Bradley R. Sturz

Orientation in trapezoid-shaped enclosures: implications for theoretical accounts of geometry learning.

Human participants learned to select 1 of 4 distinctively marked corners in a rectangular virtual enclosure. After training, control and test trials were interspersed with training trials. On control and test trials, all markers were equivalent in color, but only during test trials was the shape of the enclosure manipulated. Specifically, for each test trial, a single long wall or short wall of the enclosure increased twice as long as or decreased half as long as that present in the training enclosure. These manipulations produced 8 unique trapezoid-shaped enclosures. Participants were allowed to select 1 corner during control and test trials. Performance during control trials revealed that participants selected the correct and rotationally equivalent locations. Performance during test trials revealed that participants selected locations in trapezoid-shaped enclosures that were consistent with those predicted by global geometry (i.e., principal axis of space) but were inconsistent with those predicted by local geometry (i.e., proportion of rewarded training features present at a location). Results have implications for theoretical accounts of geometry learning.

Neither by global nor local cues alone: evidence for a unified orientation process

A substantial amount of empirical and theoretical debate remains concerning the extent to which an ability to orient with respect to the environment is determined by global (i.e., principal axis of space), local (i.e., wall lengths, angles), and/or view-based (i.e., stored representation) accounts. We developed an orientation task that allowed the manipulation of the reliability of the principal axis of space (i.e., searching at the egocentric left- and/or right-hand side of the principal axis) between groups while maintaining goal distance from the principal axis, local cues specifying the goal location (i.e., short wall left, short wall right, and obtuse angle), and visual aspects of the goal location consistent across groups. Control and test trials revealed that participants trained with a reliable principal axis of space utilized both global and local geometric cues, whereas those trained with an unreliable principal axis of space utilized only local geometric cues. Results suggest that both global and local geometric cues are utilized for reorientation and that the reliability of the principal axis of an enclosure differentially influences the use of geometric cues. Such results have implications for purely global-based, purely local-based, and purely view-based matching theoretical accounts of geometry learning and provide evidence for a unified orientation process.

Evidence against integration of spatial maps in humans

A dynamic 3-D virtual environment was constructed for humans as an open-field analogue of Blaisdell and Cooks (2005) pigeon foraging task to determine if humans, like pigeons, were capable of integrating separate spatial maps. Participants used keyboard keys and a mouse to search for a hidden goal in a 4×4 grid of raised cups. During Phase 1 training, a goal was consistently located between two landmarks (Map 1: blue T and red L). During Phase 2 training, a goal was consistently located down and left of a single landmark (Map 2: blue T). Transfer trials were then conducted in which participants were required to make choices in the presence of the red L alone. Cup choices during transfer assessed participants’ strategies: association (from Map 1), generalization (from Map 2), or integration (combining Map 1 and 2). During transfer, cup choices increased to a location which suggested an integration strategy and was consistent with results obtained with pigeons. However, additional analyses of the human data suggested participants initially used a generalization strategy followed by a progressive shift in search behavior away from the red L. This shift in search behavior during transfer was responsible for the changes in cup choices across transfer trials and was confirmed by a control condition. These new analyses offer an alternative explanation to the spatial integration account proposed for pigeons.

Facilitation of learning spatial relations among locations by visual cues: Implications for theoretical accounts of spatial learning

Human participants searched in a real environment or interactive 3-D virtual environment open field for four hidden goal locations arranged in a 2 × 2 square configuration in a 5 × 5 matrix of raised bins. The participants were randomly assigned to one of two groups: cues 1 pattern or pattern only. The participants experienced a training phase, followed by a testing phase. Visual cues specified the goal locations during training only for the cues 1 pattern group. Both groups were then tested in the absence of visual cues. The results in both environments indicated that the participants learned the spatial relations among goal locations. However, visual cues during training facilitated learning of the spatial relations among goal locations: In both environments, the participants trained with the visual cues made fewer errors during testing than did those trained only with the pattern. The results suggest that learning based on the spatial relations among locations may not be susceptible to cue competition effects and have implications for standard associative and dual-system accounts of spatial learning.

Learning of absolute and relative distance and direction from discrete visual landmarks by pigeons (Columba livia).

In an open-field search task, pigeons (Columba livia) were trained to search for a goal located at the midpoint of the hypothetical line connecting two discrete visual landmarks positioned 60 cm apart. In Experiment 1, global orienting cues were absent. After reaching training criteria, pigeons were tested with novel interlandmark distances. Search location and error on test trials suggested pigeons learned relative distance. In Experiment 2, a global orienting cue was present. After reaching training criteria, pigeons were again tested with novel interlandmark distances. Results suggested pigeons learned relative and absolute distances. In Experiment 3, pigeons searched at the midpoint of rotated arrays in both the presence and absence of an orienting cue indicating learning of relative direction. In Experiment 4, pigeons searched in the appropriate goal direction when presented with a single landmark in the presence of the orienting cue but not in its absence indicating learning of absolute direction. Results implicate a stable frame of reference as critical to spatial coding strategies and suggest pigeons are able to code location based on absolute and relative distance and direction from discrete visual landmarks.

