Is your choice my choice? The owners’ effect on pet dogs’ (Canis lupus familiaris) performance in a food choice task

This study investigates the influence of owners on their dogs’ performance in a food choice task using either different or equal quantities of food. Fifty-four pet dogs were tested in three different conditions. In Condition 1 we evaluated their ability to choose between a large and small amount of food (quantity discrimination task). In Condition 2 dogs were again presented with a choice between the large and small food quantity, but only after having witnessed their owner favouring the small quantity. In Condition 3 dogs were given a choice between two equally small quantities of food having witnessed their owner favouring either one or the other. A strong effect of the owner on the dogs’ performance was observed. In Condition 1 dogs as a group chose significantly more often the large food quantity, thus showing their ability to solve the quantity discrimination task. After observing their owner expressing a preference for the small food quantity they chose the large quantity of food significantly less than in the independent choice situation. The tendency to conform to the owner’s choice was higher when the dogs had to choose between equally small quantities of food (Condition 3) rather than between a large and a small one (Condition 2). These results provide evidence that dogs can be influenced by their owners even when their indications are clearly in contrast with direct perceptual information, thus leading dogs to ultimately make counterproductive choices.     

Fractions but not negative numbers are represented on the mental number line

The present study is the first to directly compare numerical representations of positive numbers, negative numbers and unit fractions. The results show that negative numbers and unit fractions were not represented in the same way. Distance effects were found when positive numbers were compared with fractions but not when they were compared with negative numbers, thus suggesting that unit fractions but not negative numbers were represented on the number line with positive numbers. As indicated by the semantic congruity effect, negative numbers were perceived to be small, positive numbers were perceived as large, while unit fractions were perceived neither as large nor small. Comparisons between negative numbers were faster than between unit fractions, possibly due to the smaller differences between the holistic magnitudes of the unit fractions. Finally, comparing unit fractions to 1 was faster than comparing them to 0, consistent with the idea that unit fractions are perceived as entities smaller than 1 (Kallai & Tzelgov, 2009). The results are consistent with the idea of a mental division between numbers that represent a quantity (positive numbers and unit fractions) and those that do not (negative numbers).     

Quantity-based judgments in the domestic dog (<Emphasis Type="Italic">Canis lupus familiaris</Emphasis>)

We examined the ability of domestic dogs to choose the larger versus smaller quantity of food in two experiments. In experiment 1, we investigated the ability of 29 dogs (results from 18 dogs were used in the data analysis) to discriminate between two quantities of food presented in eight different combinations. Choices were simultaneously presented and visually available at the time of choice. Overall, subjects chose the larger quantity more often than the smaller quantity, but they found numerically close comparisons more difficult. In experiment 2, we tested two dogs from experiment 1 under three conditions. In condition 1, we used similar methods from experiment 1 and tested the dogs multiple times on the eight combinations from experiment 1 plus one additional combination. In conditions 2 and 3, the food was visually unavailable to the subjects at the time of choice, but in condition 2, food choices were viewed simultaneously before being made visually unavailable, and in condition 3, they were viewed successively. In these last two conditions, and especially in condition 3, the dogs had to keep track of quantities mentally in order to choose optimally. Subjects still chose the larger quantity more often than the smaller quantity when the food was not simultaneously visible at the time of choice. Olfactory cues and inadvertent cuing by the experimenter were excluded as mechanisms for choosing larger quantities. The results suggest that, like apes tested on similar tasks, some dogs can form internal representations and make mental comparisons of quantity.     

Non-verbal numerical cognition: from reals to integers

Data on numerical processing by verbal (human) and non-verbal (animal and human) subjects are integrated by the hypothesis that a non-verbal counting process represents discrete (countable) quantities by means of magnitudes with scalar variability. These appear to be identical to the magnitudes that represent continuous (uncountable) quantities such as duration. The magnitudes representing countable quantity are generated by a discrete incrementing process, which defines next magnitudes and yields a discrete ordering. In the case of continuous quantities, the continuous accumulation process does not define next magnitudes, so the ordering is also continuous ('dense'). The magnitudes representing both countable and uncountable quantity are arithmetically combined in, for example, the computation of the income to be expected from a foraging patch. Thus, on the hypothesis presented here, the primitive machinery for arithmetic processing works with real numbers (magnitudes).     

