Similar findings with other species are discussed. Although the effects of social interaction with a human are by no means as robust as those of food to a hungry animal, the present results suggest that the human-rat interaction may be a positive adjunct to conventional behavioral training techniques, and a possible confound where its effects are uncontrolled.

The description and analysis of conditioned suppression: A critique of the conventional suppression ratio

It is argued that the conventional A/(A+B) ratio is an inappropriate tool for both the description and analysis of conditioned suppression. Conditioned suppression is a procedure that generates two separate dependent variables that cannot be meaningfully collapsed into a single index. Using a relatively simple experiment, we demonstrate that the procedure typically (1) suppresses responding during the CS and (2) generates a U-shaped function in the recovery of baseline responding. These reliable shifts in baseline rate confound the interpretation of the suppression ratio. It is further argued that comparison between individuals or groups of cases using an analysis of variance performed on suppression ratios is inappropriate because of numerous violations of the assumptions of the test. We offer a number of alternative strategies for the description and analysis of conditioned suppression. These include the use of raw data analyzed with nonparametric tests or an analysis of covariance, a procedure that accommodates the need for ipsative measurement without producing the flaws inherent in ANOVAs performed on suppression ratios.

Failure to transfer or train a numerical discrimination using sequential visual stimuli in rats

We previously reported that rats were able to discriminate among two, three, and four sequentially presented auditory stimuli (Davis & Albert, 1986). In the present paper, we describe our failure to transfer this numerical discrimination to visual stimuli and to establish the same discrimination using visual stimuli in naive animals. These negative results conflict with sporadic evidence of intermodal (auditory-visual) transfer of numerical discriminations, although all such reports have involved simpler dichotomous (many vs. few) requirements. We believe the relative difficulty of our task may have confined processing to the single salient modality (audition) in which it was taught, and precluded evidence of abstract learning by rendering intermodal transfer unattainable.

Numerically restricted food intake in the rat in a free-feeding situation

Rats were trained to leave an array of food after they had consumed a fixed number (three, four, or five) of food items. This discrimination remained in effect despite a shift from 45-mg Noyes pellets to larger and irregularly sized sunflower seeds. The present demonstration replicates work first reported 50 years ago by Otto Koehler and his associates (e.g., Marold, 1939; see also Koehler, 1950), who used avian subjects, and, like those studies, it involved both positive and negative social reinforcement. The present procedure provided a rare instance in which numerical control was exerted over behavior that was primarily consummatory in nature. The results are viewed in terms of the wider literature of numerical competence in animals and are discussed in terms of a numerical process known asprotocounting (Davis & P’erusse, 1988b).