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. 2014 Mar 25;8:39. doi: 10.3389/fnsys.2014.00039

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Copyright © 2014 Chen and Engert.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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Choice of efficient turning direction suggests sophisticated navigation ability. (A) Illustration of “efficient” vs. “inefficient” turns. For a fish approaching the virtual border (dashed yellow line) along the direction indicated by the blue arrow, in order to return to the light, a turn in one direction (green arrow) is more “efficient” than in the other direction (red arrow). Dashed black line: radial direction. (B) Histogram of the per-fish “efficiency,” summarized for all fish in the VC assay. The 50/50 probability (pure chance) is indicated with a dashed red line. The dashed cyan line marks the mean of the distribution (0.69 ± 0.016, mean ± s.e.m, n = 32). (C) “Spotlighted” Virtual Circle experiment, to control for potential asymmetries in the visual field that can be used as visual cues. The projected spotlight is centered at the fish at all times, except when the fish exits the virtual border (dashed red line) and the light is turned off. (D) Histogram of the per-fish “efficiency”, for 30 fish from the “Spotlighted” Virtual Circle experiment. The mean of this population (0.68 ± 0.016, mean ± s.e.m, n = 30) is unchanged compared to (B). (E) The average “efficiency” compared between real fish and different simulations. Simulations are labeled by all the algorithms implemented: “A” = Algorithm I [Angle], “LF” = Algorithm II [Lock/Flip], “BO” = Algorithm III [Bounce], “E” = Algorithm IV [Efficiency]. Dashed red line indicates the value of pure chance. None of the first 3 simulations (blue, green, and orange) produce an “efficiency” that is statistically different from chance. Only the simulation applying Algorithm IV, as described in (F), enhances the “efficiency” significantly to 0.59 ± 0.005 (mean ± s.e.m). (F) The lock-index for the last turn in light (LD0) and first turn in dark (LD1), plotted as a function of the length of the immediately preceding interval in light. Note that for the previous simulations, the lock-index does not change significantly with the length of the preceding light interval. For the simulation with Algorithm IV [Efficiency], the turning direction of the first turn in dark (LD1) is constrained so that this lock-index curve (in red) mimics the curve from real fish (in black). ^*p < 0.001.