Psychological Research (2010) 74:560–567 DOI 10.1007/s00426-010-0277-4

ORIGINAL ARTICLE

Encoding of variability of landmark-based spatial information Bradley R. Sturz • Kent D. Bodily

Received: 4 October 2009 / Accepted: 28 January 2010 / Published online: 24 February 2010 Ó Springer-Verlag 2010

Abstract Recent evidence suggests humans optimally weight visual and haptic information (i.e., in inverse proportion to their variances). A more recent proposal is that spatial information (i.e., distance and direction) may also adhere to Bayesian principles and be weighted in an optimal fashion. A fundamental assumption of this proposal is that participants encode the variability of spatial information. In a three-dimensional virtual-environment open-field search task, we provide evidence that participants encoded the variability of landmark-based spatial information. Specifically, participants searched for a hidden goal location in a 5 9 5 matrix of raised bins. Participants experienced five training phases in which they searched for a hidden goal that maintained a unique spatial relationship to each of four distinct landmarks. Each landmark was assigned an a priori value of locational uncertainty such that each varied in its ability to predict a goal (i.e., varied in number of potential goal locations). Following training, participants experienced conflict trials in which two distinct landmarks were presented simultaneously. Participants preferentially responded to the landmark with the lower uncertainty value (i.e., smaller number of potential goal locations). Results provide empirical evidence for the encoding of variability of landmark-based spatial

B. R. Sturz (&) Department of Psychology, Armstrong Atlantic State University, 229 Science Center, 11935 Abercorn Street, Savannah, GA 31419, USA e-mail: [email protected] K. D. Bodily (&) Department of Psychology, Georgia Southern University, P. O. Box 8041, Statesboro, GA 30460, USA e-mail: [email protected]

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information and have implications for theoretical accounts of spatial learning.

Introduction Species ranging from insects to mammals appear capable of navigation with reference to objects in the environment (for a review, see Healy, 1998), and theoretical accounts of this landmark-based navigation have focused predominantly on underlying associative processes (for a review, see Chamizo, 2003). Over the years, evidence for blocking and overshadowing in the spatial domain have provided empirical support for associative-based accounts of landmark-based navigation (e.g., Cheng & Spetch, 2001; Chamizo, AznarCasanova, & Artigas, 2003; Rodrigo, Chamizo, McLaren, & Mackintosh, 1997; for a review, see Chamizo, 2003), and the presence of these associative cue-competition effects is often taken as evidence that spatial information is processed by a unitary spatial learning system. The absence of associative cue-competition in situations in which these models predict it should have occurred seems problematic for associative-based accounts of spatial learning (for a review, see Cheng & Newcombe, 2005; however, see also Miller, 2009; Miller & Shettleworth, 2007). As a result, other theoretical accounts of spatial learning have proposed multiple spatial learning systems to account for the absence of associative cue-competition (e.g., Cheng, 1986; Cheng & Newcombe, 2005; Doeller & Burgess, 2008; Doeller, King, & Burgess, 2008; for a review, see Burgess, 2006; Gallistel, 1990; see also Steck & Mallot, 2000; c.f., Gillner, Weiß, & Mallot, 2008; for models derived from artificial agents, see Dawson, Kelly, Spetch, & Dupuis, 2010; Ponticorvo & Miglino, 2010). In general, these multiple-system accounts propose two distinct

