Data from: taking a shortcut: what mechanisms do fish use?
Data files
Apr 23, 2024 version files 16.18 MB

1000CoordinateData.csv

distanceData.csv

DistanceDataAnalysisForR.csv

distanceDataH2DDisplacement.csv

FishGroup.csv

Models.csv

Path_integration_data.csv

PathUntilDirectionBackToOrigine.csv

permutationData10000Random1D29D.csv

permutationData10000Random29Lend.csv

README.md
Abstract
Path integration is a powerful navigational mechanism whereby individuals continuously update their distance and angular vector of movement to calculate their position in relation to their departure location, allowing them to return along the most direct route even across unfamiliar terrain. While path integration has been investigated in several terrestrial animals, it has never been demonstrated in aquatic vertebrates, where movement occurs through volumetric space and sensory cues available for navigation are likely to differ substantially from those in terrestrial environments. By performing displacement experiments with Lamprologus ocellatus, we show evidence consistent with fish using path integration to navigate alongside other mechanisms (allothetic place cues and route recapitulation). These results indicate that the use of path integration is likely to be deeply rooted within the vertebrate phylogeny irrespective of the environment, and suggests that fish may possess a spatial encoding system that parallels that of mammals.
README: Taking a shortcut: What mechanisms do fish use?
Please find below all descriptions of data files and code used for the manuscript: Taking a shortcut: what mechanisms do fish use? , by Sibeaux et al. 2024
To better understand the data analyses and processing we have organised this file into 5 subsections:
1Matlab trajectory analysis
2Distance Analysis with R
3Distance to Random
4Comparison fish versus model angle and distance
5intrinsic and extrinsic effects on model chosen
6Extra analyses asked by reviewers
Some files are reused among subsections
1Matlab trajectory analysis
Please find below the description of the MATLAB code used for the analysis of the fish trajectories and the associated data files.
1_ "PathIntegrationVideoTracker.m"
MATLAB file produced by C.N. to track the fish in the experimental apparatus and extract the x and y coordinates of the fish
2_ "PathAnalysisCropingtoSize.m"
MATLAB file (by A.S.) allows to crop the fish trajectory and the model trajectories to the same size. The MATLAB file then implements 1000 points along the fish trajectory and the model trajectories. It requires the .csv files: "Model.csv" and "PathUntilDirectionBackToOrigine.csv" that gives the coordinates of the fish and of the 3 model trajectories. The output of this program can be found in "1000CoordinateData.csv" and "distanceData.csv" output files.
3_ "PathAnalysisForDDisplacementH2.m"
Similarly to the file 2, this MATLAB file (by A.S.) allows to crop the fish trajectory and the model trajectory to the same size but only focussed on the H2D trajectory = APC trajectory after diagonal displacement. The output is the "distanceDataH2DDisplacement.csv"
4_ "Model.csv" : gives the x and y coordinates of the 3 model trajectories (h1 refers to PI; h2 to APC and h3 to RR navigational strategies). The chamber origin point possess the coordinate(0;0).
Model: the three model strategies (H1, H2 or H3)
XcoordinatefromOrigine: X coordinate of the model strategy
YcoordinatefromOrigine: Y coordinate of the model strategy
lengthfromOrigine : length of the straight line from the origin of the model strategy (in pixels)
lengthSegment: length of each segment (in pixels)
cumulatedLength: cumulated length of the model strategy (in pixels)
5_ "PathUntilDirectionBackToOrigine.csv" : All information about the fish movement until the fish orient back toward the origin. The coordinate were taken every second. NaN indicates that the data is not available for the concerned cell.
