1. Idiothetic Path Integration in the Fruit Fly Drosophila melanogaster
Irene S. Kim, Michael H. Dickinson 
Current Biology 
Volume 27, Issue 15, Pages e3 (August 2017)
DOI: /j.cub
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2. Figure 1
Walking Flies Perform a Local Search after Encountering Food but Not Water
(A) Arena side and top views. Flies walked within a shallow, flat-walled bowl covered by a glass plate and were filmed from above. A featureless white wall surrounded the arena. The arena was backlit by a panel of infrared (IR) LEDs. Two white LEDs (not shown) suspended above the arena provided light for the flies. A 1 μL drop of food or water was placed at the center of the arena. The food drop is not drawn to scale.
(B) Walking trajectories and residence probabilities of starved flies before and after encounter with a food drop or water drop at the center of the arena. See also Movies S1 and S2. The left columns show the flies’ paths before they first encountered the food or water. The right columns show the flies’ paths from when they first left the food or water to when they reached the arena wall. Each trial was for 30 min. Top row: trajectories from individual flies are plotted in black. Middle row: trajectories from all flies are plotted in black (food: N = 48 flies; water: N = 20 flies). Bottom row: residence probabilities of the walking trajectories are plotted in gray scale. Each probability histogram depicts the mean of the normalized residence probability distributions for individual flies. In calculating the distributions for the before-food and -water conditions, we did not include any trajectories along the outer wall. See also Figure S4 and Table S1 for additional statistical analysis.
(C) Number of revisits to the food or water drop. The first visit to the food is not counted. Values for individual flies are plotted as black dots. The median for each condition is plotted as an open diamond. Error bars depict 95% CIs.
(D) The maximum distance walked between departures from the food or water drop to arrival at the arena wall. Values for individual flies are plotted as black dots. The median for each condition is plotted as an open diamond. Error bars depict 95% CIs.
See also Figure S1.
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3. Figure 2
Flies Perform a Local Search in the Absence of Visual, Olfactory, or Pheromonal Cues
(A) Walking trajectories and residence probabilities of flies encountering a 1 μL food drop in the dark and oe− fly trials or 500 mM sucrose in the sucrose trials. See also Movie S3. In the dark trials, we eliminated visual cues by turning off the overhead white lights and covering the arena with a black acrylic plate that transmitted IR light for imaging, but not light in the visible spectrum of the fly. In the sucrose trials, we eliminated olfactory cues by using an odorless food spot (500 mM sucrose). Prior to starvation, the diets of the flies used in the sucrose trials were supplemented with additional yeast so that they would not be protein deprived. In the oe− flies, we used flies in which the contact pheromone-producing oenocytes were genetically ablated. Sucrose trials lasted 45 min; all other trials lasted 30 min. Top row: trajectories of individual flies. Middle row: trajectories of all flies (dark: N = 53 flies; sucrose: N = 25 flies; oe−: N = 12 flies). Bottom row: mean residence probabilities for each group of flies. In calculating the distributions for the before-food conditions, we did not include any trajectories along the outer wall. See also Figure S4 and Table S1 for additional statistical analysis.
(B) Number of revisits to the food or water drop. Values for individual flies are plotted as black dots. The median for each condition is plotted as an open diamond. Error bars depict 95% CIs. The values for the yeast and water trials from Figure 1 are also plotted for ease of comparison.
(C) The maximum distance walked between departure from the food or water drop to arrival at the arena wall. Values for individual flies are plotted as black dots. The median for each condition is plotted as an open diamond. Error bars depict 95% CIs. The values for the yeast and water trials from Figure 1 are also plotted for comparison.
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4. Figure 3
Flies Continue to Search around the Location of a Food Drop after It Has Been Moved
(A) Top and side views of the arena in which the food drop can be moved. The top view shows the position of the 1 μL food drop at the center of the arena before the motion of the slider, and the left side shows the location afterward. All experiments were conducted in the dark.
(B) Walking trajectories during slider experiments. See also Movies S4, S5, and S6. The first column shows the flies’ paths before they found the food. The second column shows the flies’ paths after they left the food but before the food was moved. The third column shows the flies’ paths after the food was moved from the arena center to the arena side, but before the flies re-encountered the food drop at its new location. The fourth column shows the flies’ paths after they encounter the food spot at the new location until the end of the trial. If the fly never re-encountered the food at its new location, we do not show a trajectory. Red dots (not to scale) indicate the position of the food spot. Each trial was for 30 min. Rows 1–3: trajectories from a sample of individual flies. Row 4: trajectories from all flies (N = 21 flies; 3 flies did not re-encounter the food in its new location). Row 5: mean residence probabilities for all of the flies. In calculating the distributions for the before-food conditions, we did not include any trajectories along the outer wall.
See also Figures S2 and S4 and Table S1 for additional statistical analysis.
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5. Figure 4
Random Search Models Based on Measured Statistics Do Not Recapitulate the Flies’ Behavior
(A) Turns are detected by increases in the angular velocity of a fly trajectory. Top: walking trajectory with detected turns marked in blue (left) or magenta (right). Bottom: sample angular velocity trace. Smooth angular velocity is shown in black. Left turns are marked in blue, and right turns are in magenta; unsmoothed angular velocity is shown in light gray. Thresholds for turn detection are marked by dotted horizontal lines (at ±120°/s). Angular velocity is typically quite high when the animal is stopped due to its grooming movements, but these segments were excluded from the analysis.