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learning systems composed of separate feature- and geometry/boundary-based systems. However, recent evidence in which cue-competition has been obtained in situations in which these models predict it should not have occurred seems problematic for these multiple-systems accounts of spatial learning (e.g., Gray, Bloomfield, Ferrey, Spetch, & Sturdy, 2005; Graham, Good, McGregor, & Pearce, 2006; Pearce, Graham, Good, Jones, & McGregor, 2006; for reviews, see Cheng & Newcombe, 2006; Cheng, 2008). Given these conflicting results for and against unitaryand multiple-systems accounts of spatial learning that have historically relied on associative cue-competition as the discriminating diagnostic tool, recent empirical and theoretical efforts have shifted focus to the relative weighting of spatial cues (Newcombe & Ratliff, 2007; Ratliff & Newcombe, 2008). This adaptive-combination model suggests that spatial cues are weighted by factors such as reliability, validity, saliency, strength, and prior experience. Specifically, based on recent evidence that suggests that humans integrate visual and haptic information in a statistically optimal fashion (Ernst & Banks, 2002; for a review, see Deneve & Pouget, 2004), mechanisms that adhere to Bayesian principles have been proposed as underlying a process of the weighting of spatial information (Cheng, Shettleworth, Huttenlocher, & Rieser, 2007; see also Newcombe & Ratliff, 2007). Importantly, such a model based upon weighting of spatial information provides general mechanisms that could account for both presence and absence of associative cue-competition in spatially based tasks. Logistical problems associated with testing humans in navigational tasks have resulted in recent research utilizing three-dimensional virtual environments (e.g., Foo, Warren, Duchon, & Tarr, 2005; Mou et al., 2004; Sturz, Bodily, & Katz, 2006; Sturz & Kelly, 2009; for a review, see Kelly & Gibson, 2007). Research utilizing such software has been gaining in popularity because the resulting environments allow for ease in experimental manipulation, control of experimental design, and maintenance of ecological validity (for a review see Loomis et al. 1999; Pe´ruch & Gaunet, 1998). Further, the mechanisms used in navigating dynamic 3-D virtual environments have been argued to be similar to those used in navigating real environments (Arthur, Hancock, & Chrylser, 1997; Hartley, King, & Burgess, 2003; Montello, Hegarty, Richardson, & Waller, 2004; Klatzky, Loomis, Beall, Chance, & Golledge, 1998; Sturz, Bodily, Katz, & Kelly, 2009a; Sturz, Brown, & Kelly, 2009b; Sturz, Kelly, & Brown, 2009c). Hence, dynamic 3-D virtual environments may be ideally suited for testing spatial learning, memory, and cognition in human participants. Using an established dynamic three-dimensional virtual open-field search task (Sturz & Diemer, 2010; Sturz et al.,

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2006; Sturz et al., 2009b; Sturz & Kelly, 2009; Sturz et al., 2009c), we tested a fundamental assumption derived from an adaptive-combination model of spatial learning (Newcombe & Ratliff, 2007). According to an adaptivecombination model, the certainty and variability of a spatial cue is encoded which may directly affect its weighting relative to other spatial cues and its future reliance by a mobile organism. Specifically, an adaptive-combination model suggests that the variability of spatial information is encoded such that this information could then be weighted in inverse proportion to its variance. We tested the fundamental assumption derived from Newcombe and Ratliff (2007) that participants encode the variability of landmarkbased spatial information. Specifically, participants initially searched for a hidden goal that maintained a unique spatial relationship to each of four distinct landmarks. Each landmark was assigned an a priori value of locational uncertainty such that each varied in its ability to predict a goal location (Fig. 1). If the variability associated with each of these trained landmarks is encoded and affects participants search strategies as suggested by an adaptivecombination model, then when two of these trained landmarks are placed in conflict, participants should preferentially respond to the landmark with the lower uncertainty value (i.e., the landmark with the smaller number of potential goal locations).

Method Participants A total of 24 (Armstrong Atlantic State University and Georgia Southern University) undergraduate students (15 males and 9 females) served as participants. Participants received extra class credit. Apparatus An interactive three-dimensional virtual environment was constructed and rendered using Valve Hammer Editor and run on the Half-Life Team Fortress Classic platform. A personal computer, 19-in. flat-screen liquid crystal display (LCD) monitor, optical mouse, keyboard, and speakers served as the interface with the virtual environment. The monitor (1,152 9 864 pixels) provided a first-person perspective of the virtual environment (see bottom panel, Fig. 1). The arrow keys of the keyboard : (forward), ; (backward), / (left), and ? (right), the mouse, and the left mouse button navigated within the environment. Speakers emitted auditory feedback. Experimental events were controlled and recorded using Half-Life Dedicated Server on an identical personal computer.

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562 Fig. 1 Top and middle panels overhead perspectives of the virtual search space for one potential training trial for each landmark type. Clockwise from top-left the square, rectangle, X, and T landmarks with respective spatial locations of potential goals. For illustrative purposes, white circles denote the potential goal locations for each landmark type. One random potential goal location(s) was the actual goal location for each landmark type for each training trial (see text for details). Bottom panel first-person perspectives of the virtual search space for two potential conflict trials. Please note that participants experienced both training and testing from the first-person perspective. Participants also began each trial at position S during both training and testing

