Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Advertisement

Nature Communications
  • View all journals
  • Search
  • My Account Login
  • Content Explore content
  • About the journal
  • Publish with us
  • Sign up for alerts
  • RSS feed
  1. nature
  2. nature communications
  3. articles
  4. article
Unveiling individual and collective temporal patterns in the tanker shipping network
Download PDF
Download PDF
  • Article
  • Open access
  • Published: 27 February 2026

Unveiling individual and collective temporal patterns in the tanker shipping network

  • Kevin Teo  ORCID: orcid.org/0009-0008-3985-75691,
  • Naomi Arnold1,
  • Andrew Hone2,
  • Michael Coulon3,
  • Martin Ireland3,
  • Mauricio Santillana  ORCID: orcid.org/0000-0002-4206-418X4 &
  • …
  • István Z. Kiss  ORCID: orcid.org/0000-0003-1473-66441,5 

Nature Communications , Article number:  (2026) Cite this article

  • 3952 Accesses

  • 2 Citations

  • 29 Altmetric

  • Metrics details

We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Applied mathematics
  • Industry

Abstract

The global oil tanker shipping network emerges from individual ship and fleet decisions driven by economic, environmental, and operational factors. However, most existing shipping network analysis rely on static, time-aggregated representations, overlooking critical temporality connecting individual vessel routing strategies with both operational efficiency and global cargo flows. To address this gap, we introduce a dual-scale framework complementing sequential motif analysis—capturing recurrent patterns in vessel movement sequences—with Dynamic Mode Decomposition (DMD), extracting temporal dynamics from vessel trajectories to global cargo flows. Using tanker movement data across four vessel classes, we demonstrate that vessels exhibiting diverse regional exploration patterns spend up to 50% more time transporting rather than seeking cargo, indicating greater economic and environmental efficiency. At the system scale, DMD analysis reveals distinct seasonality with an average peak-to-trough amplitude of 16%. Major import regions show synchronous annual demand cycles, while export regions exhibit anti-synchronicity. These temporal patterns, invisible to static analysis, reveal performance differences that enable route optimization for both economic and environmental benefits.

Similar content being viewed by others

Dynamic fleet management of waterborne vessels with mixed passenger and parcel services

Article Open access 14 April 2025

Dynamic monitoring of dust transport effect on maritime visibility using multi source satellite data and advanced deep learning approach

Article Open access 21 October 2025

Enhancing global maritime traffic network forecasting with gravity-inspired deep learning models

Article Open access 19 July 2024

Data availability

The vessel voyage data that support the findings of this study are available from AlphaOcean, but restrictions apply to the availability of these data, which were used under license for the current study due to commercial confidentiality agreements, and so are not publicly available. Data are, however, available from the authors upon reasonable request and with permission of AlphaOcean (https://alphaocean.ai/). Map figures were generated with data from the coastal data by GSHHG.

Code availability

No substantial custom code was developed for this study. Sequential motif analysis was performed using the RandomWalker package (accessible via https://github.com/narnolddd/randomwalker). Dynamic mode decomposition was performed using PyDMD version 1.0.0, and singular spectrum analysis was conducted using py_ssa_lib version 0.0.1. Statistical analysis was performed in Python version 3.9.19 using standard Python libraries and packages. All libraries are freely available and can be installed via standard Python package managers.

References

  1. United Nations Conference on Trade and Development. Review of maritime transport 2017 https://unctad.org/publication/review-maritime-transport-2017 (2017).

  2. U.S. Energy Information Administration. World oil transit chokepoints https://www.eia.gov/international/analysis/special-topics/World_Oil_Transit_Chokepoints (2024).

  3. Rahim, M. M., Islam, M. T. & Kuruppu, S. Regulating global shipping corporations’ accountability for reducing greenhouse gas emissions in the seas. Mar. Policy 69, 159–170 (2016).

    Google Scholar 

  4. Brancaccio, G., Kalouptsidi, M. & Papageorgiou, T. Geography, transportation, and endogenous trade costs. Econometrica 88, 657–691 (2020).

    Google Scholar 

  5. Walker, T. R. et al. Chapter 27—environmental effects of marine transportation. In 2nd edn World Seas: An Environmental Evaluation, (ed. Sheppard, C.) 505–530 (Academic Press, 2019).

