The sample consisted of six pet dogs (Table 1). The three mixed breed dogs were all mesocephalic and medium-sized (height at the withers 45 to 55 cm). The dogs’ average age was 4.3 ± 2.6 years. The dog owners were students or workers of the University of Padua and were recruited on a voluntary basis. The criterion for dogs’ selection was a good health condition, willingness to cooperate in the laboratory setting and high motivation for food.
The experiment was conducted in a quiet room (4.7 × 5.8 m) with dim light. Two identical touch screen monitors (VG248QE, ASUSTeK Computer Inc., Taipei, Taiwan) measuring 53 × 30 cm, were used for stimuli presentation, with the refresh rate set to 100 Hz. Monitors were positioned side by side, with 25 cm in between and the vertical middle point of both monitors was set at the eye level of each subject. Both monitors were connected to a PC (Optiplex 960, Dell Inc., Round Rock, Texas, USA) which was operated through a Bluetooth keyboard (Logitech K400R, Logitech International S.A. Losanna, Switzerland). A coloured tape on the floor at 120 cm from the middle point between monitors marked the position at which the dog’s head was kept during the presentation of the stimuli (see below for details). A chair for the experimenter was placed at either side of such mark.
White geometrical shapes presented on black background were used as training stimuli. These included an equilateral triangle, which was used as a positive stimulus. Ten additional shapes were used as negative stimuli, including a square, a cross, a circle, an arch, a half-moon, a heart, a hexagon and letters “L”, “T” and “C”. One side of the triangle measured 10.5 cm and was composed of 555 pixels. The triangle had an area of 47.7 cm2 and all negative stimuli had approximately the same size. All stimuli were presented in the middle of the screen. The stimuli were created with OpenSesame (version 3.2.8 Kafkaesque Koffka, Mathôt et al. 2012).
All test stimuli consisted of three black circles with a missing sector of 60° (i.e. “pac-man” figures). The centre of the three pac-men was located in the same position as the apexes of the triangle of the training phase. The pac-men could be rotated so that the edges of the sectors of each pac-man were aligned with those of the other two pac-men, which typically generate the illusory perception of a solid triangle by humans (illusory stimulus; Fig. 1a). Alternatively, the pac-men were rotated, so that sectors were not aligned (non-illusory stimulus; Fig. 1b). Ten different non-illusory configurations were presented, including five figures where the three sectors had the same orientation as the illusory stimulus, but the pac-men were not in the same position as the illusory stimulus. All pac-men figures were presented on white background in the middle of the screen. The radius of the circle was 185 pixels, therefore the physical contours covered 2/3 (0.67) of the illusionary triangle sides.
The experiment was composed of two phases, a training and a test phase. Dogs who were not accustomed to using the touch screen apparatus were previously involved in a preliminary procedural training. Two dogs (subjects 4 and 5) were already accustomed to using the touch screen apparatus. However, the stimuli were non-illusory and of a different nature (i.e. random dot motion displays); therefore, it is unlikely that the previous experience would have affected the results of the current experiment. The preliminary training was aimed at teaching dogs to wait at the designated initial position, visually inspect the monitors and touch the screen with their snout where a 4.5 cm plain white circle was presented on a black background. The preliminary training sessions were composed of 20 trials to accustom the dogs to the trial repetition. Preliminary training was completed when the dog was comfortable and accurately performing every aspect of the procedure. In the days in which dogs were involved in the study, they were only fed in the previous evenings to keep the dogs’ food motivation high.
The training phase used a two-alternative conditioned discrimination task to teach the dog to choose the triangle over other geometrical figures. The training phase consisted of sessions of 20 trials. Each trial started with the dog standing at the designated initial position beside the experimenter, who held it gently by its harness. Once the dog was oriented towards the monitors, the experimenter closed her eyes (Macpherson and Roberts 2013; Range et al. 2014) to avoid influencing the subjects’ choice and simultaneously started the presentation of the stimuli. The positive and the negative stimuli appeared on the monitors concurrently. The experimenter held the dog for 5 s to allow the dog to inspect the stimuli before choosing. Then, the experimenter said “Go!” and released the dog, who was then free to approach and touch one of the two monitors. Both stimuli disappeared upon touching one of the screens. If the dog chose the monitor with positive stimulus, it received a verbal praise and a food reward (either a commercial dog treat or a piece of sausage) tossed on the ground by the experimenter. After eating the food, the dog was called back to the starting position for the following trial. If the dog chose the negative stimulus, it was called back to the starting position without receiving any reward. If the dog did not make a choice within 60 s, the experimenter proceeded with the next presentation and the result was recorded as “No choice”.
The training phase was organized in steps with increasing difficulty to make learning easier for dogs. In the first step of the training phase, a black screen served as a negative stimulus. In the second step, a figure “L” was used as a negative stimulus. The third step had four negative stimuli presented in random order: the figure “L”, a square, a figure “T” and a cross. The fourth step had seven negative stimuli presented in a random order: a circle, a hexagon and an arch were added to the previous shapes. The final step had ten negative stimuli: a heart, a figure “C”, a half-moon and the previously mentioned shapes. Each time the dog made 2 or less mistakes (i.e., 90% accuracy) for 3 sessions in a row, it was moved to the next step. The side of the positive stimulus was counterbalanced across the session and semi-randomised so that it never appeared on the same side more than three times in a row. Each dog underwent a maximum of five training sessions per day, with an interval between sessions of at least 30 min. The dogs were moved to the test phase when they chose the positive stimulus for at least 18 out of 20 trials (i.e., 90% accuracy) in 6 consecutive sessions in the last step (i.e., using ten different negative stimuli), distributed over two separate days.
Test phase was meant to assess the dogs´ susceptibility to the Kanisza’s triangle illusion. Test phase sessions consisted of 25 trials, which included 20 training trials and 5 test trials. On test trials, both an illusory and non-illusory stimulus were presented. Test trials were regularly presented on every fifth trial and followed a similar procedure to the training trials, except that in the test trials, the dogs were reinforced randomly half of the times regardless of their choice. In the training trials of this phase, choices of the positive or negative stimulus had the same consequences as in the training phase. If the dogs made more than two mistakes in the training trials, they were moved back to the training phase, required to reach the learning criterion, and tested again. Each dog underwent five test sessions, therefore they were presented with 25 test trials overall. The time interval between sessions performed by the same dog was at least 30 min.
Data collection and analyses
Data for the choice performed by the dogs in each trial, both in training and test phase, were automatically collected with OpenSesame. In addition, the data regarding the number of training sessions for each subject were collected. A two-tailed binomial test was run for each individual dog to test the null hypothesis (H0) that the choices were not different from chance level in the test trials. Only the test sessions where two or less mistakes were made in the training trials were considered in the final analysis. To assess whether an overall prevalence for choosing the illusionary stimuli was present in our sample, we performed a one-sample two-tailed Student’s t test on the dogs means for the type of choice (0 = non-illusionary stimulus, 1 = illusionary stimulus) expressed in the 25 test trials, testing the null hypothesis (H0) that the mean was equal to or lower than 0.5. To analyze if the length of the training phase or the age of the dog affected the choices in the test phase, a repeated measures binomial logistic regression analyses were computed. All statistical analyses were conducted using R (version 3.5.2; R Core Team 2018), with statistical significance level set at 0.05.