FishID: fish identification
TrialD/L : 1 if the displacement was diagonal, Lateral if the displacement was Lateral
FrameNumber: video frame number when the coordinate was extracted (please note that some videos were recorded at a frame rate of 30 fps and other at 20 fps)
X_coord: x coordinate of the fish in the experimental apparatus
Y_coord: y coordinate of the fish in the experimental apparatus
displacement: whether the fish experienced diagonal (D) or lateral (L) displacement
time: time in seconds
total time: total time of the trajectory before the fish orientate back toward the origin (reward chamber) in seconds
video fps: the video frame rate in frame per second
LengthSegment (pixel): Length of the segment in pixels
cumulatedLenghtPath(pixel): cumulated length of the fish trajectory in pixels
total length segment(pixel): actually the length of the entire fish trajectory until back to the origin in pixels
XcoordinatefromOrigine: x coordinate of the fish recentered on his first coordinate out (0)
YcoordinatefromOrigine: y coordinate of the fish recentered on his first coordinate out (0)
Distance from origine: straight distance from the origin in pixels
Xend: last fish x coordinate in the experimental apparatus
Yend: last fish y coordinate in the experimental apparatus
AngleSegment360degrees: the angle of the trajectory segment
AngleFromOrigine360: the angle from the point of origin
Cumulated360Angles: cumulative angles along the fish trajectory
Angle10: angle of the fish + ten degrees (to calculate deviation > 10 degrees between 2 consecutive segments)
Angle+10: angle of the fish  ten degrees (to calculate deviation > 10 degrees between 2 consecutive segments)
stopSup: stop if 2 consecutive angles deviate more than 10 degrees above the first angle, straight if 2 consecutive angles do not deviate more than 10 degrees above the first angle
stopInf: stop if 2 consecutive angles deviate more than 10 degrees below the first angle, straight if 2 consecutive angles do not deviate more than 10 degrees below the first angle
straightPath:stop if 2 consecutive angles deviate more than 10 degrees, straight if 2 consecutive angles do not deviate more than 10 degrees
xv: x velocity (in pixels/sec)
yv: y velocity (in pixels/sec)
FishDirectionBackToOrigine: yes if the fish orientate back toward the origine Yt>Yt+1
FirstOrSecondTimeDisplacedInExpTank: first or second time the fish was in the experimental apparatus
FishDisplacement: combine fish ID and displacement
Angle first straight path: angle of the first straight path of the fish (before 10degree deviation)
AngleStartEnd: angle between the start and the end of the fish trajectory
Output files:
6_ "1000CoordinateData.csv" : gives the coordinates of the 1000 extrapolated points along the model and fish trajectories
fishID: fish identity
xH1: 1000 extrapolated x coordinate for the PI model trajectory
yH1: 1000 extrapolated y coordinate for the PI model trajectory
xH2: 1000 extrapolated x coordinate for the APC model trajectory
yH2: 1000 extrapolated y coordinate for the APC model trajectory
xH3: 1000 extrapolated x coordinate for the RR model trajectory
yH3: 1000 extrapolated y coordinate for the RR model trajectory
xFishH1H2: 1000 extrapolated x coordinate for the fish trajectory matching the length of PI or APClateral trajectories
yFishH1H2: 1000 extrapolated y coordinate for the fish trajectory matching the length of PI or APClateral trajectories
xFishH3: 1000 extrapolated x coordinate for the fish trajectory matching the length of RR trajectories
yFishH3: 1000 extrapolated y coordinate for the fish trajectory matching the length of RR trajectories
7_ "distanceData.csv": gives 1000 distances between the interpolated points of the fish trajectory and the interpolated points of the 3 model trajectories.
fishID: fish identity
distanceH1 : distance to PI model trajectory in pixels
distanceH2 : distance to AC model trajectory in pixels
distanceH3 : distance to RR model trajectory in pixels
8_ "distanceDataH2DDisplacement.csv": gives 1000 distances between the interpolated points of the fish trajectory and the interpolated points of H2D model trajectory.
fishID: fish identity
distanceH2 : distance to AC model trajectory after diagonal displacement in pixels
9_ "DistanceDataAnalysisForR.csv": Combine the 7 and 8 .csv files. This.csv file containing the distances between the 1000 interpolated points along the fish trajectory and the 1000 interpolated along the model trajectories.
fishID: fish identity
distanceH1 : distance to PI model trajectory in pixels
distanceH2L : distance to AC model trajectory after lateral displacement ("NA" when the fish follow diagonal displacement) in pixels. NAs are present for the fish following a diagonal displacement.
distanceH3 : distance to RR model trajectory in pixels
Displacement : displacement in the experimental apparatus, D=diagonal, L=laterak
fishID2: fish identity (=fishID)
distanceH2D : distance to AC model trajectory after diagonal displacement ("NA" when the fish follow lateral displacement) in pixels. NAs are present for the fish following a lateral displacement.
2Distance Analysis with R
Please find below the description of the R code used for the analysis of the fish trajectories model trajectories distances and the associated data files.
9_ "DistanceDataAnalysisForR.csv": .csv file containing the distances between the 1000 interpolated points along the fish trajectory and the 1000 interpolated along the model trajectories.
fishID: fish identity
distanceH1 : distance to PI model trajectory in pixels
distanceH2L : distance to AC model trajectory after lateral displacement ("NA" when the fish follow diagonal displacement) in pixels. NAs are present for the fish following a diagonal displacement.
distanceH3 : distance to RR model trajectory in pixels
Displacement : displacement in the experimental apparatus, D=diagonal, L=laterak
fishID2: fish identity (=fishID)
distanceH2D : distance to AC model trajectory after diagonal displacement ("NA" when the fish follow lateral displacement) in pixels. NAs are present for the fish following a lateral displacement.