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Stimuli Dimensions are length 9 width 9 height and measured in virtual units (vu). The virtual environment (1,050 9 980 9 416 vu) contained 25 raised bins (86 9 86 9 38 vu) arranged in a 5 9 5 matrix (see top and middle panels, Fig. 1). Four objects served as landmarks: a blue square (32 9 32 9 48), a green rectangle (118 9 32 9 48), a yellow T (118 9 76 9 48) and a red X (118 9 118 9 48). The room was illuminated by a light source centered 64 vu below the ceiling. All walls were black. Procedure Participants experienced five training phases and one test phase. Participants were informed to ‘‘locate the bin that transports you to the next room’’. To jump into a bin, participants simultaneously moved forward (:) and jumped (left mouse button). Auditory feedback indicated a jump occurred (‘‘huh’’ sound). Successful discovery of the goal location resulted in auditory feedback and a 1 s inter-trial interval (ITI) in which the monitor was black and participants progressed to the next trial. Selection of a non-goal bin resulted in no auditory feedback and required participants to jump out of the current bin and continue searching. We attempted to assign an a priori value of locational uncertainty to each one of the four landmarks by manipulating the number of locations that could potentially contain the actual goal location (i.e., each landmark varied in its number of potential goal locations; see Fig. 1, top and middle panels). Specifically, the square landmark was assigned one potential goal location; the rectangle landmark was assigned two potential goal locations; the T landmark was assigned three potential goal locations, and the X landmark was assigned four potential goal locations. As a result, each landmark specified these number(s) of unique spatial locations that could contain the actual goal location for the duration of the experiment. Training Training consisted of five phases. Each phase consisted of 16 trials. For Phases 1–4, one of the four landmark–goal spatial relations was trained in each phase so that by the end of Phase 4 all four unique landmark–goal spatial relations had been trained. To control for order effects, sequences of trained landmark–goal spatial relations were completely counterbalanced across the 24 participants. For each trial of each phase, the actual location of the goal was randomly assigned to one of the 25 bins, and the landmark was then randomly positioned north-west (NW), north-east (NE), south-west (SW), or south-east (SE) of the goal location. Please note that the directions of landmark spatial

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locations are given with respect to the start location (labeled S in Fig. 1). Please also note that the rectangle landmark was rotated 90° clockwise when positioned NE or SW of the actual goal location, and the T landmark was rotated a random orientation of 90°, 180°, or 270° clockwise when positioned SW of the actual goal location. The actual goal location (only one per trial) was always located at one of the potential goal locations associated with each landmark type, but the actual goal location varied randomly among the potential goal locations associated with each landmark type from trial to trial (refer to top and middle panels, Fig. 1). Phase 5 combined the four previously experienced landmark–goal spatial relations into a single phase which contained four 4-trial blocks with each block composed of one landmark–goal relation from each training phase. The sequences of landmark–goal spatial relations presented during Phase 5 were randomized within each block. Upon completion of Phase 5, testing began. Please note that participants were not informed of any landmark–goal spatial relations. Testing Testing was similar to Phase 5 training except that during testing, participants completed 30 trials composed of six 5-trial blocks. Each block contained one landmark–goal spatial relation from each of the first four training phases and one test trial. The sequences of training trials and the test trial presented during testing were randomized within each block. On training trials, the location of the actual goal location and landmark were determined as described above. On test trials, two of the trained landmarks (e.g., the Square and the X) were placed in conflict in pseudorandom locations. Thus, two landmarks were present during each test trial (see bottom panel, Fig. 1). Importantly, the two landmarks indicated conflicting information about the location and number of potential goal locations (i.e., locational uncertainty). Participants were allowed to make a single response during each test trial which was followed by the 1 s ITI and progression to the next trial. As there were four training landmark–goal spatial relations, a total of six unique two-landmark combinations were tested. Each of these six possible two landmark combinations was presented once during the test phase. The sequences of landmark–goal spatial relations presented during testing as well as the location of the test trial were randomized within each trial block. To control for landmark distance from the participant, potential goal location distance from the participant, and landmark visibility, all test trials placed both landmarks equidistant from the participants’ start location, oriented both landmarks in such a way that the nearest potential goal location(s) were equidistant from the start location, and placed both landmarks so that they were both

