A comparative study of geometric rule learning by nutcrackers (Nucifraga columbiana), pigeons (Columba livia), and jackdaws (Corvus monedula)

A harbour seal (Phoca vitulina) can learn geometrical relationships between landmarks

Marine mammals travel the world's oceans. Some species regularly return to specific places to breathe, haul-out or breed. However, the mechanisms they use to return are unknown. Theoretically, landmarks could mediate the localisation of these places. Occasionally, it might be beneficial or even required to localise places using geometrical information provided by landmarks such as to apply a 'middle rule'. Here, we trained a harbour seal to find its goal in the middle of numerous vertically and horizontally orientated two-landmark arrays. During testing, the seal was confronted with unfamiliar two-landmark arrays. After having successfully learnt to respond to the midpoint of multiple two-landmark arrays, the seal directly and consistently followed a 'middle rule' during testing. It chose the midpoint of the two-landmark arrays with high precision. Harbour seals with the ability to localise goals based on geometrical information would be able to home in on places even from unknown positions relative to goal-defining features. Altogether, the results obtained with our harbour seal individual in the present and a previous study, examining the basis of landmark orientation, provide evidence that this seal can use landmark information very flexibly. Depending on context, this flexibility is adaptive to an environment in which the information content can vary over time.

How harbour seals (Phoca vitulina) encode goals relative to landmarks

Visual landmarks are defined as object with prominent shape or size that distinguish themselves from the background. With the help of landmarks, animals can orient themselves in their natural environment. Yet, the way in which landmarks are perceived and encoded has previously only been described in insects, fish, birds, reptilians and terrestrial mammals. The present study aimed to provide insight into how a marine mammal, the harbour seal, is encoding goals relative to landmarks. In our expansion test, three harbour seals were trained to find a goal inside an array of landmarks. After diagonal, horizontal or vertical expansion of the landmark array, the search behaviour displayed by the animals was documented and analyzed regarding the underlying encoding strategy. The harbour seals mainly encoded directional vector information from landmarks and did neither search arbitrarily around a landmark nor used a rule-based approach. Depending on the number of landmarks available within the array, the search behaviour of some harbor seals changed, indicating flexibility in landmark-based search. Our results present first insight in how a semi-aquatic predator could encode landmark information when swimming along the coastline in search for a goal-location.

Middle identification for rhesus monkeys is influenced by number but not extent

Abstract concept learning provides a fundamental building block for many cognitive functions in humans. Here we address whether rhesus monkeys (Macaca mulatta) can learn the abstract concept of “middle” in a series of objects. First, we trained monkeys to select the middle dot in a horizontal series of three dots presented on a touchscreen. Monkeys maintained a preference to choose the middle dot despite changes in the appearance, location, and spacing of the horizontal series of dots. They maintained high performance when the color, shape and the length of the stimuli were new, indicating that their responses did not depend upon the particular appearance of the array items. Next, we asked whether monkeys would generalize the middle concept to a 7 dot series. Although accuracy decreased when the number of dots was increased, monkeys continued to preferentially select the middle dot. Our results demonstrate that rhesus macaques can learn to use a middle concept for a discrete set of items.

Mother-child communication about relative proximity to a landmark: What role does prototypicality play?

This investigation examined how prototypicality affects mother-child communication about relative proximity. In the first two experiments, mothers of 2.5-, 3.0-, and 3.5-year-old children verbally disambiguated a target hiding container from an identical non-target hiding container when the two containers were placed at a smaller (more prototypical) or larger (less prototypical) distance from a landmark. Children then searched for the hidden object. When the absolute distance was smaller, mothers used more consistent frames of reference in their directions and even 2.5-year-olds largely followed those directions successfully. When the absolute distance was larger, mothers used multiple reference frames in their directions (a "kitchen sink" strategy) and children had more difficulty in following directions (especially 2.5-year-olds). A third experiment in which we controlled mothers' directions confirmed that the increased absolute distance, and not the mothers' direction-giving strategies, led to 2.5-year-olds' impaired search performance. These results indicate that young children's understanding of relative proximity develops from more prototypical cases (smaller distances) to less prototypical cases (larger distances) and that mothers' attempts to compensate for young children's difficulty with less prototypical cases did not improve their search performance.

