Reviewer #2 (Public review):
Summary:
The manuscript by Canever et al was assessed by three Referees at another journal, who brought up a range of critical points. I will not repeat a summary of the work; this can be found in the first-round reviews.
Strengths:
In their revised manuscript, the authors include substantial changes and additional reasoning. Along with their rebuttal letter, I think they make a very convincing case. While the claims are well supported by the analysis, I do not see that the findings need to be universal to be relevant. It might be rather surprising to me if there existed such a universality, in fact. I think that the findings are solid and interesting in their own right and are worthy of publication, especially with the amended discussion in this revision.
Weaknesses:
However, while the more bio-oriented parts are not fully accessible to me, I do have a few points from the data analysis point of view that need amendment.
(1) The used mathematical models need to be specified more precisely. First, the authors confuse Levy flights and walks. These are distinct processes in the sense that a Levy flight does not have a finite variance and thus no finite speed. The proper model here would be Levy walks. As in a big body of the literature, both notions are used interchangeably here, while they are distinct processes. Then the authors speak about a "superdiffusive model", for which I do not find a proper definition. There exists an entire range of superdiffusive models, each with a different physical background, so this needs more clarity. The authors may consult one of the standard reviews for more details, e.g., Soft Matter 8, 9043 (2012) or Phys Chem Chem Phys 16, 24128<br /> (2014). Overall, a few equations (maybe in the Supplement) would help to be more specific.
(2) For fractional Brownian motion, the authors should check the displacement correlation function; it should show slowly decaying, positive correlations. More details on the practical analysis of FBM can be found, e.g., in Phys Chem Chem Phys 27, 14350 (2025). These correlations should decay as a function of the bin time, e.g., as discussed for the opposite case of subdiffusion in Phys Rev E 88, 010101(R) (2013) [cf Fig 3b]. In general, FBM was determined to be a highly relevant process for a number of systems, including amoeba cells at shorter times, see the detailed analysis in Phys Rev Res 4, 033055 (2022). In this paper, there are also different ways to characterise the motion in terms of scaling. Exponents are detailed.
(3) Some relevant approaches discussed in literature that should be discussed in the context of this work: eLife 9, e52224 (2020); Rep Prog Phys 86, 126601 (2023); Chaos 35, 023145 (2025). In the context of non-Gaussianity for active particles: Phys Rev E 104, 064615 (2021); New J Phys 25, 013010 (2023).
(4) In the abstract, I am having some issues with the formulation in the sentence: "This directional memory emerges from fractional Brownian motion". It sounds as if FBM were a fully clarified phenomenon. I would prefer some statement along the lines that the data are consistent with such a mathematical modelling approach.
After fixing these points, I think the manuscript will clearly warrant being shared.