Is Surface-based Orientation Influenced by a Proportional Relationship of Shape Parameters?

We investigated the extent to which parameters of environmental shape – namely the major and minor principal axes of space which pass through the centroid and approximate length and width of the entire space, respectively, were subject to similar psychophysical principles as those involved in distance discriminations. We developed an orientation task that allowed us to manipulate the ratio of the major to the minor principal axes of an enclosure during training and control for orientation by alternative cues other than principal axes such as wall lengths or corner angles during testing. Participants trained in an environment with a larger hypothetical discriminability ratio allocated more responses to locations specified by the principal axes of space across novel enclosure types compared to a group trained with a smaller hypothetical discriminability ratio. Results suggest that psychophysical principles may operate on the discrimination of environmental shape parameters and delineate a potential mechanism for experiential and developmental changes in orientation ability.

Abstract-concept learning carryover effects from the initial training set in pigeons (Columba livia).

Three groups of pigeons were trained in a same/different task with 32, 64, or 1,024 color-picture stimuli. They were tested with novel transfer pictures. The training-testing cycle was repeated with training-set doublings. The 32-item group learned the same/different task as rapidly as a previous 8-item group and transferred better than the 8-item group at the 32-item training set. The 64- and 1,024-item groups learned the task only somewhat slower than other groups, but their transfer was better and equivalent to baseline performances. These results show that pigeons trained with small sets (e.g., 8 items) have carryover effects that hamper transfer when the training set is expanded. Without carryover effects (i.e., initial transfer from the 32- and 64-item groups), pigeons show the same degree of transfer as rhesus and capuchin monkeys at these same set sizes. This finding has implications for the general ability of abstract-concept learning across species with different neural architectures.

Reorienting when cues conflict: A role for information content in spatial learning?

In two experiments, human participants searched in dynamic three-dimensional virtual-environment rectangular enclosures. Unlike previous studies involving learning of features and geometry, we trained features and geometry separately before placing them in conflict. Specifically, participants learned to respond to rewarded features located along the principle axis of a rectangular search space and to respond to rewarded geometry of a rectangular search space in separate training phases followed by a single test trial. During the test trial, features and geometry were placed in conflict by situating rewarded bins during feature training in unrewarded geometric corners from geometry training and unrewarded bins during feature training in rewarded geometric corners from geometry training. Results of Experiment 1 indicated that although all participants learned features and geometry at an equivalent rate and to an equivalent level, performance during the test trial indicated no preferential responding to features or geometry. However, choice reaction time was significantly longer during the test trial compared to that of last feature and last geometry training trials. Experiment 2 attempted to dissociate information content of features and geometry from their acquired associative strength by rewarding only one geometric corner during geometry training. Results of Experiment 2 indicated that although features had presumably acquired greater associative strength relative to that of geometry by the end of training, performance during the test trial indicated no preferential responding to features or geometry. As in Experiment 1, choice reaction time was significantly longer during the test trial compared to that of last feature and last geometry training trials. Collectively, results seem to provide converging evidence against a view-based matching account of spatial learning, appear inconsistent with standard associative-based accounts of spatial learning, and suggest that information content of spatial cues may play an important role in spatial learning.

Domain is a moving target for relational learning

The domain for relational learning was manipulated by varying the training set size for pigeons that had learned the same/different (S/D) concept. Six pigeons that had learned a S/D task with pairs of pictures with a set size of 1024 picture items had their training set size reduced to 8 items. Training on the reduced 8-item set was followed by transfer testing that was repeated four times. Transfer performance following reduction of the training set to 8 items was 9.2% less than it had been when the pigeons were trained with the 1024-item set, but 25.8% above chance. This partial abstract-concept learning remained constant over the four tests with novel stimuli. The results show that a broad domain established by a large expanding training set can once again become restricted by further training with a small training set.

Solving for two unknowns: An extension of Vector-based models of Landmark-based Navigation.

Vectors are mathematical representations of distance and direction information that take the form of line segments where length represents distance and orientation in space represents direction. Vector-based models have proven beneficial in understanding the spatial behavior of a variety of species in tasks that require landmark-based navigation via vector addition and vector averaging to determine a location. Extant research regarding vector-based representational and computational accounts of landmark-based navigation has involved tasks that required solving for one unknown (i.e., a location). Using a novel landmark-based navigation task, we provide evidence consistent with a form of vector algebra that involves solving two simultaneous equations with two unknowns in order to determine a location in space. Results extend vector-based accounts of landmark-based navigation and provide a novel methodological approach to the testing of mobile organisms.