  6. Shi, Z. et al. Perspectives on shipping emissions and their impacts on the surface ocean and lower atmosphere: an environmental-social-economic dimension. Elementa Sci. Anthr. 11, 00052 (2023).

    Google Scholar 

  7. Ducruet, C. The geography of maritime networks: a critical review. J. Transp. Geogr. 88, 102824 (2020).

    Google Scholar 

  8. Kaluza, P., Kölzsch, A., Gastner, M. T. & Blasius, B. The complex network of global cargo ship movements. J. R. Soc. Interface 7, 1093–1103 (2010).

    Google Scholar 

  9. Álvarez, N. G., Adenso-Díaz, B. & Calzada-Infante, L. Maritime traffic as a complex network: a systematic review. Netw. Spat. Econ. 21, 387–417 (2021).

    Google Scholar 

  10. Faure, M.-A. & Ducruet, C. The Blue Connection. A Systematic and Critical Review of Shipping Network Research. Netw. Spat. Econ. https://doi.org/10.1007/s11067-025-09705-y (2025).

  11. Ducruet, C. Shipping network analysis: state-of-the-art and application to the global financial crisis. In Port Systems in Global Competition, 300–333 (Routledge, 2023).

  12. Hu, Y. & Zhu, D. Empirical analysis of the worldwide maritime transportation network. Phys. A Stat. Mech. Appl. 388, 2061–2071 (2009).

    Google Scholar 

  13. Ge, J., fu, Q., Zhang, Q. & Wan, Z. Regional operating patterns of world container shipping network: a perspective from motif identification. Phys. A Stat. Mech. Appl. 607, 128171 (2022).

    Google Scholar 

  14. Peng, P., Poon, J. P., Yang, Y., Lu, F. & Cheng, S. Global oil traffic network and diffusion of influence among ports using real time data. Energy 172, 333–342 (2019).

    Google Scholar 

  15. Liu, Q., Yang, Y., Ke, L. & Ng, A. K. Structures of port connectivity, competition, and shipping networks in Europe. J. Transp. Geogr. 102, 103360 (2022).

    Google Scholar 

  16. Zhang, Q., Pu, S., Luo, L., Liu, Z. & Xu, J. Revisiting important ports in container shipping networks: a structural hole-based approach. Transp. Policy 126, 239–248 (2022).

    Google Scholar 

  17. Ducruet, C. & Notteboom, T. The worldwide maritime network of container shipping: spatial structure and regional dynamics. Glob. Netw. 12, 395–423 (2012).

    Google Scholar 

  18. González Laxe, F., Jesus Freire Seoane, M. & Pais Montes, C. Maritime degree, centrality and vulnerability: port hierarchies and emerging areas in containerized transport (2008-2010). J. Transp. Geogr. 24, 33–44 (2012).

    Google Scholar 

  19. Guerrero, D., Letrouit, L. & Pais-Montes, C. The container transport system during covid-19: an analysis through the prism of complex networks. Transp. Policy 115, 113–125 (2022).

    Google Scholar 

  20. Asgari, N., Farahani, R. Z. & Goh, M. Network design approach for hub ports-shipping companies competition and cooperation. Transp. Res. Part A Policy Pract. 48, 1–18 (2013).

    Google Scholar 

  21. Seebens, H., Schwartz, N., Schupp, P. J. & Blasius, B. Predicting the spread of marine species introduced by global shipping. Proc. Natl. Acad. Sci. USA 113, 5646–5651 (2016).

    Google Scholar 

  22. Seebens, H., Gastner, M. T. & Blasius, B. The risk of marine bioinvasion caused by global shipping. Ecol. Lett. 16, 782–790 (2013).

    Google Scholar 

  23. Yan, Z. et al. Analysis of global marine oil trade based on automatic identification system (ais) data. J. Transp. Geogr. 83, 102637 (2020).

    Google Scholar 

  24. Peng, P., Yang, Y., Cheng, S., Lu, F. & Yuan, Z. Hub-and-spoke structure: characterizing the global crude oil transport network with mass vessel trajectories. Energy 168, 966–974 (2019).

    Google Scholar 

  25. International Maritime Organization. Guidelines for voluntary use of the ship energy efficiency operational indicator (eeoi). Circular MEPC.1/Circ.684, International Maritime Organization, London (2009). https://www.cdn.imo.org/localresources/en/OurWork/Environment/Documents/Circ-684.pdf.