Superior abstract-concept learning by Clark's nutcrackers (Nucifraga columbiana)

The ability to learn abstract relational concepts is fundamental to higher level cognition. In contrast to item-specific concepts (e.g. pictures containing trees versus pictures containing cars), abstract relational concepts are not bound to particular stimulus features, but instead involve the relationship between stimuli and therefore may be extrapolated to novel stimuli. Previous research investigating the same/different abstract concept has suggested that primates might be specially adapted to extract relations among items and would require fewer exemplars of a rule to learn an abstract concept than non-primate species. We assessed abstract-concept learning in an avian species, Clark's nutcracker (Nucifraga columbiana), using a small number of exemplars (eight pairs of the same rule, and 56 pairs of the different rule) identical to that previously used to compare rhesus monkeys, capuchin monkeys and pigeons. Nutcrackers as a group (N = 9) showed more novel stimulus transfer than any previous species tested with this small number of exemplars. Two nutcrackers showed full concept learning and four more showed transfer considerably above chance performance, indicating partial concept learning. These results show that the Clark's nutcracker, a corvid species well known for its amazing feats of spatial memory, learns the same/different abstract concept better than any non-human species (including non-human primates) yet tested on this same task.

Effects of landmark distance and stability on accuracy of reward relocation

Although small-scale navigation is well studied in a wide range of species, much of what is known about landmark use by vertebrates is based on laboratory experiments. To investigate how vertebrates in the wild use landmarks, we trained wild male rufous hummingbirds to feed from a flower that was placed in a constant spatial relationship with two artificial landmarks. In the first experiment, the landmarks and flower were 0.25, 0.5 or 1 m apart and we always moved them 3-4 m after each visit by the bird. In the second experiment, the landmarks and flower were always 0.25 m apart and we moved them either 1 or 0.25 m between trials. In tests, in which we removed the flower, the hummingbirds stopped closer to the predicted flower location when the landmarks had been closer to the flower during training. However, while the distance that the birds stopped from the landmarks and predicted flower location was unaffected by the distance that the landmarks moved between trials, the birds directed their search nearer to the predicted direction of the flower, relative to the landmarks, when the landmarks and flower were more stable in the environment. In the field, then, landmarks alone were sufficient for the birds to determine the distance of a reward but not its direction.

Evidence consistent with the multiple-bearings hypothesis from human virtual landmark-based navigation

One approach to explaining the conditions under which additional landmarks will be learned or ignored relates to the nature of the information provided by the landmarks (i.e., distance versus bearings). In the current experiment, we tested the ability of such an approach to explain the search behavior of human participants in a virtual landmark-based navigation task by manipulating whether landmarks provided stable distance, stable direction, or both stable distance and stable direction information. First, we incrementally shaped human participants’ search behavior in the presence of two ambiguous landmarks. Next, participants experienced one additional landmark that disambiguated the location of the goal. Finally, we presented three additional landmarks. In a control condition, the additional landmarks maintained stable distances and bearings to the goal across trials. In a stable bearings condition, the additional landmarks varied in their distances but maintained fixed bearings to the goal across trials. In a stable distance condition, the additional landmarks varied in their bearings but maintained fixed distances to the goal across trials. Landmark stability, in particular, the stability of landmark-to-goal bearings, affected learning of the added landmarks. We interpret the results in the context of the theories of spatial learning that incorporate the nature of the information provided by landmarks.

Angular amplitude matters: exploring the functional relationship of geometric cue use by Clark's nutcrackers (Nucifraga columbiana)

Four groups of Clark's nutcrackers (Nucifraga columbiana) learned to search for food hidden at one of two geometrically identical corners of a parallelogram-shaped enclosure. The corners of the enclosure projected either 40° and 140° angles or 60° and 120° angles. Tests using both rhomboid and rectangular enclosures examined whether birds had encoded angular amplitude and the length of walls, respectively. Cue conflict tests using a mirror-image of the training parallelogram reversed the relationship between wall length and corner angle, allowing for the examination of cue weighing. Furthermore, cue conflict tests which manipulated the angular amplitude allowed for the investigation of whether the encoding of angular information was similar among the training groups. Our results showed that nutcrackers encoded both angular amplitude and wall length. During cue conflict tests that maintained the training angular amplitudes, birds did not show a strong weighing of angular cues at a population-level but rather considerable individual differences were found. Finally, manipulating angular amplitude in the direction towards the unrewarded angle resulted in reduced weighing of angular cues whereas manipulating angular amplitude in the direction away from the unrewarded angle resulted in greater weighing of angular cues. In summary, our results support the importance of using multiple exemplars during training and testing to better understand the functional relationship between geometric cues during a spatial search task.

