Figure 1

<p>Flight patterns and their representations. a) An example flight pattern of a <i>Drosophila</i> within a circular chamber of diameter 1000 mm and depth 600 mm. The trajectory was recorded with a stereo video system at 30 frames per second and lasts for about 11.3 s. There was no odour stimuli and the visual background was uniform and white. b) Representation of a projected flight path as straight-line movements between the positions (•) at which changes in flight direction occurred. A change in flight direction is deemed to have arisen when the direction of the current flight segment (joining two successive recorded positions) and that of the flight segment immediately following the last deemed change in direction, is equal or more than 90°.</p

Figure 5

<p>Assessment of the fractal dimension associated with the representations of the <i>Drosophila</i> flights. The average number, <i>n_l</i>, of boxes of size <i>l_box</i> required to enclose the representations of the 3-dimensional <i>Drosophila</i> flights is plotted against <i>l_box</i> (dots). A power-law relationship of the form would be indicative of a scale-free characteristic with fractal dimension D, and here, a linear least squares fit shows that D = 1.2. Fractal scaling is evident for spatial scales between about 5 and 75 mm. The insert shows the same plot for a series of simulated Lévy-flights with <i>μ</i> = 2.</p

Figure 6

<p>An example of the cumulative number of ‘saccade cycles’ made by a <i>Drosophila</i> as a function of the distance, L, flown. One ‘cycle’ corresponds to a series of body saccades in which the animal's heading changes ±360° within the arena. Positive cycles are made in clockwise direction whilst negative cycles are made in an anticlockwise direction. The flight pattern consists of straight-line flight-segments punctuated by saccades (Insert). The locations of the saccades along the flight path are indicated(•).</p

Figure 3

<p>The distribution, <i>n_l</i>, of lengths, <i>l</i>, of ‘straight-line flight segments’ (inter-saccade intervals). The sizes of the data collection bins are logarithmically distributed and numbers of straight-line flight segments have been normalised by the bin sizes. The straight line with slope -1.3 constitutes a linear least squares fit to the data for 10<<i>l</i><100 <i>mm</i> (Pearson's correlation coefficient, <i>R</i>² = 0.87).</p

Figure 7

<p>Searching efficiencies and persistent turning. a) Searching efficiencies, <i>η</i>, for the location of targets placed at = the vertices of a square lattice with spacing, <i>λ</i>, as a function of the Lévy exponent, <i>μ</i>, characterising the distribution of flight segment lengths. The searching efficiency is the reciprocal of the mean distance travelled before first encountering a target. Simulation data are shown <i>λ</i>/<i>r</i> = 100 where r is the range at which a target can be detected for the case when flight-segments are randomly orientated (dashed-line) and for the case when the angle between successive flight segments is 45° and 90° (solid lines). Searching commences from just beyond (r, r). The searching is optimal when <i>μ</i>≈2 and when the turning angle is equal to or greater than 90°. The results of simulations (not shown) reveal that this is also optimal for <i>λ</i>/<i>r</i> = 10 and <i>λ</i>/<i>r</i> = 1000. Spiralling Lévy flights remain optimal if the sense of turning switches back and forth between 90° and −90° after completing two or more turns of the spiral. More frequent switching leads to a searching strategy that is less efficient than Lévy flights with randomly distributed turning angles. b) Simulation data for the optimal searching, efficiency, <i>η_opt</i> = max(<i>η</i>(<i>μ</i>)), as a function of the turning angle, <i>ϑ</i> (•). The solid-line is added to guide the eye. c) <i>μ</i> = 2 Lévy flights with random turns and with 90° turns. The spiralling promotes the revisiting of territory and thereby reduces the probability that nearby targets will be missed. d) A non-optimal Gaussian (<i>μ</i> = 4) spiral flight pattern.</p