(B) Top: cumulative distribution of the absolute value of turn angles from before (black; N = 6,266 turns) and after (red; N = 33,890 turns) contacting food for all yeast trials (includes trials with the light on and trials in the dark; N = 101 flies). The 95% CIs are shaded in gray or light red but are too narrow to see clearly. Bottom: histogram of the absolute value of turn angles from before and after food encounters. Data are the same as in the top panel.
(C) Top: cumulative distribution of run lengths from before (black; N = 5,573 runs) and after (red; N = 33,561 runs) contacting food for all yeast trials (same trials as B; N = 101 flies). Bottom: histogram of run lengths from before and after food encounters. Data are the same as in the top panel.
(D) Flow chart illustrating our biased run-and-tumble simulation. A simulated fly initially starts at the center of the arena at an angle of 0°. A turn angle is drawn randomly from the experimental distribution shown in (B), top. The turn direction, to the right or left, is based on the direction of the previous turn. In the simulated data shown in (E), the probability of two consecutive turns being the same direction is The fly is rotated by the selected turn angle and direction. A run length is drawn randomly from the experimental distribution shown in (C), top. The fly is translated by the selected run length. The turn-and-run selection process is repeated until the fly position is outside the bounds of the arena.
(E) Simulated walking trajectories from simulations (light blue background) and from experiments (gray background). The probability of two consecutive turns being in the same direction in the simulations is 0.50, 0.75, or The probability in the experiments is A red circle marks the arena center.
(F) Centers of mass for walking trajectories from simulations (light blue background) and experiments (gray background). The experimental walking trajectories are from all yeast trials (includes trials with the light on and trials in the dark; N = 101 flies). The SDs of the distances between the centers of mass and the arena center are shown as black circles.
(G) Minima in the distance from food are plotted as a function of total distance walked (see STAR Methods). Minima from the experimental yeast trials (includes light-on and dark trials; n = 101 flies) are plotted as black dots, and minima from simulated trials are plotted in light blue. The best-fit lines are based on least-squares regression.
(H) The maximum distance walked between departure from a food drop to arrival at the arena wall. The experimental values are from all yeast trials (includes light-on and dark trials; N = 101 flies). Values for individual flies are plotted as black dots. The median for each condition is plotted as an open diamond. Error bars depict 95% CIs.
See also Figure S3.
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6. Figure 5
Flies Initiate Turns When Walking away from Food and Turn Back toward the Food during the Turn
(A) We define food angle as the angle between the heading vector of a fly and a vector pointing from the fly to the food. The positions of the food drop relative to a fly at three different food angles are shown at the right. A food angle of 0° indicates that the fly is walking straight toward the food, 90° indicates that it is walking in a circle around the food, and 180° indicates that it is walking directly away from the food. Food angle <1 indicates that the food is to the fly’s right; food angle >1 means that the food is to the fly’s left.
(B) Diagram illustrating how food angle changes as the fly walks along a trajectory. In the outer trajectory, the food angles of the fly are labeled at different points before and after each turn. The points on the inner trajectory where a fly is at the same food angle as on the outer trajectory are marked.
(C) Polar histograms of food angles immediately preceding or following turns in the after-food (N = 101 flies; 33,890 turns) or after-water trajectories (N = 20 flies; 297 turns). Turns are defined as shown in Figure 4A and only the after-food or -water distributions are shown. Yeast trials pool data from experiments under light and dark conditions. The direction pointing to the food drop (0°) is marked by a red circle. Turns were mirrored such that the food or water was to the left of the fly as it entered the turn; thus, the negative half of the polar graph is unpopulated and shaded gray. Medians are marked by blue triangles. In the water trials, the medians of the two lobes in the after-turn distributions are calculated separately (see text for more details).
(D) Distributions of run lengths following food contact initiated at three different distances from the food drop (N = 101 flies; n = 33,561 runs). Red: runs initiated 0–10 mm from food (n = 7,865 runs). Yellow: runs initiated 20–30 mm from food (n = 6,531 runs). Blue: runs initiated 50–60 mm from food (n = 1,723 runs).
(E) Median run lengths (black lines within colored boxes) for runs after contacting food initiated at different distances from the food drop (N = 101 flies; 33,561 runs). The 95% CIs are shown as colored boxes. The color scheme is the same as in (D), with (D) showing three of the distributions in (E). Median run lengths for randomly shuffled data are shown as gray bars. The 95% CIs for these data are too small to be visible on the plot.
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7. Figure 6 Flies Periodically Return to the Food Drop
(A) Distance from the food drop plotted against the total distance walked by two example flies.
(B) The normalized autocovariances for the two sequences plotted in (A).
(C) Pseudo-color representation of autocovariance functions for all yeast trials (including both light-on and dark trials; N = 81 flies). Each row represents the autocovariance of the longest continuous trajectory following food contact for each yeast trial, ranked according to the delay between primary and secondary peaks. Trajectories less than 500 mm in total distance walked were excluded.
(D) Distance from food plotted for two simulated trajectories. We increased the diameter of the simulated arena to three times that of the experimental arena (note higher values on the y axis) to obtain trajectories long enough to calculate a meaningful autocovariance.
(E) Data as in (B), but for the simulated trajectories.
(F) Analysis as in (C), but for the simulated trajectories.
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