10_ "DistanceAnalysisR.R": This is the R code used to run the statistical analysis to determine if the distances between the fish trajectory and each of the model trajectories were significantly different. This code also allows to generate the figure S3
3Distance to Random
Please find below the description of the MATLAB code, R code and associated .csv code used to determine if the fish trajectory was random or followed one of the model trajectory.
11_ "permutation.mat": MATLAB code used to generate 10 000 random model trajectories and calculate the distance between the fish trajectory and the each of the 10 000 randomly generated trajectories. Gives output files "permutationData10000Random1D29D.csv" and
"permutationData10000Random29Lend.csv"
12_ "permutationData10000Random1D29D.csv" and "permutationData10000Random29Lend.csv" : These data files contains the 10000 mean distances between the fish trajectory and the 10000 random trajectories in pixels.
fishID: fish identity
distanceRandomFish: average distance between the fish and the random model trajectory in pixels
AngleofRandomTrajectory: The angle of the random trajectory
13_ "StatDistanceModelRandom.R" : the R code file containing the analysis of the distance between the fish trajectory and the random trajectories versus the three model trajectories. Gives also the code for the Figure 4 and the Figure S4 of the paper
4Comparison fish versus model angle and distance
Please find below the description of the R code used for the analysis of the trajectory expected angle and the fish observed angle along with the associated data files. The MATLAB code is used to generate the figure 3.
14_ "AngleDistanceStats.R" : R code and statistical analysis testing the differences between the angle and distances expected by the model and observed (gives the output presented in table 2). Allows also to generate figure 2.
Require: "PathUntilDirectionBackToOrigine.csv", "FishGroup.csv", "Path integration data.csv"
15_ "FishGroup.csv" : Fish are grouped under one of the three model trajectories or Random trajectory.
FishDisplacement: Fish identity (association of fish ID and the displacement of the fish for the trial).
RandomPermutationAndSDUniform: Fish identified trajectory (H1=PI model trajectory, H2D= APC after diagonal displacement, H2L= APC after lateral displacement, H3= Route Recapitulation, Random=Random). The fish was assigned to one of the model trajectories or random by checking if the average distance between each fish and the model trajectories were smaller than the average distance to 10000 randomly generated model trajectories SD uniform.
16_ "Path integration data.csv" : dataset containing information about the experimental trial for each fish. NAs indicate that the data is not available for a given cell (the fish did not enter the tunnel or the trapping chamber).
date: date of the trial
fish ID: fish identity
displacement: the displacement in the experimental apparatus (lateral or diagonal)
population: the fish population
Age: age of the fish tested (in years)
timeINAcclimation(previousday): time of acclimation for the fish acclimation was over night so the day before the experiment (over 24 hours)
temperatureAcclimation: temperature in the experimental apparatus when the fish was placed in for acclimation (in degree celsius)
TimeDoorOpen : Time at which the door of the reward chamber was open so the fish could travel through the tunnel to receive a food reward.
TemperatureExpDay: Temperature in the experimental apparatus before to start the experiment (in degree celsius)
FirstTimeInTunnel: The first time the fish entered the tunnel
beforeEnteringTunnel(min): latency before the fish entered the tunnel for the first time (in minutes)
GoInTunnelFirstBranch: number of time the fish entered the first branch of the tunnel
GoInTunnelsecondBranch: number of time the fish entered the second branch of the tunnel (branch from which the food reward was visible and leading to it by a straight path)
TimeInChamber: Time when the fish entered the reward chamber
timeBeforeToEnterChamber(min): latency before the fish entered the reward chamber in minutes
LatencyDisplacement(min.sec): time between the door closing (once the fish entered the reward chamber) and the door openning (after displacement of the chamber, removing all the landmark cues and stirring the sand) in minutes:secondes
timeBeforeEnteringChamber(in h:min): latency before the fish entered the reward chamber in hour:minutes
test: first or second time in the experimental apparatus
FishDisplacement: Fish identity linked with the displacement in the experimental apparatus.
5_ "PathUntilDirectionBackToOrigine.csv" : All information about the fish movement until the fish orient back toward the origin. The coordinate were taken every second. NaN indicates that the data is not available for the concerned cell.
