An open-source closed-loop Virtual Reality system to investigate social interactions and collective behavior in fish

Key results

1. SuggestedFollowing is specific to the fish image: real fish stayed nearer to, and moved more in step with, a virtual conspecific than a similar-sized dark sphere moving on the same circle.

   Mean real-to-virtual distance 9.3 cm ± 7.0 SD with the fish model vs 15.3 cm ± 7.2 SD with the sphere; peak velocity cross-correlation C ≈ 0.77 vs C ≈ 0.27, at lags of −0.133 s and −0.067 s. Path radius 10 cm, 10 cm/s, depth 5 cm; 7 one-hour repetitions, fish model for 30 min then sphere for 30 min. · 3.6.2 Experimental procedure; 4.1 Control condition with a non-social stimulus; Figure legends

2. ShownReal fish adjusted their speed to the virtual fish. At 10 cm/s (which the authors call the comfort speed) they followed closely with negligible lag. A 5 cm/s partner was overshot and circled, and at 15 cm/s they lagged or cut corners. Separation and depth stayed the same throughout.

   Real-fish mean speeds 6.3, 9.4 and 11.7 cm/s for virtual speeds 5, 10 and 15 cm/s; lag at peak cross-correlation 0.4 s, 0 s and −0.267 s respectively. Inter-fish distance probability density function (PDF) peaks near 2.5 cm and depth near 4.5 cm in all three; speed PDFs differ (Hellinger distance > 0.2), distance and depth PDFs do not. 10 one-hour repetitions per condition. · 4.2.1 Impact of the virtual fish’s swimming…; 8.1 Captions of the Supplementary Figures; 8.2 Captions of the Supplementary Tables; Figure legends

3. ShownReal fish tracked the virtual fish's depth, usually swimming slightly above it. With the partner near the bottom, the smaller vertical room shrank the area the real fish covered and reduced mean separation, while the most frequent separation stayed the same.

   Virtual depths 3.5, 5 and 8 cm at 10 cm/s: mean inter-fish distance 7.97, 7.83 and 6.25 cm; distance PDF peak near 2.5 cm in all; x-range covered around the virtual fish (radius of the density maps) reaches about 38 cm in the shallower cases vs 15 cm at 8 cm depth; depth deviations rarely beyond ±1.5 cm. Hellinger distance > 0.2 for inter-fish distance at 8 cm and for real-fish depth across conditions. · 4.2.2 Impact of virtual fish’s swimming depth on…; 8.2 Captions of the Supplementary Tables; Figure legends

4. SuggestedWith the virtual fish 10.4 cm from the wall, the real fish often swam between it and the wall. It was responding to an image projected on the far side of the bowl and seen through the water, which the authors read as evidence of a convincing anamorphic illusion.

   Trajectories and relative-position maps (Figs 7D, 8, 11) with wall distances from 2.4 to 10.4 cm at 10 cm/s and 5 cm depth; real-fish speed and depth distributions did not differ across wall distances, and only the 2.4 cm condition (C7) gave a larger inter-fish distance than 10.4 cm (C6), with Hellinger distance > 0.2. · 4.2 Behavioral response of real fish to the…; 4.2.3 Impact of the virtual fish’s distance to…; 8.2 Captions of the Supplementary Tables; Figure legends

5. SuggestedReal fish also followed virtual fish on three-petal rose (rhodonea) paths that cross the optically distorted bowl centre. They followed less well when the petals were sharp, and tended to sit on the inner side of the partner's turn.

   Peak velocity cross-correlation C ≈ 0.65 for broad-petal Rose 1 (n = 3, d = 5) vs C ≈ 0.51 for sharp-petal Rose 2 (n = 3, d = 1), at lags −0.23 s and −0.1 s; inter-fish distance PDF still peaks at 2.5 cm; speed PDFs centred on 10 cm/s but wider than for circles; perception-angle PDFs asymmetric toward the turn side. 5 one-hour repetitions per rose. · 4.3 Behavioral response of real fish to the…; 8.1 Captions of the Supplementary Figures; Figure legends