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Supplemental information:
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Correlation across intra-individual’s differences.
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Navigating ants rely on both memorized views and motor routine in order to
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recapitulate a route. The use of such memories is not totally rigid as ants do not reproduce
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perfectly the same route over trials. The ants thus tolerate some extant of mismatch
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between what is memorized and what is currently perceived and display and might also
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possess a mismatch tolerance threshold (MTT) to distinguish between being on the
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familiar route or not (Wystrach 2009). The “intra-individual” path variability across
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successful trials measured here is an indirect measure of the ant’s tolerance to mismatch
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in the view perceived and motor routine displayed. The higher the individual’s tolerance
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to mismatch is, the higher her path variability across trials should be. A high tolerance to
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mismatch should result in a high propensity of displaying errors. Accordingly to this
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prediction, the “Intra-individual” path variability (measured from the non-error trials
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only) is significantly positively correlated with the frequencies of corner choice errors
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(r=0.342; p=0.039)(Figure S1A).
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The intra-individual path variability tends to be smaller when calculated between
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successive trials rather than between random trials. This could be explained by two
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hypotheses. The ants could have displayed either sudden switches or a progressive
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evolution in their path layout. We observed a significant positive correlation between
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sequential and random variability across individuals (r = 0.895 ; p < 0.001 ) (Figure S1B).
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This correlation supports the second hypothesis (i.e., progressive evolution of the path)
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but not the first one (i.e., sudden switches at particular trials). Indeed, if an ant would
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display sudden switches at particular trials only, the extent of their random path
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variability would be strongly increased while the sequential variability would stay lower.
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In contrast, if an ant displays a progressive evolution in her path layout, the extent of her
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random path variability would reflect directly the extent of its sequential variability,
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causing a strong correlation between the two variables. Such a progressive evolution of
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the path layout indicates that ants updated their memory from trial to trial.
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Interestingly, the best-fit slope of this correlation (Figure S1B) is less than 1
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(slope = 0.763). This indicates that it is the individuals having a high sequential
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variability that displayed a more apparent path evolution. This makes sense with the idea
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that individuals where constrained by a constant MTT and were updating their memory
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on each trial. Indeed, the higher the individual’s MTT, the more its paths should vary
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from trial to trial (high sequential variability), and thus the more its memory is altered,
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and therefore, the quicker its path layout should evolve (lower ratio sequential/random
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variability).
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The actual linear regression slope of this correlation (Figure S1B) depends on the
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extent to which the memory of the last trial overrides the previous memory. As shown by
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the simulations, a “memory override” value of 0 (no updating of the memory) leads
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roughly to a slope of 1 (simulated slope = 0.9379), which means no path evolution. A
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“memory override” value of 1 (only the last trial is used), however, leads to a smaller
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slope (simulated slope = 0.2060) than the one observed in ants (observed slope = 0.7630).
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Therefore, the ants might refresh only partially their memory at each trial. The simulated
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slope that matches best the observed slope was obtained for a “memory override” value
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of 0.25 (simulated slope = 0.7315).
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The range of MTT values attributed to the population of simulated ants is directly
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reflected by the distribution of the individual’s sequential variability. The best matching
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simulated distribution of individuals’ sequential variability (Gaussian distribution: mean
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= 7.96, SD = 2.92), compared with the observed distribution (Gaussian distribution: mean
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= 8.02, std = 2.78), has individuals’ MTT values ranging from 5 cm to 30 cm (uniform
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distribution). The MTT value corresponds here to the maximum variation tolerated by the
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individual between its memorized path and the path it actually takes (See Figure S2),
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encompassing both visual and motor mismatch tolerance.
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Memory override computer simulation methods
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We used the software Matlab to run simulations and find out to what extent the last trial
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overrides the memory. We ran twenty simulations with different “memory override”
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values: from 0 (no override or memory fixed) to 1 (complete override of the memory,
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with only the previous trial used) by steps of 0.05.
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In order to get precise best-fit lines, each simulation processed 1000 model ants.
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A MTT value was randomly chosen within a particular range for each simulated ant (best
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fit simulation obtained for MTT values uniformly distributed between 5 and 30 cm)
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(Figure S2). Each simulated ants displayed 40 trials (as the real ants on average did). The
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path taken on a trial was represented by a simple value. The variability between two paths
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was simply calculated as the difference between the two paths’ values. We thus obtained
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one inter-path comparison value for each pair of paths compared (as we did with the real
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ants’ data).
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All the simulated ants started with a “memorized path” of 0. The first path taken
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was equal to the “memorized path” plus or minus a random “variation”. This “variation”
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value was randomly chosen within the range given by the MTT value of the individual
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(uniform distribution). Thus,
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path takenn = memorized pathn–1 + variationn
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Then the “memorized path” value is updated as a function of the “memory override”
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value of the simulation:
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memorized pathn = memorized pathn–1 + (variationn  memory override)
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If memory override = 1 then memorized pathn = path takenn–1. The next trial (n+1) started
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with memorized pathn. As a result, the path taken by an individual drifts from trial to
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trial; the extent of this drifting depends of both the individual’s MTT value and the
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memory override value (fixed across all individuals for a given simulation). In the arena
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(80 cm  40 cm), the real ants’ paths were constrained by the walls. The biggest inter-
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path values theoretically possible to obtain from a pair of successful paths (i.e., ending in
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the same corner and shorter than 250 cm) reach approximately 80 cm. To simulate the
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presence of the walls of the arena, the “paths taken” values were thus constrained
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between –40 to +40, setting the biggest inter-path value possible at 80.
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Supplemental Figures
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Figure S1.
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Figure S1. Plots of the individual ants according to their intra-individual path variability
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calculated across random trials (x axis) and two other variables (y axis). The random
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inter-trial path variability measures the non-constancy of the path layouts across the
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successful (i.e., non-error) trials within individuals. It is an indirect measure of the ant’s
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tolerance to mismatch. Each dot represents an individual ant; the lines represent the linear
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best-fit trends. A) Results obtained with real ants. The percentage of errors (y axis) refers
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to the frequency of choice for other corners than the preferred one. B) The sequential
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variability (y axis) results from the comparison of paths from successive trials. The
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results obtained in real ants (top left) show that ants having a high sequential inter-trial
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variability have an even higher random inter-trial variability (i.e., the path layout tends to
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evolve from trial to trial). Simulations of 1000 ants show that the extent to which the
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memory of the last trial overrides the previous memory modifies the slope of the
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correlation. The results of the simulations are shown for 3 possible memory updating
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extent: no updating of the memory at all, with only the first trial used (bottom-left:
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memory override value = 0); complete replacement of the memory, with only the
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previous trial used (bottom-right: memory override value = 1); the slope that best
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matches the real ants’ data has been obtained for a partial updating of the memory (top-
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right: memory override value = 0.25).
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Figure S2.
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Figure S2. Examples of the inaccuracy (gray areas) to which a path memory (black paths)
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can lead to as a function of the individual’s MTT (Mismatch Tolerance Threshold). The
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MTT is not expressed here in terms of visual mismatch tolerated but in terms of distance
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away from the memorized path tolerated. It thus encompasses both visual and motor
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routine mismatches. The simulations’ results that matched the best the real ants’ data
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were obtained for MTT values ranging from 5 cm (left panel) to 30 cm (right panel) in
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the population of simulated ants.
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