taking a shortcut: what mechanisms do fish use?

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.

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 captive-bred laboratory population (standard body length = 3-5cm). 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 m2 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 L-shaped 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 inter-shell 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 L-shaped 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  m2). 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 L-shaped tunnel and chamber were placed into the experimental tank. A high-quality 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 right-down (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 L-shape 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 10-megapixel, 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 ever-increasing 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 model-based 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 start-end 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 0-180° (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 well-fitted 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 right-angle 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 ± IC95% are presented in the supplementary material Table S2 and Figure S3 respectively. For further details, see raw data and model output in R Code-Dryad 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 randomly-generated 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 SDuniform of all random trajectories, then the fish was assigned to the model trajectory category (Figure 5a). If the average distance minus SDuniform 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 start-end (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 start-end 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 one-way bootstrap t-test 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, p-value = 0.51, AClateral group W = 0.77, p-value = 0.06, RR group W = 0.92, p-value = 0.55). We performed the same analysis to determine if the angle start-end of the fish trajectory was different from the expected model direction (normality test: PI group: W = 0.78, p-value = 0.02, AClateral group W = 0.93, p-value = 0.60, RR group W = 0.95, p-value = 0.72). The expected angle start-end of RR model was 45 degrees. When normality was not verified (PI group) we performed a signed-rank 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 one-way t-test 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 one-way bootstrap t-test (number of bootstrap replicates = 9999) was used. Otherwise, a signed-rank 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…).