Infants’ auditory enumeration: Evidence for analog magnitudes in the small number range

Vigorous debate surrounds the issue of whether infants use different representational mechanisms to discriminate small and large numbers. We report evidence for ratio-dependent performance in infants’ discrimination of small numbers of auditory events, suggesting that infants can use analog magnitudes to represent small values, at least in the auditory domain. Seven-month-old infants in the present study reliably discriminated two from four tones (a 1:2 ratio) in Experiment 1, when melodic and continuous temporal properties of the sequences were controlled, but failed to discriminate two from three tones (a 2:3 ratio) under the same conditions in Experiment 2. A third experiment ruled out the possibility that infants in Experiment 1 were responding to greater melodic variety in the four-tone sequences. The discrimination function obtained here is the same as that found for infants’ discrimination of large numbers of visual and auditory items at a similar age, as well as for that obtained for similar-aged infants’ duration discriminations, and thus adds to a growing body of evidence suggesting that human infants may share with adults and nonhuman animals a mechanism for representing quantities as “noisy” mental magnitudes.     

Never getting to zero: Elementary school students' understanding of the infinite divisibility of number and matter

Clinical interviews administered to third- to sixth-graders explored children's conceptualizations of rational number and of certain extensive physical quantities. We found within child consistency in reasoning about diverse aspects of rational number. Children's spontaneous acknowledgement of the existence of numbers between 0 and 1 was strongly related to their induction that numbers are infinitely divisible in the sense that they can be repeatedly divided without ever getting to zero. Their conceptualizing number as infinitely divisible was strongly related to their having a model of fraction notation based on division and to their successful judgment of the relative magnitudes of fractions and decimals. In addition, their understanding number as infinitely divisible was strongly related to their understanding physical quantities as infinitely divisible. These results support a conceptual change account of knowledge acquisition, involving two-way mappings between the domains of number and physical quantity.     

More or less: spontaneous quantity discrimination in the domestic cat

We examined spontaneous quantity discrimination in untrained domestic cats in three food choice experiments. In Experiment 1, we presented the cats with two different quantities of food in eight numerical combinations. Overall, the subjects chose the larger quantity more often than the smaller one, and significantly so when the ratio between the quantities was less than 0.5. In Experiment 2, we presented the cats with two pieces of food in four different size combinations. Again, subjects chose the larger piece above chance, although not in the combination where the largest item was presented. In Experiment 3, a subset of the cats was presented multiple times with two different quantities of food, which were hidden from view. In this case, the cats did not choose the larger quantity more often than the smaller one, suggesting that in the present experiments they mainly used visual cues when comparing quantities. We conclude that domestic cats are capable of spontaneously discriminating quantities when faced with different numbers or sizes of food items, and we suggest why they may not always be motivated to choose the larger quantity. In doing so, we highlight the advantages of testing spontaneous choice behavior, which is more likely to reflect animals’ everyday manner of responding than is the case when training them in order to test their absolute limits of performance which may not always coincide with their daily needs.     

Do fish count? Spontaneous discrimination of quantity in female mosquitofish

The spontaneous tendency to join the largest social group was used to investigate quantity discrimination in fish. Fish discriminated between shoals that differed by one element when the paired numbers were 1vs2, 2vs3 and 3vs4, but not when 4vs5 or larger. Using large numerosities (>4), the ability to discriminate between two numbers improved as the numerical distance between them increased and a significant discrimination was found only with ratios of 1:2 or smaller (4vs8, 8vs16 and 4vs10). Experiments to control for non-numerical variables evidenced the role played by the total area of stimuli with both large and small numerosities; the total quantity of movement of the fish within a shoal appeared also important but only when large numerosities were involved. Even though the pattern of discrimination exhibited by female mosquitofish is not fully consistent with any of the existing models of quantity representation, our results seem to suggest two distinct mechanisms in fish, one used to compare small numbers of objects and one used when larger numerosities are involved.     

Cross-domain transfer of quantitative discriminations: Is it all a matter of proportion?

Meck and Church (1983) estimated a 5:1 scale factor relating the mental magnitudes representing number to the mental magnitudes representing duration. We repeated their experiment with human subjects. We obtained transfer regardless of the objective scaling between the ranges; a 5:1 scaling for number versus duration (measured in seconds) was not necessary. We obtained transfer even when the proportions between the endpoints of the number range were different. We conclude that, at least in human subjects, transfer from a discrimination based on continuous quantity (duration) to a discrimination based on discrete quantity (number) is mediated by the cross-domain comparability of withindomain proportions. The results of our second and third experiments also suggest that the subjects compare a probe with a criterion determined by the range of stimuli tested rather than by trial-specific referents, in accordance with the pseudologistic model of Killeen, Fetterman, and Bizo (1997).     

The mental number line in depth revealed by vection

To explore how numbers are represented in depth in our mental space, we asked participants to sequentially speak random numbers while they observed forward/backward vection. We found that participants tended to generate larger numbers when they perceived backward self-motion. The results suggest that numerical magnitudes were topographically mapped onto our mental space from front to rear in an ascending order.     

