Reviewer #3's Review (Gonzalo de Polavieja)

“• What are the main claims of the paper?

The paper by Maye et al. claim that generated search algorithms (Levy flights) but not random noise account for the inter-spike-intervals obtained in spontaneous yaw behaviour of a fly at a flight simulator.

I believe the ms should be finally published as it raises an important question and gives tools and results that may help to answer the important question of spontaneous behavior.

In the following I give some suggestions. Whether these suggestions are major or minor modifications of the text is for the editor and authors to decide. I personally think that quite a few more tests would improve the ms.

• Are the claims properly placed in the context of the previous literature?

The authors reference some of the main papers of previous work. I miss references to other noise models (see below).

• Do the experimental data support the claims? If not, what other evidence is required?

Although the authors make the general statement that their data is best explained by search algorithms (neural control), they explicitly disproof the simplest noise model (Poisson). In the following I list a number of random processes that may account for the data or that, in any case, should be rejected as hypotheses.

The authors correctly claimed that their data is best fitted by a power-law distribution and not a Poisson distribution. But that the ISI data is not Poisson is obvious from the outset as the data is bursty and that implies more probability for short and long durations.

I believe some noise models should be tested. For example, in the following I show that a sum of Poisson noises (imagine it as different parts of the brain producing Poisson noises but with different rates) results in a power law of the degree 2, exactly as the authors find in their data.

1. Sum of Poisson models. The authors reject the single Poisson model and claim that that their data is best fit with a power-law of degree two, P(ISI) proportional t^(-2). In the following I proof that a sum of Poissons, something that sounds more biologically plausible, is in fact a power-law of degree two.

A sum of equally contributing Poisson distributions with rate lambda, lambda exp(-lambda t), can be calculated as:

Integral (lambda Exp(- lambda t)) from 0 to Infinity = t^(-2)

Also, for limits from 0 to any value, the integral results in a more complicated expression that behaves as a power law for large time t, as in experimental data.

2. Poisson process through a linear filter. A Poisson process through a linear filter results in shot noise with fractal characteristics when the impulse response funcion is a power-law. One should try even nonlinear filters. I wonder how the methodology of the authors would work on Poisson data through nonlinear filters.

3. Doubly stochastic Poisson process. A simple Poisson process has a fixed rate. However, a more reasonable assumption in a biological system is that the rate itself might be drawn from a distribution. This distribution also has a long tail. See Cox work for details.

4. Cascades and branching of Poisson processes. These are complicated versions of random processes that have been found useful in the analysis of optics. Again, they are more realistic than the single Poisson and in many occassions they have long tails. See the work of Teich in optics.

5. Barabasi model. I would favor the hypothesis that animals spontaneous behaviour is half-way between purely random and purely deterministic. But this means little without a testable model. The Barabasi model, proposed for human dynamics, consists of a ordered list of behaviors and a probability rule of how to move among them. Interestingly this also produces a power law. This sounds simple but probably biologically plausible. For example, Heisenberg and cols showed that the fly goes through several behaviours to find the one that controls the flight arena. This intrinsic behaviour sounds as if it could in principle be modeled by something like the Barabasi model. I do not believe something like this should be within the scope of the paper, but probably something to take into account in the future. For this, experiments on how the fly switches from one behaviour to another would be needed.

• Who would find this paper of interest? And why?

The question raised by the authors is of interest to a broad audience, including all neuroscientits. Deviations from average or typical behaviour are typically taken as noise and not as intrinsic dynamics. This is probably fine for the analysis of single neurons, maybe even very early sensory networks, but sounds unrealistic for large networks. Spontaneous activity should probably be major concern for neuroscientists, especially those interested in behavior initiation, decision-making, attention, etc.

• What further directions would it be useful to take the current research?

Experiments on switching behaviors and comparison with models of the type of Barabasi might something interesting to try.

• Is the manuscript written clearly enough that it is understandable to non-specialists? If not, how could it be improved?

The paper is clearly written. I find two things difficult to follow, though. First, the main text includes too much philosophical discussion for me. Second, the methods are complicated for the reader and the main text does little to help. One need to go to the Supplementary material to see what is really done. I really believe the authors should make an effort to explain the ideas behind their methodology in the main text.

• Have the authors provided adequate proof for their claims without overselling them?

I think there is enough proof that the simple noise models do not explain the data. However, I think the abstract is overselling the result as it says that 'spontaneously generated search algorithms but not random noise can account for the temporal structure...'. The authors mainly disproof the simplest random noise case and I cannot see a proof that the Levy flights are search algorithms in their experimental setting.

• Have the authors treated the previous literature fairly?
I think they do, except for papers on more sophisticated noise models.

• Does the paper offer enough details of its methodology that its experiments could be reproduced?
The experimental methodology is explained in detail. The analysis is also explained in detail in Suppl Info.

• PLoS ONE encourages authors to publish detailed protocols as supporting information online. Do any particular methods used in the manuscript warrant such a protocol?
Their analysis is explained in a lot of detail in their Suppl Info. Little help on the ideas behind are given though. Maybe a more geometrical explanation would help readers.”

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.