The synthetic approach to the study of spatial memory: have we properly addressed Tinbergen's "four questions"?

In 1963, Niko Tinbergen suggested that to truly understand the behavior of an animal, the ultimate causes (e.g., adaptive value, evolutionary history) as well as the proximate mechanisms (e.g., neurobiology, development) that result in the production of the behavior must be understood in an integrated framework. We examine whether the study of spatial memory in food storing birds has adequately addressed Tinbergen's questions and highlight the work of Sara Shettleworth, who has made a tremendous contribution to this area of study, and whom this issue honors. Our conclusion is that while the study of food caching and spatial memory in birds has been a very good model of a program of research that has addressed Tinbergen's questions, additional work remains.

Proximity to an edge affects search strategy in adults and children

When searching for a hidden goal, search patterns are often defined according to one of two main search strategies: an absolute strategy, which usually involves searching at a fixed learned distance and direction from a particular reference point, or a relational strategy, which involves searching at a point that maintains the relationship between two or more other points. Past research has shown that humans tend to prefer a relational strategy whereas most non-humans prefer an absolute strategy. However, recent research (Hartley et al., 2004) used a simulated 3D environment to demonstrate that proximity to a boundary affects strategy. In particular, when searching close to an edge, human participants were more likely to use an absolute strategy whereas when searching at a central location, participants were more likely to use a relational strategy. The current studies extend the findings of Hartley et al. Experiment 1 showed that adult humans use different strategies based on the goal's proximity to the edge of a search space, and that strategies differed between males and females. Experiment 2 suggested that children also use different strategies based on the goal's proximity to a boundary, and that some goal locations may be harder to learn than others. Taken together, our results show that search strategies are flexible and context-specific.

Place learning by mechanical contact

For some animals (e.g. the night-active wandering spider) the encounters with the habitat that result in place learning are predominantly mechanical. We asked whether place learning limited to mechanical contact, like place learning in general, entails vectors tied to individual landmarks and relations between landmarks. We constructed minimal environments for blindfolded human participants. Landmarks were raised steps. 'Home' was a mechanically indistinct location. Travel was linear. The mechanical contacts were those of walking, stepping, and probing with a soft-tipped cane. Home-orienting activities preceded tests of finding home from a given location with landmarks unchanged or (unbeknown to participants) shifted. In a one-landmark environment, perceived home shifted in the same direction, with the same magnitude, as the shifted landmark. In an environment of two landmarks located in the same direction from home, shifting the further landmark toward home resulted in a change in home's perceived location that preserved the original ratio of distances separating home, nearer landmark, and further landmark. Both findings were invariant over the travel route to the test location and repetitions of testing. It seems, therefore, that for humans (and, perhaps, for wandering spiders), mechanical contact can reveal the vectors and relations specifying places.

What scatter-hoarding animals have taught us about small-scale navigation

Many animals use cues for small-scale navigation, including beacons, landmarks, compasses and geometric properties. Scatter-hoarding animals are a unique system to study small-scale navigation. They have to remember and relocate many individual spatial locations, be fairly accurate in their searching and have to remember these locations for long stretches of time. In this article, we review what is known about cue use in both scatter-hoarding birds and rodents. We discuss the importance of local versus global cues, the encoding of bearings and geometric rules, the use of external compasses such as the Sun and the influence of the shape of experimental enclosures in relocating caches or hidden food. Scatter-hoarding animals are highly flexible in how and what they encode. There also appear to be differences in what scatter-hoarding birds and rodents encode, as well as what scatter-hoarding animals in general encode compared with other animals. Areas for future research with scatter-hoarding animals are discussed in light of what is currently known.

Features enhance the encoding of geometry

Successful navigation within an environment requires that the traveler establish the correct heading--a process referred to as orienting. Many studies have now shown that humans and non-human animals can use the geometric properties of an enclosure to orient. In the present study, two groups of Clark's nutcrackers (Nucifraga columbiana) were trained, in a reference memory task, to find food hidden in one of four containers arranged to form a rectangular array. One group had unique objects placed next to each of the containers, whereas the second group had identical objects placed next to each of the containers. Here, I show for the first time that for the Clark's nutcracker, the distinctive properties of these objects enhanced the encoding of the array's geometry compared to the learning of geometric properties from an array of identical objects, which remained at chance after substantial amounts of training. Subsequent transformation tests showed that an object not associated with reward, but sharing the same geometric properties as the correct object, may have had inhibitory qualities. Furthermore, by systematically removing objects from the array, I show that although nutcrackers encoded the geometry of the array, they did not encode a complete featural representation of the objects within the array.