FishID: fish identification
TrialD/L : 1 if the displacement was diagonal, Lateral if the displacement was Lateral
FrameNumber: video frame number when the coordinate was extracted (please note that some videos were recorded at a frame rate of 30 fps and other at 20 fps)
X_coord: x coordinate of the fish in the experimental apparatus
Y_coord: y coordinate of the fish in the experimental apparatus
displacement: whether the fish experienced diagonal (D) or lateral (L) displacement
time: time in seconds
total time: total time of the trajectory before the fish orientate back toward the origin (reward chamber) in seconds
video fps: the video frame rate in frame per second
LengthSegment (pixel): Length of the segment in pixels
cumulatedLenghtPath(pixel): cumulated length of the fish trajectory in pixels
total length segment(pixel): actually the length of the entire fish trajectory until back to the origin in pixels
XcoordinatefromOrigine: x coordinate of the fish recentered on his first coordinate out (0)
YcoordinatefromOrigine: y coordinate of the fish recentered on his first coordinate out (0)
Distance from origine: straight distance from the origin in pixels
Xend: last fish x coordinate in the experimental apparatus
Yend: last fish y coordinate in the experimental apparatus
AngleSegment360degrees: the angle of the trajectory segment
AngleFromOrigine360: the angle from the point of origin
Cumulated360Angles: cumulative angles along the fish trajectory
Angle10: angle of the fish + ten degrees (to calculate deviation > 10 degrees between 2 consecutive segments)
Angle+10: angle of the fish  ten degrees (to calculate deviation > 10 degrees between 2 consecutive segments)
stopSup: stop if 2 consecutive angles deviate more than 10 degrees above the first angle, straight if 2 consecutive angles do not deviate more than 10 degrees above the first angle
stopInf: stop if 2 consecutive angles deviate more than 10 degrees below the first angle, straight if 2 consecutive angles do not deviate more than 10 degrees below the first angle
straightPath:stop if 2 consecutive angles deviate more than 10 degrees, straight if 2 consecutive angles do not deviate more than 10 degrees
xv: x velocity (in pixels/sec)
yv: y velocity (in pixels/sec)
FishDirectionBackToOrigine: yes if the fish orientate back toward the origine Yt>Yt+1
FirstOrSecondTimeDisplacedInExpTank: first or second time the fish was in the experimental apparatus
FishDisplacement: combine fish ID and displacement
Angle first straight path: angle of the first straight path of the fish (before 10degree deviation)
AngleStartEnd: angle between the start and the end of the fish trajectory
17_ "PlotTrajectoriesForPaper.m" : MATLAB code allowing to generate the figure 3 presented in the paper. Requires the .csv files: "Models.csv", "FishGroup.csv" and "PathUntilDirectionBackToOrigine.csv" already described.
5intrinsic and extrinsic effect on model choosen
Please find below the description of the R code used to test the effect of the intrinsic and extrinsic factors on the fish propensity to choose one or the other model trajectory.
18_ "statPopAgeSpeed.R" : R code and statistical analysis testing the effect of fish age, fish swimming speed, displacement in the experimental apparatus and trial number on the fish propensity to choose one of the model trajectory.
Require: "PathUntilDirectionBackToOrigine.csv", "FishGroup.csv", "Path integration data.csv" files already described
5_ "PathUntilDirectionBackToOrigine.csv" : All information about the fish movement until the fish orient back toward the origin. The coordinate were taken every second. NaNs indicate that the data is not available for the concerned cell.
FishID: fish identification
TrialD/L : 1 if the displacement was diagonal, Lateral if the displacement was Lateral
FrameNumber: video frame number when the coordinate was extracted (please note that some videos were recorded at a frame rate of 30 fps and other at 20 fps)
X_coord: x coordinate of the fish in the experimental apparatus
Y_coord: y coordinate of the fish in the experimental apparatus
displacement: whether the fish experienced diagonal (D) or lateral (L) displacement
time: time in seconds
total time: total time of the trajectory before the fish orientate back toward the origin (reward chamber) in seconds
video fps: the video frame rate in frame per second
LengthSegment (pixel): Length of the segment in pixels
cumulatedLenghtPath(pixel): cumulated length of the fish trajectory in pixels
total length segment(pixel): actually the length of the entire fish trajectory until back to the origin in pixels
XcoordinatefromOrigine: x coordinate of the fish recentered on his first coordinate out (0)
YcoordinatefromOrigine: y coordinate of the fish recentered on his first coordinate out (0)
Distance from origine: straight distance from the origin in pixels
Xend: last fish x coordinate in the experimental apparatus
Yend: last fish y coordinate in the experimental apparatus
AngleSegment360degrees: the angle of the trajectory segment
AngleFromOrigine360: the angle from the point of origin
Cumulated360Angles: cumulative angles along the fish trajectory
Angle10: angle of the fish + ten degrees (to calculate deviation > 10 degrees between 2 consecutive segments)
Angle+10: angle of the fish  ten degrees (to calculate deviation > 10 degrees between 2 consecutive segments)
stopSup: stop if 2 consecutive angles deviate more than 10 degrees above the first angle, straight if 2 consecutive angles do not deviate more than 10 degrees above the first angle
stopInf: stop if 2 consecutive angles deviate more than 10 degrees below the first angle, straight if 2 consecutive angles do not deviate more than 10 degrees below the first angle
straightPath:stop if 2 consecutive angles deviate more than 10 degrees, straight if 2 consecutive angles do not deviate more than 10 degrees
xv: x velocity (in pixels/sec)
yv: y velocity (in pixels/sec)
FishDirectionBackToOrigine: yes if the fish orientate back toward the origine Yt>Yt+1
FirstOrSecondTimeDisplacedInExpTank: first or second time the fish was in the experimental apparatus
FishDisplacement: combine fish ID and displacement
Angle first straight path: angle of the first straight path of the fish (before 10degree deviation)
AngleStartEnd: angle between the start and the end of the fish trajectory
15_ "FishGroup.csv" : Fish are grouped under one of the three model trajectories or Random trajectory.