Figure 8

<p>Mean times in the local active searching phase, <i>t_s</i>, comprised of short flight-segments having length <i>L</i><30 <i>mm</i> and in the relocation phase, <i>t_r</i> (X), comprised of long flight-segment having length <i>L</i>>30 <i>mm</i>. Mean times do not change significantly when the length scale <i>L</i> is increased or decreased by a factor of 2. Mean times for a diverse range of organisms with intermittent locomotion (•) (phorid fly, general locomotion; arctic grayling, food search with small and large prey; cricket, spontaneous walking and in presence of a calling mate; copepod nauplius, general swimming with food present; <i>Drosophila meglanogaster</i> larva, crawling on a non-feeding substrate; octopus, moving over reef while foraging) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0000354#pone.0000354-Kramer1" target="_blank">[30]</a>. The scaling relation <i>t_r</i>∝<i>t_s</i>^2/3 predicted by the Lévy-flight model of optimal searching <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0000354#pone.0000354-Reynolds1" target="_blank">[5]</a> is shown (solid line).</p

Figure 2

<p>Structure function analysis. a) Structure functions characterizing the displacements, Δ<i>X_τ</i>, in a time increment <i>τ</i> of hungry <i>Drosophila</i> in an odorless arena with white walls (symbols). <i>Drosophila</i> flights were projected onto the horizontal (x-y) plane. Power-scaling of the structure functions is indicated (dashed line). This scaling was obtained from least squares fitting of logarithms of the structure functions to logarithms of the time intervals, <i>τ</i>, for<i>τ</i>≤1<i>s</i>. b) Scaling-exponents, <i>ζ</i>, obtained in this manner are typically prescribed with a standard error of about ±0.01<i>q</i> and Pearson's correlation coefficient, <i>R</i>² = 0.99 Scaling exponents (symbols, o) are well represented by <i>ζ</i> = 0.9<i>q</i> (solid line) (<i>R</i>² = 1).</p

Figure 9

<p>Flight patterns in chamber with an odor source. a) An example of a sequence of intra-saccade flight lengths, <i>l</i>, for a <i>Drosophila</i> within an arena containing an odor source and lined with a high-contrast random checkerboard panorama (solid-line). Saccades occurring within 100 mm of the odor source are indicated (•). Sustained bouts of short length flights tend to occur in the vicinity of the odor source. The most pronounced of these occur between 50 and 60 s, and between 70 and 80 s (within shaded boxes). These bouts interrupt the Lévy flight searching. b) A projection of the flight pattern. The odor source is hidden in the floor of the arena and is located in the top left-hand quadrant of the projection. c) Structure functions characterizing the displacements, Δ<i>X_τ</i>, in a time increment <i>τ</i> of the <i>Drosophila</i> flights projected onto the horizontal (x-y) plane. d) Power-scaling of the structure functions is indicated (dashed line). This scaling was obtained from least squares fitting of the structure functions for <i>τ</i>≤1<i>s</i>. Scaling-exponents, <i>ζ</i>, obtained in this manner are typically prescribed with a standard error of about ±0.01<i>q</i> and Pearson's correlation coefficient, <i>R</i>² = 0.99 Scaling exponents (symbols, •) are well represented by <i>ζ</i> = 0.9<i>q</i> (solid line) (<i>R</i>² = 1).</p

Pulse Width dependency of fMRI BOLD signal.

<p>A) Comparison of data from left unilateral NAc stimulation at 5 V 130 Hz 500 µs (i; n = 3) with stimulation at 3 V 130 Hz 100 µs (ii; n = 3). Both pulse widths showed regions of activation in the prefrontal cortex, insula, dorsal anterior cingulate, caudate. There was an additional area of activation in parahippocampal cortex present only with stimulation at 5 V 130 Hz 500 µs. B) i. Region of interest cluster sizes (mm³) comparing the percent size of areas of activation with 5 V 130 Hz 100 µs (yellow; n = 3) and 5 V 130 Hz 500 µs (red; n = 3), represented by the relative size of the two circles. ii. Event-related time course of percent change in BOLD signal from baseline with 100 µs (yellow; n = 3) and 500 µs (red; n = 3) pulse widths at 5 V and 130 Hz.</p

Significant Clusters in the General Linear Model comparing Stimulation “on” periods to baseline.

<p>I = Ipsilateral, AP = Anterior/Posterior, ML = Medial/Lateral; DV = Dorsal/Ventral.</p><p>Stimulation Parameters = 5 V 130 Hz 500 µs.</p