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To confirm participants learned the landmark–goal spatial relations for each landmark type, we analyzed the proportion of responses that occurred to potential goal locations during the training trials presented during the test phase. We believe such an analysis of training trials presented during the test phase served as the best indicator of learning because these trials were presented after initial training with each landmark type. Mean proportions of responses to potential goal locations for each landmark type were statistically greater than chance [i.e., 1/25 (0.04), 2/25 (0.08), 3/25 (0.12), 4/25 (0.16), respectively, for the square (M = 1.0, SD = 0), rectangle (M = 0.98, SD = 0.07), T (M = 0.97, SD = 0.08), and X (M = 1.0, SD = 0) landmarks] as confirmed by one-sample t tests [square (no t value; SD = 0), rectangle (t(23) = 59.41, p \ 0.001), T (t(23) = 52.04, p \ 0.001), and X (no t value; SD = 0) landmarks]. Such results show that participants responded nearly exclusively to the potential goal locations associated with each landmark and indicate that participants learned the landmark–goal spatial relations for each landmark type. To confirm that each landmark varied in its ability to predict a goal location as anticipated, we analyzed the mean errors to complete a trial during the same training trials presented during the test phase (Fig. 2, top panel). A repeated measures analysis of variance (ANOVA) on mean errors to complete a trial with landmark type (square, rectangle, T, X) as a factor revealed a main effect, F(3, 69) = 356.39, p \ 0.001. Fisher’s least significant difference (LSD) post hoc tests revealed mean errors to complete a trial for each landmark type were statistically different from all other landmark types (ps \ 0.001). In conjunction with the above results from proportion of responses to potential goal locations, these results suggest that despite participants’ nearly perfect responding to potential goal locations for each landmark type, these individual landmarks did vary in locational uncertainty because mean errors to find the actual goal location differed across all landmark types. Given the above evidence that landmarks varied in locational uncertainty, performance during the test trials in which two trained landmarks with differing values of locational uncertainty were placed in conflict provided the opportunity to assess whether these values of locational uncertainty influenced participants’ search performance. In fact, during the test trials, when two landmarks with differing values of locational uncertainty were placed in

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Training Trials Presented During Testing

Mean Errors to Complete Trial

Results

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2.0

1.5

1.0

0.5

0.0 Square

Rectangle

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Landmark Type Mean Proportion of Responses to Landmark with Smaller Number of Potential Goal Locations

simultaneously visible from the start location. Please note that participants were not informed there would be conflict trials.

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Test Trials Presented During Testing 1.0

0.8

0.6 Chance 0.4

0.0 0.25

0.33

0.5

0.67

0.75

Conflict Ratio

Fig. 2 Top panel mean errors to complete training trials (i.e., locate the goal) presented during testing plotted across landmark type. Bottom panel Mean proportion of responses during testing to the landmark with lower uncertainty value (i.e., smaller number of potential goal locations) plotted across conflict ratio (i.e., value of landmark with smaller number of potential goal locations divided by the value of the landmark with larger number of potential goal locations). Dashed line represents chance performance. Bars represent 95% confidence intervals of the mean

conflict, participants responded preferentially to the landmark with the lower uncertainty value (i.e., the landmark with the smaller number of potential goal locations). Figure 2 (bottom panel) shows mean proportion of responses during testing to the landmark with lower uncertainty value (i.e., smaller number of potential goal locations) plotted across conflict ratio (i.e., value of landmark with smaller number of potential goal locations divided by the value of the landmark with larger number of potential goal locations). A repeated measures ANOVA on mean proportion of responses to the landmark with the smaller number of potential goal locations with conflict ratio (0.25, 0.33, 0.5, 0.67, 0.75) as a factor did not reveal an effect, F(4, 92) = 1.72, p [ 0.15. One-sample t tests revealed each mean proportion was statistically greater than chance (i.e., 0.5), t(23) = 4.29, p \ 0.001; t(23) = 11.00, p \ 0.001; t(23) = 4.37, p \ 0.001; t(23) = 5.44, p \ 0.001; t(23) = 7.23, p \ 0.001, respectively for each conflict ratio from left to right across the abscissa.