Relative temporal representations in Pavlovian conditioning

The transfer of relative temporal representations was assessed in a series of three experiments. In each experiment, rats (Rattus norvegicus) received one set of conditioned stimulus (CS) and intertrial interval (ITI) durations in Phase 1 and another set in Phase 2. The ratio between the CS and ITI intervals was either changed or maintained across phases. On the hypothesis that relative temporal representations are learned, groups receiving maintained temporal ratios across phases were expected to display greater change in responding upon encountering the new intervals. When the CS duration decreased across phases, maintaining the temporal ratio did lead to greater change in Day 1 of Phase 2 towards the final pattern of responding. However, when the CS increased across phases, maintaining the temporal ratio across phases did not facilitate adjustment to the new intervals, suggesting that extinction of previously reinforced times induced new learning. These results provide evidence that under some conditions, relative relationships in temporal maps may survive transformation-of-scale, like relative relationships in spatial maps.

Spatial decisions and cognitive strategies of monkeys and humans based on abstract spatial stimuli in rotation test

We showed previously that macaque monkeys (Macaca mulatta) could orient in real space using abstract visual stimuli presented on a computer screen. They made correct choices according to both spatial stimuli (designed as an abstract representation of a real space) and nonspatial stimuli (pictures lacking any inner configuration information). However, we suggested that there were differences in processing spatial and nonspatial stimuli. In the present experiment we show that monkeys could also use as a cue abstract spatial stimuli rotated with respect to the real response space. We studied the ability of monkeys to decode abstract spatial information provided in one spatial frame (computer screen) and to perform spatial choices in another spatial frame (touch panel separated from the screen). We analyzed how the monkeys were affected by the type of training, whether they perceived the stimuli as "spatial" or "nonspatial," and which cues they used to decode them. We compared humans to monkeys in a similar test to find out which cognitive strategy they used and whether they perceive spatial stimuli in the same way. We demonstrated that there were two possible strategies to solve the task, simple "fitting" ignoring rotations and "remapping," when the stimulus was represented as an "abstract space" per se.

Sexual selection and the evolution of obligatory sex

Background

Among the long-standing conundrums of evolutionary theory, obligatory sex is one of the hardest. Current theory suggests multiple factors that might explain the benefits of sex when compared with complete asexuality, but no satisfactory explanation for the prevalence of obligatory sex in the face of facultative sexual reproduction.

Results and Conclusion

We show that when sexual selection is present obligatory sex can evolve and be maintained even against facultative sex, under common scenarios of deleterious mutations and environmental changes.

Age and sex differences in children’s spatial search strategies

Male and female children, 3, 4, and 5 years old, searched for a sticker that was hidden in 1 of 15 linearly aligned boxes. Two identical bear-shaped landmarks cued the sticker location, which was always in the middle of 3 boxes that separated the two landmarks. The absolute locations of the landmarks and sticker varied across training trials, but the distance in relation to each other remained constant. Training continued until the child chose the correct box first for 3 consecutive trials or for a maximum of 20 trials. Striking age and sex differences emerged in acquisition: The percentage of children who reached criterion increased over age groups to 100% for the boys but stayed at approximately 20% for the girls. A landmark expansion test (with the landmarks moved farther apart) given to children who met criterion revealed that most of these children chose the middle location.

