Sub-strategy characterization.

<p>Characterization of all sub-strategies used by subjects for the purpose of copying a block regarding the involvement of memory (M: model, W: workspace, and R: resource area). Each sub-strategy is given a name which is used throughout the manuscript.</p

Linear cost optimization.

<p>Experimental data for a) costs for memorization (i.e., duration of 1st model visit) with power function fits for simple (dashed line) and complex (dotted line) patterns, b) costs for acquisition (i.e., overall time for transitions) with linear regression lines for near (gray) and far conditions (black), and c) total time costs (i.e., overall response time; regressions indicate quadratic functions). All data are shown as a function of the ratio between ‘high-memory’ and ‘low-memory’ sub-strategies. d) Model: Total costs are divided in costs for memorization (C<b>_Me</b>) and acquisition (C<b>_Ac</b>). If more information is processed at each model visit (i.e., if the task is solved with fewer visits), memory costs increase while acquisition costs decrease. These individual costs vary also with the experimental conditions for walking distance (near and far) and pattern complexity (simple and complex). Total costs for the complex/far condition are depicted as the sum of the according individual cost curves (blue line), leading to an optimum of processed information per model visit at point <i>b</i>. The location of each optimum for the four experimental groups is indicated with <i>a–d</i>.</p

Task setup and analysis of walking trajectory.

<p>a) Scheme of the experimental setup with the spatial arrangement of the three operating areas (M: model, W: workspace, R: resource area, S: start and end point of a subjects' trajectory) for the two distance conditions (black boxes: far distance condition, gray boxes: near distance condition). b) Example of a subject's single trial trajectory in the long distance and complex pattern condition. Temporal course is coded with a gray-scale gradient. b) Relevant sub-strategies (together with their names) and their demand on WM from low to high usage. The W-M-W sub-strategy was applied as ‘control’ strategy without any block operation. ‘Other’ denotes all remaining sub-strategies which had individual frequencies of occurrence below 2% (for a detailed explanation see section ‘walking sub-strategies’).</p

Task performance: error rate and overall response time.

<p>a) Box-Whisker plot of proportion of errors made during copying the ten simple patterns (left) and the ten complex patterns (right) for the far and the near distance conditions. Black boxes display the pattern errors: the proportion of false on all patterns (n = 10) averaged over subjects of the respective group. White boxes display the block errors: the proportion of false blocks on all blocks in all ten patterns (n = 6 blocks×10 patterns = 60) averaged over subjects of the respective group. b) Box-Whisker plot of response time to complete a single trial averaged over all subjects of the respective group for the simple (left) and complex (right) pattern situations and for the far (black boxes) and near (gray boxes) distance conditions. Statistical effects (post-hoc analyses) are presented for each pattern complexity/distance combination (^★p<.05; ^★★p<.01; ^★★★ p<.001).</p

Proportion of walking sub-strategies.

<p>Box-Whisker plot of proportion of walking sub-strategies used by subjects during copying the simple patterns (left) and the complex patterns (right) averaged over all subjects of the respective group. Black boxes display the frequencies of walking sub-strategies for the far distance condition and gray boxes these for the near distance condition. Post-hoc analyses are calculated for ‘low-memory’ and ‘high-memory’ referring the proportion of walking sub-strategies between far and near and simple and complex pattern conditions (^★p<.05; ^★★p<.01; ^★★★ p<.001; n.s. not significant). The characteristics of all individual sub-strategies are explained in detail in the results chapter (see section ‘walking sub-strategies’).</p

Location-dependent vectors from Fig. 5, rotated to align the air-line directions from all interview locations to 0 degrees (letters indicate interview locations).

<p>Vectors are significantly biased towards the theoretical direction (green line, ). Vector length reaches from zero to one (radius of circle) and is a measure of concentration of the location-dependent vectors.</p

Examples of sketches of the “Holzmarkt” from four participants.

<p>The blue arrows indicate the orientation the sketch was rated in. Note the inscriptions “Stiftskirche” or “Kirche” referring to the landmark church building located at this square (see also view A3 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0112793#pone-0112793-g001" target="_blank">Figure 1a</a>). The parallel lines mark a flight of stairs leading from the square to the church, the circles mark a fountain at the Western side of the square.</p

Downtown map of Tübingen with interview locations (A–J) for the near condition and target square “Holzmarkt”.

<p>The vectors show the average sketch map orientation at the respective interview site. At seven (blue circles) out of ten near sites sketch orientations were found to point from the interview location in the direction of the target square ( or better). At one location, a strong tendency was indicated (A, cyan, ). For two locations (F,G; red), no significant orientation effect could be found. Vector length ranges from zero to one (radius of circle) and is a measure of concentration of the location-dependent vectors. Map source: © Open-StreetMap contributors.</p

View-based model of spatial long-term memory.

<p>Upper case letters A, B, C denote places, numbers (1–4) denote views visible at each place. E.g., view A3 depicts a church building when standing at the “Holzmarkt” (A), facing south. a) Place representation composed of a collection of directional views (1–4) obtained at a place A. Views may be represented multiply, or overlapping, allowing to represent viewing direction in a population code. The size of the circles indicates the frequency with which each view is stored, or the likelihood that it is read out in recall. (Tübingen Holzmarkt icons are sections of a panoramic image retrieved with permission from <a href="http://www.kubische-panoramen.de" target="_blank">www.kubische-panoramen.de</a>.) b) View-graph of 12 views (A1-C4) belonging to three places. Within each place, views are linked by turning movements. Views of different places are linked by movements involving translations. Note that these links are unidirectional; for example a path from A to B starts from view A3, while the return from B to A will end on A1. c) A view-based model of spatial working memory is obtained by extracting a sub-graph from the total view-graph. It contains the current view (B1) which also marks the current observer position and forward direction, and its outward neighborhood of order 1, i.e., the directly adjacent views (A1, B2, B4, C1). Outward neighborhoods of higher orders may also be represented but are not shown in the figure. The polar grid is added to indicate that metric updating may take place in the working memory, which, however, does not play a role in the experiment reported in this paper. Map source: © OpenStreetMap contributors.</p

Downtown map of Tübingen with target square “Marktplatz”, near interview locations (A–H) and location-dependent vectors drawn at these locations.

<p>Vectors at six (blue circles) out of eight interview sites point towards the target square ( or better). For two locations (C, D; red), no significant orientation effect could be found. Vector length reaches from zero to one (radius of circle) and is a measure of concentration of the location-dependent vectors. Map source: © OpenStreetMap contributors.</p