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. 2022 Aug 29;12:14713. doi: 10.1038/s41598-022-18950-x

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© The Author(s) 2022

Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Time evolution of migration patterns. (A) Time-dependent ensemble-averaged radial displacement, $⟨ d_{r} (t_{i}) ⟩$ , versus time, t, (mean ± SEM) for GA (N=177) and GFA (N = 305) on a double-logarithmic scale. Dashed lines correspond to results obtained from BPRW (blue) and PRW (red) simulations. Insets: Sketches defining the radial displacement, $d_{r} (t_{i})$ , for GA and GFA, respectively. (B) Time evolution of the ensemble-averaged directionality, $⟨ D (t_{i}) ⟩$ (mean ± SEM) for GA (N = 177) and GFA (N = 305). The dashed lines are averages over simulated tracks for BPRW (blue) and PRW (red). Insets: Distribution of the directionality of the entire trajectories, $D$ . (C) Distribution of directionalities of the trajectories after $t = 75$ min, $D (75 min)$ , at different distances from initial position, $⟨ d_{r} (75 min) ⟩$ , for GA (blue) and GFA (red). (D) Time-evolution of the ensemble-averaged radial velocity, $⟨ v_{r} (t_{i}) ⟩$ , (mean ± SEM) for GA and GFA and simulated trajectories (dashed lines) from BPRW (blue) and PRW (red). In all four cases, $⟨ v_{r} (t_{i}) ⟩$ was binned over 15 min with a moving average of 10 data points.