Multiple landmarks, the encoding of environmental geometry and the spatial logics of a dual brain

A series of place learning experiments was carried out in young chicks (Gallus gallus) in order to investigate how the geometry of a landmark array and that of a walled enclosure compete when disoriented animals could rely on both of them to re-orient towards the centre of the enclosure. A square-shaped array (four wooden sticks) was placed in the middle of a square-shaped enclosure, the two structures being concentric. Chicks were trained to ground-scratch to search for food hidden in the centre of the enclosure (and the array). To check for effects of array degradation, one, two, three or all landmarks were removed during test trials. Chicks concentrated their searching activity in the central area of the enclosure, but their accuracy was inversely contingent on the number of landmarks removed; moreover, the landmarks still present within the enclosure appeared to influence the shape of the searching patterns. The reduction in the number of landmarks affected the searching strategy of chicks, suggesting that they had focussed mainly on local cues when landmarks were present within the enclosure. When all the landmarks were removed, chicks searched over a larger area, suggesting an absolute encoding of distances from the local cues and less reliance on the relationships provided by the geometry of the enclosure. Under conditions of monocular vision, chicks tended to rely on different strategies to localize the centre on the basis of the eye (and thus the hemisphere) in use, the left hemisphere attending to details of the environment and the right hemisphere attending to the global shape.

Small-scale spatial cognition in pigeons

Roberts and Van Veldhuizen's [Roberts, W.A., Van Veldhuizen, N., 1985. Spatial memory in pigeons on the radial maze. J. Exp. Psychol.: Anim. Behav. Proc. 11, 241-260] study on pigeons in the radial maze sparked research on landmark use by pigeons in lab-based tasks as well as variants of the radial-maze task. Pigeons perform well on open-field versions of the radial maze, with feeders scattered on the laboratory floor. Pigeons can also be trained to search precisely for buried food. The search can be based on multiple landmarks, but is sometimes controlled by just one or two landmarks, with the preferred landmarks varying across individuals. Findings are similar in landmark-based searching on a computer monitor and on a lab floor, despite many differences between the two kinds of tasks. A number of general learning principles are found in landmark-based searching, such as cue competition, generalization and peak shift, and selective attention. Pigeons also learn the geometry of the environment in which they are searching. Neurophysiological studies have implicated the hippocampal formation (HF) in avian spatial cognition, with the right hippocampus hypothesized to play a more important role in the spatial recognition of goal locations. Most recently, single-cell recording from the pigeon's hippocampal formation has revealed cells with different properties from the classic 'place' cells of rats, as well as differences in the two sides of the hippocampus.

Spatial relational learning in rufous hummingbirds (Selasphorus rufus)

There is increasing evidence that animals can learn abstract spatial relationships, and successfully transfer this knowledge to novel situations. In this study, rufous hummingbirds (Selasphorus rufus) were trained to feed from either the lower or the higher of two flowers. When presented with a test pair of flowers, one of which was at a novel height, they chose the flower in the appropriate spatial position rather than the flower at the correct height. This response may also have been influenced by a preference for taller flowers as acquisition of the task during experimental training occurred more readily when the reward flower was the taller of the pair. Thus, it appears that although learning abstract relationships may be a general phenomenon across contexts, and perhaps across species, the ease with which they are learned and the context in which they are subsequently used may not be the same.

Cognitive ornithology: the evolution of avian intelligence

Comparative psychologists interested in the evolution of intelligence have focused their attention on social primates, whereas birds tend to be used as models of associative learning. However, corvids and parrots, which have forebrains relatively the same size as apes, live in complex social groups and have a long developmental period before becoming independent, have demonstrated ape-like intelligence. Although, ornithologists have documented thousands of hours observing birds in their natural habitat, they have focused their attention on avian behaviour and ecology, rather than intelligence. This review discusses recent studies of avian cognition contrasting two different approaches; the anthropocentric approach and the adaptive specialization approach. It is argued that the most productive method is to combine the two approaches. This is discussed with respects to recent investigations of two supposedly unique aspects of human cognition; episodic memory and theory of mind. In reviewing the evidence for avian intelligence, corvids and parrots appear to be cognitively superior to other birds and in many cases even apes. This suggests that complex cognition has evolved in species with very different brains through a process of convergent evolution rather than shared ancestry, although the notion that birds and mammals may share common neural connectivity patterns is discussed.

Is there a geometric module for spatial orientation? Squaring theory and evidence

There is evidence, beginning with Cheng (1986), that mobile animals may use the geometry of surrounding areas to reorient following disorientation. Gallistel (1990) proposed that geometry is used to compute the major or minor axes of space and suggested that such information might form an encapsulated cognitive module. Research reviewed here, conducted on a wide variety of species since the initial discovery of the use of geometry and the formulation of the modularity claim, has supported some aspects of the approach, while casting doubt on others. Three possible processing models are presented that vary in the way in which (and the extent to which) they instantiate the modularity claim. The extant data do not permit us to discriminate among them. We propose a modified concept of modularity for which an empirical program of research is more tractable.