Estimation of the probability of fighting in fallow deer (Dama dama) during the rut

Fighting between males is a frequent component of the rutting behavior of Cervidae. Frequent conflicts are exhausting; fighting may be risky and can lead to serious injuries or even death. We focused on the process of assessment of the opponent's fighting ability and escalation of the combat, estimating the probability of fighting based on the encounter components such as groaning and parallel walk. In this study, we observed the agonistic behavior of fallow deer bucks (Dama dama) during the rut over four seasons. During this time, we recorded 205 encounters between bucks. Non-contact display, which allows contestants to assess their opponents fighting ability, occurred in 83% of the encounters. The highest predicted probability of a fight was found when both of the males vocalized and turned into the parallel walk. The chance of a clear outcome decreased when the males were fighting in comparison to when they did not fight. The initiator of the competitive encounter won 41% of the cases, while the attacked buck won 23% of the encounters. If the contestants avoided fighting, however, the initiator won 78% of encounters. Therefore, the initiator was more successful when no fight occurred compared to when the encounters escalated into fighting. In most cases where ritualized behavior occurred, one of the opponents left after vocalization or parallel walk occurred. Thus, vocalization and parallel walk increased the probability for a clear outcome. The probability of a fight was lowest in situations where the males displayed asymmetric behavior. Increased symmetry of the contestants' behavior was strongly correlated with a higher probability of a fight. Thus, these results indicate that fallow deer bucks use efficient tactic during the rut, which, in turn, minimizes the chance of injury while fighting during the breeding season.     

Putting the elephant back in the herd: elephant relative quantity judgments match those of other species

The ability to discriminate between quantities has been observed in many species. Typically, when an animal is given a choice between two sets of food, accurate performance (i.e., choosing the larger amount) decreases as the ratio between two quantities increases. A recent study reported that elephants did not exhibit ratio effects, suggesting that elephants may process quantitative information in a qualitatively different way from all other nonhuman species that have been tested (Irie-Sugimoto et al. in Anim Cogn 12:193-199, 2009). However, the results of this study were confounded by several methodological issues. We tested two African elephants (Loxodonta africana) to more thoroughly investigate relative quantity judgment in this species. In contrast to the previous study, we found evidence of ratio effects for visible and nonvisible sequentially presented sets of food. Thus, elephants appear to represent and compare quantities in much the same way as other species, including humans when they are prevented from counting. Performance supports an accumulator model in which quantities are represented as analog magnitudes. Furthermore, we found no effect of absolute magnitude on performance, providing support against an object-file model explanation of quantity judgment.     

Increasing magnitude counts more: asymmetrical processing of ordinality in 4-month-old infants

While infants' ability to discriminate quantities has been extensively studied, showing that this competence is present even in neonates, the ability to compute ordinal relations between magnitudes has received much less attention. Here we show that the ability to represent ordinal information embedded in size-based sequences is apparent at 4months of age, provided that magnitude changes involve increasing relations. Infants in Experiments 1A and 1B discriminated changes in ordinal relations after habituation to ascending sequences, but did not show evidence of discrimination after habituation to descending sequences. In Experiment 2 we replicated this asymmetry in magnitude discrimination even when additional cues known to boost ordinal competence were provided. The presence of an asymmetry between ascending vs. descending order during infancy suggests a developmental continuity in the underlying code used to represent magnitude, whereby the reported addition advantage in children and adults' arithmetic performance emerges.     

Variability signatures distinguish verbal from nonverbal counting for both large and small numbers

Humans appear to share with animals a nonverbal counting process. In a nonverbal counting condition, subjects pressed a key a numeral-specified number of times, while saying “the” at every press. The mean number of presses increased as a power function of the target number, with a constant coefficient of variation (c.v.), both within and beyond the proposed subitizing range (1–4 or 5), suggesting small numbers are represented on the same continuum as larger numbers and subject to the same noise process (scalar variability). By contrast, when subjects counted their presses out loud as fast as they could, the c.v. decreased as the inverse square root of the target value (binomial variability instead of scalar variability). The unexpected power-law relation between target value and mean number of presses in nonverbal counting suggests a new hypothesis about the development of the function relating number symbols to mental magnitudes.     

Discrimination of small quantities by fish (redtail splitfin, Xenotoca eiseni)

Discrimination of quantity has been argued to rely on two non-verbal representational systems: an object file system (OFS) for representing small values (≤3–4) and an analog magnitude system (AMS) for representing large magnitudes (>4). Infants’ ability to discriminate 1 versus 2, 1 versus 3, 2 versus 3, but not 1 versus 4 or 2 versus 4 seems to prove the independence of such systems. Here, we show that redtail splitfin fish (Xenotoca eiseni) performed relative quantity estimations preferring to approach the location previously occupied by the larger in number between two groups of conspecifics (no longer visible at test) in sets of 1 versus 2 and 2 versus 3 items, but failed at 3 versus 4 items, thus showing the same set-size limit as infants for discrimination of small quantities. However, when tested with quantities that spanned the boundary of the two systems, that is, 1 versus 4 and 2 versus 4, fish succeeded. These results thus point to either the use of continuous physical variables and/or the use of the AMS also for small numerousness in fish in this task.     