FishDisplacement: Fish identity (association of fish ID and the displacement of the fish for the trial).
RandomPermutationAndSDUniform: Fish identified trajectory (H1=PI model trajectory, H2D= APC after diagonal displacement, H2L= APC after lateral displacement, H3= Route Recapitulation, Random=Random). The fish was assigned to one of the model trajectories or random by checking if the average distance between each fish and the model trajectories were smaller than the average distance to 10000 randomly generated model trajectories SD uniform.
16_ "Path integration data.csv" : dataset containing information about the experimental trial for each fish. NAs indicate that the data is not available for a given cell (the fish did not enter the tunnel or the trapping chamber).
date: date of the trial
fish ID: fish identity
displacement: the displacement in the experimental apparatus (lateral or diagonal)
population: the fish population
Age: age of the fish tested (in years)
timeINAcclimation(previousday): time of acclimation for the fish acclimation was over night so the day before the experiment (over 24 hours)
temperatureAcclimation: temperature in the experimental apparatus when the fish was placed in for acclimation (in degree celsius)
TimeDoorOpen : Time at which the door of the reward chamber was open so the fish could travel through the tunnel to receive a food reward.
TemperatureExpDay: Temperature in the experimental apparatus before to start the experiment (in degree celsius)
FirstTimeInTunnel: The first time the fish entered the tunnel
beforeEnteringTunnel(min): latency before the fish entered the tunnel for the first time (in minutes)
GoInTunnelFirstBranch: number of time the fish entered the first branch of the tunnel
GoInTunnelsecondBranch: number of time the fish entered the second branch of the tunnel (branch from which the food reward was visible and leading to it by a straight path)
TimeInChamber: Time when the fish entered the reward chamber
timeBeforeToEnterChamber(min): latency before the fish entered the reward chamber in minutes
LatencyDisplacement(min.sec): time between the door closing (once the fish entered the reward chamber) and the door openning (after displacement of the chamber, removing all the landmark cues and stirring the sand) in minutes:secondes
timeBeforeEnteringChamber(in h:min): latency before the fish entered the reward chamber in hour:minutes
test: first or second time in the experimental apparatus
FishDisplacement: Fish identity linked with the displacement in the experimental apparatus.
6Extra Analyses asked by reviewers
19_ "CircMLEandExtraAnalyses.R" : R code and statistical analysis to answer multiple reviewers comments. (1) use modelbased approaches with maximum likelihood to determine if the fish follow uniform, unimodal or multimodal distribution. (2) test path length and straightness and compare it between groups. (3) plot distance to cutoff point. (4)Test homogeneity of means with Circular statistics.
Require: "PathUntilDirectionBackToOrigine.csv", "FishGroup.csv", "Path integration data.csv" files already described
Methods
Ethics and Approval
The study was approved by the University of Oxford’s Animal Welfare and Ethical Review Body (AWERB) (project code: APA/1/5/ZOO/NASPA/Burt/DistanceEstimation).
Animal husbandry
We used 40 naive adult male cichlids (Lamprologus ocellatus, Figure 4), sourced from a captivebred laboratory population (standard body length = 35cm). Individuals came originally from 6 subpopulations: B (n=4), C (n=7), D (n=1), E (n=4), F (n=16), G (n=8, Table S3). Subjects were housed individually in tanks measuring 35 cm x 32 cm x 60 cm (width x height x length) containing a sand substrate to a depth of 4 cm and a single home shell. Illumination via fluorescent light followed a 12h light/dark cycle. Individuals were fed twice a day, in the morning and the afternoon, with commercial flake food, supplemented with Mysis shrimps once a week. The tanks were cleaned once a week and the water quality checked to maintain constant pH, gH and KH of 8.4, 23 and 12ppm respectively. Ammonia and nitrites were kept at 0ppm, while nitrates were maintained below 10ppm. The water temperature was maintained at 26±1° C.