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Discussion In the present virtual-environment open-field search task, participants learned the landmark–goal spatial relations for each landmark type. When these trained landmarks were placed in conflict on critical test trials, participants responded preferentially to the landmark with the lower uncertainty value (i.e., smaller number of potential goal locations). Thus, performance on critical test trials indicates that the certainty and variability of the landmarkbased spatial information was encoded and influenced participants’ search strategies. Present results appear consistent with a fundamental assumption of an adaptive-combination model of spatial learning that incorporates a weighting mechanism of landmark-based spatial information that adheres to Bayesian principles (Cheng et al., 2007; Newcombe & Ratliff, 2007; Ratliff & Newcombe, 2008). Specifically, results suggest that uncertainty about the spatial location of the goal location associated with each landmark was encoded and exhibited during conflict trials. Thus, like visual and haptic information (Ernst & Banks, 2002), the variability of spatial information is encoded, and our results have implications for theoretical accounts of spatial learning that are silent with respect to the role of certainty and variability (e.g., Chamizo, 2003; Cheng & Newcombe, 2005). Although the present results are not explicitly inconsistent with either unitary- or multiple-systems account of spatial learning because the present experiment did not attempt to explicitly discriminate between these two theoretical accounts of spatial learning, our results do suggest that these two theoretical accounts of spatial learning should be modified to incorporate encoding of the variability of spatial information. Importantly, the empirical support of such encoding of variability of spatial information obtained from the present experiment provides the possibility that this spatial information is then processed by general mechanisms that adhere to Bayesian weighting principles (see Cheng et al., 2007 for detailed discussion). For example, the optimal weights for any two trained landmarks, A and B, with variances of r2A and r2B could be calculated as follows (Bayes, 1763):
ð1Þ WA ¼ r2B = r2A þ r2B
WB ¼ r2A = r2A þ r2B : ð2Þ If these two trained landmarks differ in the amount of information conveyed about a goal location (i.e., variances), when they are placed in conflict a Bayesian weighting of their sources of spatial information will result in highly discrepant weighting values. Given these discrepant weighting values, optimal weighting of this

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landmark-based spatial information would predict preferential responding to the landmark with the lower uncertainty value (e.g., in the present experiment the landmark with the smaller number of potential goal locations). Future research could explore such Bayesian weighting of spatial information through repeated testing with response options that allow for metric adjustment in a continuous search space. Evidence for general mechanisms that adhere to Bayesian weightings could seemingly account for both presence and absence of associative cue-competition in spatially based tasks (for reviews, see Cheng, 2008; Cheng et al., 2007). Such general weighting mechanisms that adheres to Bayesian principles may also account for emerging evidence suggesting the encoding of multiple spatial cues stored in a hierarchical fashion by delineating how these multiple sources of spatial information are organized (Kamil & Jones, 2000; Jones, Antoniadis, Shettleworth, & Kamil, 2002; Singer, Abroms, & Zentall, 2006; Sturz & Katz, 2009; Sutton, 2002; for a review, see Spetch & Kelly, 2006). It is worth noting that the encoding of the variability associated with each landmark is not exclusive to an adaptive-combination model of spatial learning. For example, such a result presumably could also be accounted for by standard information processing models of conditioning (for a review, see Gallistel, 2003; Gallistel & Gibbon, 2001; Rescorla, 1988). Specifically, if objective information concerning the variability of spatial information is encoded (as suggested by present results), then information processing models of conditioning may be able to explain the computation and decision rules guiding spatial behavior. Regardless, present results suggest that any model of spatial learning will need to incorporate and explain the encoding and representation of spatial information and the ability of this information to be subjected to decision rules based upon computation. Finally, it seems relevant to discuss possible experiential differences between real and virtual environments that may impact participants’ navigation abilities and strategies (see Sturz et al., 2009a). Although by no means exhaustive, some potential critical differences include: physical effort required to navigate each environment, availability and amount of proprioceptive and vestibular feedback received during the locomotor task, amount and quality of auditory, olfactory, and visual cues, and visual angle. Seemingly, any of these experiential differences have the possibility to produce differences in results across environments; yet despite these differences, results in the present virtualenvironment task suggest that participants encoded the variability of each training landmark and this variability differentially affected participant’s choice responses during conflict trials. As a result, results from the present virtual-

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environment search task appear consistent with a fundamental assumption of an adaptive-combination model of spatial information processing suggesting the encoding of variability of spatial information (Cheng et al., 2007; Newcombe & Ratliff, 2007; Ratliff & Newcombe, 2008). Specifically, we found evidence that participants encoded the areas of locational uncertainty associated with each landmark and this variability influenced participant responses during conflict trials. Such lines of research exploring the encoding of spatial information should continue to advance an understanding of the mechanisms underlying navigation strategies and inform theoretical accounts of spatial learning, memory, and cognition. Acknowledgments This research was conducted following the relevant ethical guidelines for human research. We thank Paul Cooke, Stephanie Diemer, Sebastian Krzywanski, Martha Forloines, Shrinidhi Subramaniam, and especially Caroline Eastman and Rebecca Hattaway for their invaluable assistance with data collection and scoring. We are grateful for the comments by Fabio Ferlazzo, Kristin Ratliff, and an anonymous reviewer on an earlier version of this manuscript.

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