Contextual effects on number-time interaction

Time perception has long been known to be affected by numerical representations. Recent studies further demonstrate that when participants estimate the duration of Arabic numbers, number magnitude, though task-irrelevant, biases duration judgment to produce underestimation for smaller numbers and overestimation for larger numbers. Such effects were found in the present study to be significantly reduced when a weight unit gram was suffixed to the numbers rendering the mental magnitude differences between different numbers less distinctive. The effects were enhanced when a different unit kilogram was suffixed to the numbers enlarging the perceived magnitude differences between different numbers. The results indicate that effects of number magnitude on duration estimation should not be attributed to the mathematical differences between numbers but to how the numbers are perceived to differ from each other in magnitude in specific contexts when they denote concrete items. The results also provide new evidence for the theoretical proposal of a common generalized magnitude system and indicate that the system must be extended to include other action-oriented magnitudes, such as weight.     

Cost of mental set reconfiguration between digits and their photisms in synaesthesia

In this study we present an experiment investigating the reconfiguration process elicited by the task switching paradigm in synaesthesia. We study the time course of the operations involved in the activation of photisms. In the experimental Group, four digit-color synaesthetes alternated between an odd-even task and a color task (to indicate the photism elicited by each digit). In both tasks, the target stimuli were numbers between 1 and 9 written in white. One of the control groups ran the same tasks but this time with colored numbers (Naive Control Group). The results of these studies showed the expected pattern for the control group in the case of regular shift: a significant task switch cost with an abrupt offset and a cost reduction in long RSI. However for the experimental group, we found switch cost asymmetry in the short RSI and non-significant cost in the long RSI. A second control group performed exactly the same tasks as the experimental group (with white numbers as targets and a second imaginary color task) -Trained Control Group-. We found no cost for this second control group. This means that the cost of mental set reconfiguration between numbers (inducers) and their photisms (concurrent sensations) occurs, that there is a specific cost asymmetry (from photisms to inducers) and that this cost cannot be explained by associative learning. The results are discussed in terms of exogenous and endogenous components of mental set reconfiguration.     

Approaching stimuli bias attention in numerical space

Increasing evidence suggests that common mechanisms underlie the direction of attention in physical space and numerical space, along the mental number line. The small leftward bias (pseudoneglect) found on paper-and-pencil line bisection is also observed when participants 'bisect' number pairs, estimating (without calculating) the number midway between two others. Here we investigated the effect of stimulus motion on attention in numerical space. A two-frame apparent motion paradigm manipulating stimulus size was used to produce the impression that pairs of numbers were approaching (size increase from first to second frame), receding (size decrease), or not moving (no size change). The magnitude of pseudoneglect increased for approaching numbers, even when the final stimulus size was held constant. This result is consistent with previous findings that pseudoneglect in numerical space (as in physical space) increases as stimuli are brought closer to the participant. It also suggests that the perception of stimulus motion modulates attention over the mental number line and provides further support for a connection between the neural representations of physical space and number.     

Perceiving numbers affects the subjective temporal midpoint

Temporal experience can be modulated by several environmental factors. There is increasing evidence that numerical quantity may also influence temporal processes. Here, it is shown that merely looking at numbers causes a bias in a time-bisection task that depends on its magnitude. In the first experiment, a group of healthy subjects was submitted to a time-bisection task in which numerical cues were blocked (blocked design). In the second experiment, a new group of participants performed a time-bisection task in which the previous numbers were all randomly arranged in the same block (intermingled design). Results show that temporal performance is biased when numbers of different magnitude are arranged in an intermingled design. These findings argue for a functional interaction between time and numbers, depending on the implicit extrapolation of the size difference between the displayed numbers rather than on the numerical size itself.     

Number-space associations without language: Evidence from preverbal human infants and non-human animal species

It is well known that humans describe and think of numbers as being represented in a spatial configuration, known as the ‘mental number line’. The orientation of this representation appears to depend on the direction of writing and reading habits present in a given culture (e.g., left-to-right oriented in Western cultures), which makes this factor an ideal candidate to account for the origins of the spatial representation of numbers. However, a growing number of studies have demonstrated that non-verbal subjects (preverbal infants and non-human animals) spontaneously associate numbers and space. In this review, we discuss evidence showing that pre-verbal infants and non-human animals associate small numerical magnitudes with short spatial extents and left-sided space, and large numerical magnitudes with long spatial extents and right-sided space. Together this evidence supports the idea that a more biologically oriented view can account for the origins of the ‘mental number line’. In this paper, we discuss this alternative view and elaborate on how culture can shape a core, fundamental, number–space association.