One individual (C39d), from subpopulation G, died between its two test sessions from an unknown cause and was replaced by individual C39 (Table S1).
Experimental apparatus
We used a 1.3 m^{2} experimental tank (height: 0.45 m), with 0.06 m of sand substrate and 0.18 m of water. Water parameters and water changes were managed as for the home tanks. On the top left corner of the experimental tank, a shell was placed in front of an Lshaped tunnel 0.6 m long (the two external walls were 0.3 m and 0.3 m, Figure 1) and 0.07 m diameter. The 0.6 m length of the tunnel was chosen because it produced an average beeline distance in the centre of the tunnel of 0.53 m, which is within the average range of intershell distance for this species ^{16}. The tunnel led to a transparent holding chamber of diameter 0.1 m where a food reward was placed. The holding chamber had a sliding door connected to the Lshaped tunnel. The sliding door was operated by the experimenter, situated outside the experimental apparatus. The sides of the experimental tank were covered by white opaque Perspex (31 cm in height). A plain white curtain (length: 6 m; height: 1.5 m) covered the entire tank to eliminate external visual cues. An achromatic checkerboard pattern printed on fabric was suspended above the experimental tank 1.5 m^{2}). Two holes (1 cm diameter) were cut in two different black squares of the checker pattern and cameras was mounted in these positions. The first camera was positioned above the reward chamber (top left corner of the experimental tank) and was used to visually ensure that the fish entered the chamber before the door was closed. The second camera was positioned in the centre of the experimental tank and used to record the trajectories of the fish.
Testing procedure
Individual fish were placed in the experimental tank for acclimation the day before the test (between 15:00 – 17:00). They were transferred from their home tank to the experimental apparatus within their home shell to limit their stress (see Figure 1a for position in the experimental tank). The following morning, the Lshaped tunnel and chamber were placed into the experimental tank. A highquality food reward (bloodworm) was placed in the chamber and the sliding door was then opened. Fish eventually swam into the reward chamber in search of food. Only once the fish reached the reward chamber and began eating, was the door shut. A black plastic sheet was then clipped onto the chamber to prevent the fish from seeing the experimenter. Once the tunnel and shell were removed, the holding chamber was slowly displaced either laterally: 0.5m to the right (Figure 1c) or diagonally: 0.71 m rightdown (Figure 1d). Those two displacement positions were chosen to ensure that the predicted search areas were at least 0.5 m from any tank walls, and reducing the likelihood that fish used the walls as navigational cues. The two positions were marked by white Perspex squares fixed to the bottom of the experimental tank and hidden under the sand. To ensure the chamber was displaced to an exact position, the experimenter aligned the Perspex squares with the chamber. After displacement, the sand substrate was mixed thoroughly and relevelled to scramble any visual or odour cues. The plastic sheet covering the reward chamber was then removed and the door was opened (mean ± sd latency before opening the reward chamber after displacement = 210 ± 50 sec). Following release, the fish was allowed to swim in the experimental tank for 5 min. If the fish did not exit the reward chamber after 15 minutes, the trial was terminated.
Subjects were divided into two groups of 20 individuals (Table S1). Each individual was tested in a lateral and a diagonal displacement test (Figure 1b, 1c), with an interval of two weeks between tests. Group 1 was tested first for lateral displacement and then for diagonal displacement and group 2 was tested for displacement diagonal and then lateral (see Table S1).
Data collection
The water temperature and times were recorded on both the acclimation and experiment day. The number of times each fish swam backwards and forward into the first and second branch of the Lshape tunnel before entering the holding chamber was recorded. The time taken to 1) enter the tunnel, 2) enter the chamber, and 3) exit the chamber after displacement was also recorded.
All trials were recorded using an overhead web camera (ELP Webcam 10megapixel, Model X000VD0KT5). Videos were manually processed using custom code written for MATLAB version R2022a, MathWorks Inc. Every second, the position of the fish was identified by clicking on the head of the fish. X and Y coordinates were then extracted and used to produce a continuous 2D trajectory. Fish movements were analysed for one minute after exiting the chamber. Individuals did not display any search behaviour, such as loops of everincreasing size around the expected location of the starting point ^{19}. Therefore, each trajectory, beginning at the opening of the reward chamber, was cropped once the fish oriented back to the chamber, following e.g., Holbrook & Burt de Perera ^{20} (Figure S1).
Of the 40 fish tested, 24 completed one or both trials successfully (n = 37 successful trials). In the remaining trials, fish failed to enter the reward chamber (21 individuals, 26 trials), exit the reward chamber after displacement (6 individuals, 7 trials) or did not move away from the reward chamber after exiting (10 individuals, 10 trials).
