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Distance estimation in the Goldfish (Carassius auratus)


Sibeaux, Adelaide; Karlsson, Cecilia; Newport, Cait; Burt de Perera, Theresa (2022), Distance estimation in the Goldfish (Carassius auratus), Dryad, Dataset,


Neurophysiological advances have given us exciting insights into the systems responsible for spatial mapping in mammals. However, we are still lacking information on the evolution of these systems and whether the underlying mechanisms identified are universal across phyla, or specific to the species studied. Here we address these questions by exploring whether a species that is evolutionarily distant from mammals can perform a task central to mammalian spatial mapping – distance estimation. We developed a behavioural paradigm allowing us to test whether goldfish (Carassius auratus) can estimate distance and explored the behavioural mechanisms that underpin this ability. Fish were trained to swim a set distance within a narrow tank covered with striped pattern. After changing the background pattern, we found that goldfish use the spatial frequency of their visual environment to estimate distance; doubling the spatial frequency of the background pattern resulted in a large overestimation of the swimming distance. These results provide robust evidence that goldfish can accurately estimate distance, and show that they use local optic flow to do so. These results provide a compelling basis to utilise goldfish as a model system to interrogate the evolution of the mechanisms that underpin spatial cognition, from brain to behaviour.


Experimental overview.

We trained goldfish to a target distance in a long and narrow tank and then tested whether they could continue to swim the target distance given different optic flow information. In training, the fish were exposed to an achromatic striped pattern of 2cm and they were given an external cue to indicate when they reached the target distance. We then removed the external cue and measured if the fish continued to swim the set distance. Finally, we changed the optic flow pattern to determine whether the fish would change their estimate of distance travelled. Trial videos were then analysed to test whether alternative mechanisms, including fin beats and time, could have been used for distance estimation.

Animal husbandry

Nine naive goldfish (Carassius auratus), sourced from a local supplier (The Goldfish Bowl, 118-122 Magdalen Rd, Cowley, Oxford OX4 1RQ) were used in experiments. Individuals were housed in 0.35m x 0.32m x 0.60m (width x height x length) tanks enriched with 0.5 cm of gravel, a terracotta pot, and plastic plants. Because C. auratus is a social species, individuals were kept in groups of two to three fish. The illumination by fluorescent light followed a 12h light /12h dark cycle. Individuals were fed twice a day; once in the morning with pellets (Fancy Goldfish Sinking Pellets, FishScience) and once in the afternoon with spinach or bloodworms to add supplementary nutrients. Tanks were cleaned weekly and water quality was maintained at healthy levels for this species (pH: 8.2; KH: 7dKH; GH: 8.2; Nitrite: 0ppm; Ammonia, Nitrate: < 10ppm).

Experimental apparatus

We used the experimental apparatus built by Karlsson et al. (2019). Briefly, fish were trained and tested in an acrylic tank (0.25 m high x 0.16 m wide x 1.80 m length, Figure 1) set within a flow-through tank. The tank was connected to the home water system to maintain consistent water parameters, but the water flow was stopped during training and testing sessions. A white and black vertical 2 cm width stripe pattern (2 cm pattern) on the floor and walls of the tunnel produced optic flow cues. Three additional patterns were used to interrogate which optic flow features were used by the goldfish.

  1. Checker pattern: a 2 cm2 checkerboard pattern with the same optic flow frequency as the training pattern was used to evaluate the impact of pattern change on fish distance estimation.
  2. High-frequency optic flow pattern: a 1cm width vertical stripe pattern, used to test the impact of increased optic flow on distance estimation.
  3. No optic flow pattern: a 2 cm horizontal stripe pattern used to test the impact of removing optic flow cues on distance estimation.

To control for the use of external visual cues to estimate distance, a moveable start area (0.25 m high x 0.16 m wide x 0.20 m length) was placed at one of six start positions (10 cm apart). Three start positions (20 cm apart) were used to train the fish and three different start positions (20 cm apart) were used to test them. Therefore, while the target travel distance remained constant, the absolute position where the fish must turn was different in training and testing. A white partition was placed at the end of the tunnel to block external visual stimuli, and a second one was placed 20 cm behind the start door. An overhead camera (Point Grey GrassHopper 3M- FLIR Machine Vision Cameras), placed 1.05m above the water level and connected to a computer displaying individual movement in real-time. All training and testing trials were recorded using StreamPix 7 video capture software (video frame rate = 50 fps).