Egocentric search for disappearing objects in domestic dogs: evidence for a geometric hypothesis of direction

In several species, the ability to locate a disappearing object is an adaptive component of predatory and social behaviour. In domestic dogs, spatial memory for hidden objects is primarily based on an egocentric frame of reference. We investigated the geometric components of egocentric spatial information used by domestic dogs to locate an object they saw move and disappear. In experiment 1, the distance and the direction between the position of the animal and the hiding location were put in conflict. Results showed that the dogs primarily used the directional information between their own spatial coordinates and the target position. In experiment 2, the accuracy of the dogs in finding a hidden object by using directional information was estimated by manipulating the angular deviation between adjacent hiding locations and the position of the animal. Four angular deviations were tested: 5, 7.5, 10 and 15 degrees . Results showed that the performance of the dogs decreased as a function of the angular deviations but it clearly remained well above chance, revealing that the representation of the dogs for direction is precise. In the discussion, we examine how and why domestic dogs determine the direction in which they saw an object disappear.

Transitive responding in hooded crows requires linearly ordered stimuli

Eight crows were taught to discriminate overlapping pairs of visual stimuli (A+ B-, B+ C-, C+ D-, and D+ E-). For 4 birds, the stimuli were colored cards with a circle of the same color on the reverse side whose diameter decreased from A to E (ordered feedback group). These circles were made available for comparison to potentially help the crows order the stimuli along a physical dimension. For the other 4 birds, the circles corresponding to the colored cards had the same diameter (constant feedback group). In later testing, a novel choice pair (BD) was presented. Reinforcement history involving stimuli B and D was controlled so that the reinforcement/nonreinforcement ratios for the latter would be greater than for the former. If, during the BD test, the crows chose between stimuli according to these reinforcement/nonreinforcement ratios, then they should prefer D; if they chose according to the diameter of the feedback stimuli, then they should prefer B. In the ordered feedback group, the crows strongly preferred B over D; in the constant feedback group, the crows' choice did not differ significantly from chance. These results, plus simulations using associative models, suggest that the orderability of the postchoice feedback stimuli is important for crows' transitive responding.

Generalization in place learning and geometry knowledge in rats

Rats were trained to search for a food reward hidden under sawdust in the center of a square-shaped enclosure designed to force orientation on the basis of the overall geometry of the environment. They were then tested in a number of enclosures differing in shape and in size (rectangular-, double-side square-, and equilateral triangle-shaped enclosures). Results showed that rats transferred their place-finding ability to the novel enclosures. Our results add evidence to the hypothesis that the evolutionary roots of spatial cognition entail a primitive encoding of geometric relationships, as already shown using other tasks in rats.

Searching in the Center: Pigeons (Columba livid) Encode Relative Distance From Walls of an Enclosure

Pigeons (Columba livia) searched for food hidden in the center of a square enclosure. On occasional tests without food, the enclosure was (a) unchanged from training (control tests), (b) moved to different corners of the testing room (corner tests), or (c) doubled in size (expansion tests). The birds showed localized search in the center of the enclosure on control and corner tests. On expansion tests, some birds searched near the center of the enclosure, suggesting relative-distance encoding. Other birds searched at locations that maintained the training distance from walls, suggesting absolute-distance encoding. These results are consistent with previous studies on chicks (Gallus gallus) in similar enclosures and contrast with previous results on pigeons' responses to expansions of discrete landmark arrays.

Searching by rules: pigeons' (Columba livia) landmark-based search according to constant bearing or constant distance

Pigeons (Columba livia) searched for a goal location defined by a constant relative spatial relationship to 2 landmark. For one group, landmark-to-goal bearings remained constant while distance varied. For another group landmark-to-goal distances remained constant while direction varied. Birds were trained with 4 interlandmark distances and then tested with 5 novel interlandmark distances. Overall error magnitude was similar across groups and was large than previously reported for Clark's nutcrackers (Nucifraga columbiana). During training, error magnitude increased with interlandmark distance for constant-bearing but not constant-distance birds. Both groups searched less accurately along the parallel to landmarks than along the perpendicular axis. Error magnitude increased with novel extrapolated interlandmark distances but not with novel interpolated distances. Results suggest modest geometric rule learning by pigeons.