Statistical analysis
Trajectory analysis was performed using custom MATLAB code. All statistical analyses were performed using R studio (version 2022.07.1, R version 4.0.2).
Statistics and reproducibility
Trajectory analysis was performed using custom MATLAB code. All statistical analyses were performed using R studio (version 2022.07.1, R version 4.0.2). The significance threshold was set at .05
Multimodal trajectories
We used a modelbased approach with maximum likelihood to investigate circular orientation. The CircMLE package ^{25} was used to determine if our trajectories followed uniform, unimodal or multimodal model orientation (for further details see Fitak & Johnsen ^{25}). We first used the package circular ^{44} to obtain “circular” class data with angles in radians and modulo = π, as our data could spread only from 0 to 180°. We used the ‘check_data’ function from the CircMLE package to ensure our data were in the correct format and ran the ‘circ_mle’ function to test our orientation data including (a) first orientation data and (b) start to the end of the trajectory orientation data. The first orientation data followed model M5A (Homogenous bimodal) and the startend orientation data followed M5B (Bimodal) models (see Supplementary Tables S2a and S2b for full details). This analysis indicates that multimodal orientation defines our data significantly better than uniform or unimodal. Grouping our data following navigational model trajectories can then be applied. We computed the circular mean direction ^{44} as a descriptive statistic and performed the following analyses on angles using ordinary statistics that are robust and powerful as our angles are restricted to 0180° (after recommendation by Dr U J Lund, authors of the circular package ^{44}).
Deviation from the model trajectories
To measure the extent to which observed trajectories deviated from the three model trajectories (PI, AC and RR) prediction, we measured the average distance between both trajectories: We first cropped the smallest of either the model trajectory or the observed trajectory so that they were both of equal length. We then fitted the observed data using 1,000 evenly spaced points using a modified akima interpolation (makima, MATLAB) and did the same with the model trajectories. Finally, we calculated the Euclidian distance between each pair of interpolated points (i.e. distance between the tenth interpolated point in the trajectory from the tenth interpolated point in the model trajectory). Average distances between the observed and the model trajectories are presented in Table S2. All interpolated trajectories are presented in the supplementary material Figure S2.
Determination of the closest model trajectory
A generalised mixed linear model (GLMM) was used to test the similarity between observed trajectories and the three model trajectories. We used glmmTBM (glmmTBM package ^{34}), which fits models using maximum likelihood estimation via 'TMB' (Template Model Builder). For each fish, the distances between the 1,000 points interpolated along the observed trajectory and the 1,000 points interpolated model trajectories were added as the response variable. Model trajectory (i.e. PI, AC, RR) was added as the explanatory variable and as a random intercept. Distribution and dispersion of residuals were assessed using the DHARMa package ^{35}. No overdispersion of residuals was detected for any of the fish tested (p > 0.05). A wellfitted statistical model predicts normality of the residuals and homoscedasticity, but this was rarely observed in our models. The lack of residual normality was due to both the large number of samples (n = 1000) and inclusion of “model” as a categorial fixed effect. A large number of samples often leads to statistical significance even if deviations are minor. The lack of homoscedasticity can be explained by the difference in shape of the three model trajectories: two trajectories (PI, AC) are straight, while the third (RR) includes a right angle. Therefore, if the fish trajectory closely follows PI or AC we can expect a significantly higher variance to the rightangle trajectory. While these issues prevent obtaining a perfect fit between the models and the data, the models we selected provided a better fit than alternatives, determined by comparison of 10 model structures using different GLMM packages, distributions and data transformations. Average distance ± SD between the observed fish trajectory and the model trajectories and Average distance ± IC_{95% }are presented in the supplementary material Table S2 and Figure S3 respectively. For further details, see raw data and model output in R CodeDryad depository.
Deviation from random trajectories
To determine whether an individual’s trajectory was closer to a random trajectory than to one of the three model trajectories (PI, AC, RR), we measured the distance between the observed trajectory and 10,000 randomly generated trajectories. Each random trajectory was a straight line of a given length and angle and was generated using a custom MATLAB code. The angle, between 0 and 180 degree, was randomlygenerated on the MATLAB code. The length and was the same as the smaller of either the individual’s trajectory or the PI model trajectory. We then measured the distance between the 1,000 interpolated points of the randomly generated trajectories and the 1,000 interpolated to the observed trajectory. We did this for 10,000 randomly generated trajectories. We then calculated the average distance between the observed trajectory and the 10,000 random trajectories. The distribution of the average distance between the observed trajectory and the 10,000 randomly generated trajectories was assessed using a Cullen and Frey graphic analysis from the “descdist” function (fitdistrplus package ^{36}, Rstudio version 2022.12.0). It followed a continuous uniform distribution (See supplementary Figure S4).