We used an operant training paradigm with a food reward to train the fish to swim to a target distance of 0.70 m. For each training session, the start area was randomly assigned to one of the three training start positions. During the first stage of training, bloodworms were placed along the bottom of the tank to encourage the fish to swim through. A transparent acrylic barrier was placed 70 cm apart from the door to stop the fish from swimming further than the target distance. Bloodworms were then spaced throughout the tunnel to provide motivation for exploration. The number of bloodworms gradually decreased throughout training until only one bloodworm was placed at the barrier and one at the start position. Gradually, the barrier was replaced by a 5 cm partition, then a 0.5 cm stick, and finally the physical barrier was removed from the tank altogether. Those intermediate steps were necessary as they provided a physical cue indicating that the target distance was reached but also allowed the fish to get around it, swim further than the target distance and explore the tank. If the fish swam further than the target distance, no food reward was provided when it came back to the start position. The experimenter stood 1 m apart from the experimental tank, observing the fish movements on the computer screen. The experimenter was not visible to the fish. The experimenter waved at the fish when it reached the target distance (with the 5 cm partition, 0.5 cm stick, and without a physical barrier) to provide a cue for turning. At the final stage of training, the fish had to swim and turn when the experimenter waved above the experimental tank and then come back directly to the start position to receive their food reward. If the fish returned to the start position before reaching the target distance or explored the tunnel further away, no food reward was given. The training was completed once a fish reached the target distance in 80% of trials (i.e., swim out to the wave and come back directly to the start area) over three consecutive sessions. Training sessions lasted for 10 minutes or until 10 trials were completed. Fish were trained twice a day, once in the morning and once in the afternoon, five days a week.


During testing, three start positions (different from the three training start positions) were randomly assigned and 15 trials per fish were completed at each start position. As a result, 45 distance estimation tests were recorded for each fish. For each session, fish first performed six to seven training trials with the experimenter providing a turning cue. The training start position was then moved to the test start position and the fish were tested for three to four trials with no turning cues. A food reward was given in all test trials regardless of the distance travelled. To test alternative optic flow patterns, fish were returned to their home tank after training while the experimenter changed the optic flow pattern. Fish were then moved back into the experimental tank and tested for a further three to four trials. A total of 45 distance estimation tests were also recorded for each optic flow pattern.

A few exceptions led to discarding a trial: (i) if the fish reached the very end of the experimental tank or if it only got its body length out of the start position before turning. (ii) If the fish turned multiple times in the tunnel before returning to the start position. (iii) If the fish showed erratic swimming movement indicating stress for the individual. In this final case, the trial was discarded, the session was ended and the fish returned to its home tank and monitored. Six of the nine fish were tested with the four different patterns. The power achieved to test the effect of the change of optic flow pattern on distance travelled with six individuals was above the 80% threshold criteria (power for 1000 iterations of the generalised linear mixed model= 94,50%, confident interval95% [92.90; 95.83], R package simr, Green et al., 2016).

Data collection

The videos were recorded using StreamPix7 software. To measure the goldfish distance estimate for each test trial, frames were extracted from video recordings at the point when the fish exited the start area and when it turned into the experimental tank. The pixel coordinates of the fish mouth were then manually recorded for those two events using custom video tracking software (Matlab version R2022a, MathWorks Inc.). The difference in pixel coordinate between the exit of the start area and the turn position was then converted into a distance estimate measured in centimetres (ratio 1 pixel = 0.0664 cm). The absolute turn position was measured using the coordinate of the turn frame converted in cm.  

The time taken to turn in seconds was measured using the number of frames elapsed between the exit of the start area and the turn position. The frame rate (50 fps) was used to convert the number of frames to seconds. The number of caudal fin beats for each test trial was manually counted by the experimenter using StreamPix software that allowed frame-by-frame video inspection.

To determine if the goldfish used optic flow to estimate distance, we compared the average turning distance and the absolute turn position obtained with the 2cm checker pattern (same density optic flow), the 1cm vertical stripes pattern (high-frequency optic flow), and the horizontal stripes pattern (no optic flow).


Human Frontier Science Program, Award: RGP0016/2019