Reviewer #1's Review

“The main claim of this paper is that brains exhibit a level of operational complexity that can not be explained by simple reflex circuits. The authors claim that the common perception is that the brain is a simple input-output device: that for each and every input, there is one unique and reliable output. In my view, this is a provocative, overly simple statement. It seems to me that just the opposite is true; we are astonished when any brain, even a simple one, actually does behave like a linear transform function. It is under these rare circumstances that one can get a handle on specific neural processes. In any event, this is just the sort of philosophical conversation that deserves the open review venue of PLoS ONE.

The authors present a mathematical analysis of steering behavior in the fruit fly, they attempt to establish that the random spontaneous fluctuations in steering left and right not driven by a Brownian distribution, but rather show a different random distribution altogether, a Levy distribution that could be optimized for active searching phases interspersed with relocation phases.

I applaud the effort; this is indeed a fascinating account. However there are critical methodological errors that cannot be overlooked. In particular, Major Comment #3 identifies a critical weakness of the analysis.


Major comments:

1. The authors claim that 'spontaneously generated search algorithms (Levy flights), but not random noise can account for the temporal structure in spontaneous yaw torque fluctuations in tethered Drosophila'. This claim is both unfounded and confusing. It is unfounded because the analysis of yaw time series is not sufficient to establish the presence or otherwise of Levy-flight movement patterns. Their presence can be only be established by analysing flight pattern data per se, i.e. by showing that the lengths an animal moves between saccades are distributed according to an inverse square law and by showing that entire flight patterns are fractal and isotropic. The claim is confusing because it does not distinguish clearly between 'spontaneously generated' signals and 'random' signals. Levy-flights are, in fact, random. They are distinguished from other random processes by having distribution functions with power-law tails. Finally, do the authors assume that Inter Saccade Interval (ISI) is directly proportional to flight length between saccades? I.e., does a longer ISI necessarily mean a longer flight path? This is not necessarily a safe assumption, since the animals could be modifying thrust independently from yaw torque.

2. Spontaneous behavior is not simply random: The subtitle is confusing because the authors do not distinguish clearly between spontaneous and random, Levy flights are random. From the first paragraph it seems that by 'random' they mean a Poisson process. The authors point out correctly that 'given a certain mean spike rate, the most straightforward assumption is to expect a stochastic procedure to behave according a Poisson process.' But why should the spike rate have a well defined characteristic mean value. This is an arbitrary assumption and if relaxed, the stochastic procedure will, as observed, behave according to a Levy process. On page 6 the authors state erroneously that the 'flying behavior is not entirely random'. What they really mean is that it is not Poisson, i.e. that they assumed wrongly that there is a 'certain mean spike rate'.

3. **The authors claim that the ISI (inter-spike intervals) decays according to a Levy distribution mu=2. No evidence is provided for this and this is a key weakness with the manuscript. The authors need to show a plot of the distribution of ISI on log-log scales. The data should be binned using logarithmically sized bins. A power-law must be clearly evident over at least one decade to be convincing. The authors should also plot the data on log-linear scales to rule out the possibility of an exponential distribution. The authors use the term 'Levy distribution' when they really mean a distribution with a power-law tail. The distinction is important because Levy-distributions have power-law tails and a very specific core. Their presence would indicate that ISI result from the summation of many underlying signals that are power-law distributed. There absence would indicate that the ISI are a one-step random process. This is a consequence of the so-called Generalized Central Limit Theorem. The authors state without qualification that mu=2 constitute an optimal searching strategy. It is optimal only when targets are randomly and sparsely distributed and can be repeatedly revisited. The authors have also overlooked the fact that the strategy is optimal when angles between successive flights are uniformly and randomly distributed between 0 and 360 degrees. It is not evident from published literature that the strategy is optimal when, as in the case of Drosophila, most turns are through +/- 90 degrees.”

n.b. These are the general comments made by the reviewer when reviewing the originally submitted version of this paper. The manuscript was revised before publication. Specific minor points addressed during revision of the paper are not shown.