Figure 5. Control and brain blocked larvae movements.

Example of larva trajectories for each of 8 experimental treatments. Each treatment is signified by the Drosophila brain outlines and colour coding on the left of panels (A). BL/+ (light grey) and shi^ts/+ (dark grey) treatments were conducted at normal (22°C) and restrictive temperatures (33°C) whereas MB247/+ and MB247 >shi^ts (light blue), and BL >shi^ts (pink) and BLsens > shi^ts (red) were tested at 33°C. (B) For each treatment an example larva trajectory is given with paths showing complex patterns of movement. All trajectories showed similar complexity across scales but which are not possible to illustrate in a single panel as here, but which are evident from path tortuosity analysis. Scale of paths are denoted by the x,y coordinates in mm. (C) Tortuosity analysis shows complex alternations of long, straighter move steps (higher straightness index, S.I., values) with short, spatially intensive clusters of move steps of different size (lower values). Note the BL >shi^ts larva with no function in the brain and a section of the suboesophageal ganglion (SOG), and BLsens > shi^ts larva with blocked brain lobes, SOG and all somatosensation, both show complex exploration movements similar to controls. (D) MLE model fitting and selection demonstrates larvae move-step length rank frequency distributions best fit by truncated Lévy power laws for each experimental treatment (fitted red line) compared to a Brownian walk (exponential model; blue line). Move step length frequency distributions were well approximated by a truncated Lévy power law across all treatments, with exponents ranging from 1.3 to 2.0. It is striking that BLsens > shi^ts larvae exponents were close to the theoretical optimum (µ ~2.0) indicating Lévy-like movements must be generated intrinsically within thoracic and abdominal neural circuitry.

Figure 5—figure supplement 1. The distributions of turning angles along larva paths.

Comparison of (A) the raw distribution of turn angles with (B) the turn angle distribution after determining significant turns. The raw distribution in (A) is dominated by a very high frequency of small angle deviations around 0^o that may be unrelated to actual turning behaviour (interruptions in the movement path). The high frequency of small deviations with relatively few larger angle turns does not fit the expectation of a uniform random turn-angle distribution of an uncorrelated random walk. The distribution of significant turns in (B) identifies a relatively higher frequency of larger angle turns that is more consistent with a uniform turn angle distribution of idealised random Lévy walks (note that there are far fewer significant turns than raw turns). The significant turns identified between 50 and −50^o indicate the presence of short-range angle correlations, however, Lévy walks are independent of short-range correlations and the estimated value of µ_opt = 2 remains unchanged (see main text for details).