If the difference between the observed trajectory and one of the model trajectories was less than the average distance minus SD_{uniform} of all random trajectories, then the fish was assigned to the model trajectory category (Figure 5a). If the average distance minus SD_{uniform} from all random trajectories was less than the distance between the fish trajectory and the model trajectories, then the fish was assigned to the random trajectory category (Figure 5c). If the standard deviation was calculated assuming a normal distribution for the 10,000 distances (see formula below), two fish trajectories (3L and 29L) would be assigned to a random trajectory instead of AC.
Finally, using a 20% threshold on the cumulative distribution function of the 10,000 distances (Figure 5b, 5d) resulted in the same path categorisation as that obtained using the standard deviation calculated assuming a normal distribution.
Calculation of the fish First angle (first orientation when exiting the chamber) and Angle startend (orientation from the first point out of the chamber to the end of the trajectory)
Each observed trajectory was made up x and y coordinate indicating the fish position and extracted every second from the time the individual excited the reward chamber. The trajectory was therefore divided into multiple segments between each coordinate points. The first direction taken by the fish was calculated as the angle of the first straight displacement (in degrees). The first straight displacement length was the addition of segments that does not deviate by more than 10 degrees from the previous segment. We took the coordinate of the first point out of the chamber and the coordinate from the point as the end of the first straight displacement and measure the angle of the first direction taken by the fish.
The angle startend was calculated using the coordinates of the first point out of the chamber and the last point before the fish turn back toward the origin.
Comparison of model and observed angle swum
To test whether the direction taken by the fish when first exiting the chamber was significantly different from the model prediction, a oneway bootstrap ttest was used (number of bootstrap replicates = 9999). For each grouping (PI, AC or RR), the angle of the first straight displacement of the fish trajectories was tested against the expected model angle (PI: 45°; AC: 135° ; RR: 90°). Normality of the data was tested using a Shapiro test (PI group: W = 0.93, pvalue = 0.51, AC_{lateral} group W = 0.77, pvalue = 0.06, RR group W = 0.92, pvalue = 0.55). We performed the same analysis to determine if the angle startend of the fish trajectory was different from the expected model direction (normality test: PI group: W = 0.78, pvalue = 0.02, AC_{lateral} group W = 0.93, pvalue = 0.60, RR group W = 0.95, pvalue = 0.72). The expected angle startend of RR model was 45 degrees. When normality was not verified (PI group) we performed a signedrank Wilcoxon test.
Only two fish were found to adopt an AC strategy after diagonal displacement. The expected angle for those two fish was 180 degree. However, a sample of two individuals is insufficient for statistical analysis therefore the raw values only are reported in the results.
To draw Figure 2, we used circular statistics (package circular ^{37}). For each group, mean circular directions were calculated using the mean function on circular data (units = degrees). The uniformities of direction were assessed with a Rayleigh test. The length of the arrow on the figure indicate the strength of uniformity.
Comparison of model and observed distance travelled
A oneway ttest was used to test whether the first trajectory length was different from the expected model length. For each grouping (PI, AC or RR), the length of the fish trajectory was tested against the expected model length (PI: 38.6 cm; AC first vector: 38.6 cm; RR: 54.5 cm). Note that for this analysis the entire trajectory before orienting back to the origin was used, not the cropped trajectory used to group fish trajectories into different model types. Normality of the data was tested using a Shapiro test (PI: W = 0.72, p = 0.003; AC: W = 0.76, p = 0.047; RR: W = 0.94, p = 0.67). Where normality was confirmed, a oneway bootstrap ttest (number of bootstrap replicates = 9999) was used. Otherwise, a signedrank Wilcoxon test was performed. Only two fish were found to adopt an AC strategy following diagonal displacement. The expected distance for those two fish was 27.3 cm. However, a sample of two individuals is insufficient for statistical analysis therefore the raw values only are reported.
Testing the effect of age, speed, trial number and displacement on chosen strategy.
To determine if individual age, swimming speed, trial number (first or second time in the experimental tank) and displacement direction (lateral versus diagonal) had an impact on the strategy chosen, we performed a multinomial mixed effects regression (“mblogit” function, mclogit package; ^{38}). Strategy (PI, AC, RR or random) was added as the multinomial response variable. Fish age, swimming speed, displacement direction and trial number were added as explanatory variables. Fish identity was added as a random intercept. No overdispersion was detected (dispersion function, mclogit package ^{38}). A posthoc analysis was performed using “emmeans” and “contrast” functions with Holm Bonferroni adjustment (emmeans package ^{39}) it allowed to evaluate the effect of the explanatory variables on paired response variable (i.e. probability to follow a strategy rather than another: PI vs AC, PI vs RR, AC vs random…).