  26. Xu, J., Wickramarathne, T. L. & Chawla, N. V. Representing higher-order dependencies in networks. Sci. Adv. 2, e1600028 (2016).

    Google Scholar 

  27. Teo, K., Arnold, N., Hone, A. & Kiss, I. Z. Performance of higher-order networks in reconstructing sequential paths: from micro to macro scale. J. Complex Netw. 13, cnae050 (2025).

    Google Scholar 

  28. Scholtes, I. When is a network a network? Multi-order graphical model selection in pathways and temporal networks. In Proc. 23rd ACM SIGKDD international conference on knowledge discovery and data mining, 1037–1046 (ACM, 2017).

  29. Cliff, N. Dominance statistics: ordinal analyses to answer ordinal questions. Psychol. Bull. 114, 494–509 (1993).

    Google Scholar 

  30. Hess, M. R. & Kromrey, J. D. Robust confidence intervals for effect sizes: a comparative study of cohen’sd and Cliff’s delta under non-normality and heterogeneous variances. in Annual Meeting of the American Educational Research Association, vol. 1 (Citeseer, 2004).

  31. Benjamini, Y. & Yekutieli, D. The control of the false discovery rate in multiple testing under dependency. Ann. Stat. 29, 1165–1188 (2001).

    Google Scholar 

  32. Stopa, J. E. & Cheung, K. F. Periodicity and patterns of ocean wind and wave climate. J. Geophys. Res. Oceans 119, 5563–5584 (2014).

    Google Scholar 

  33. Inchauspe, J., Li, J. & Park, J. Seasonal patterns of global oil consumption: implications for long term energy policy. J. Policy Model. 42, 536–556 (2020).

    Google Scholar 

  34. Raju, T. B., Chauhan, P., Tiwari, S. & Kashav, V. Seasonality in freight rates. J. Int. Logist. Trade 18, 149–157 (2020).

    Google Scholar 

  35. Schmid, P. J. Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28 (2010).

    Google Scholar 

  36. Askham, T. & Kutz, J. N. Variable projection methods for an optimized dynamic mode decomposition. SIAM J. Appl. Dyn. Syst. 17, 380–416 (2018).

    Google Scholar 

  37. Sashidhar, D. & Kutz, J. N. Bagging, optimized dynamic mode decomposition for robust, stable forecasting with spatial and temporal uncertainty quantification. Philos. Trans. R. Soc. A 380, 20210199 (2022).

    Google Scholar 

  38. Müller-Plath, G. & Lüdecke, H.-J. Normalized coefficients of prediction accuracy for comparative forecast verification and modeling. Res. Stat. 2, 2317172 (2024).

    Google Scholar 

  39. Hassani, H. & Mahmoudvand, R. Multivariate singular spectrum analysis: a general view and new vector forecasting approach. Int. J. Energy Stat. 1, 55–83 (2013).

    Google Scholar 

  40. U.S. Energy Information Administration. Monthly energy review September 2024. Tech. Rep., U.S. Department of Energy. https://www.eia.gov/totalenergy/data/monthly/. Accessed: 2024-08-27 (2024).

  41. Wu, X. & Chen, G. Global overview of crude oil use: from source to sink through inter-regional trade. Energy Policy 128, 476–486 (2019).

    Google Scholar 

  42. U.S. Energy Information Administration. Petroleum supply annual, volume 1. Tech. Rep., U.S. Department of Energy. https://www.eia.gov/petroleum/supply/annual/volume1/. Accessed: 2024-09-27 (2024).

  43. Chen, X. et al. Intelligent ship route planning via an a* search model enhanced double-deep q-network. Ocean Eng. 327, 120956 (2025).

    Google Scholar 

  44. Chen, X. et al. Ship energy consumption analysis and carbon emission exploitation via spatial-temporal maritime data. Appl. Energy 360, 122886 (2024).

    Google Scholar 

  45. Hylleberg, S. Seasonality in Regression (Academic Press, 2014).

  46. LaRock, T., Xu, M. & Eliassi-Rad, T. A path-based approach to analyzing the global liner shipping network. EPJ Data Sci. 11, 18 (2022).

    Google Scholar 

  47. Si, R., Jia, P., Li, H. & Zhao, X. Assessing the structural resilience of the global crude oil maritime transportation network: a motif-based approach from network to ports. J. Transp. Geogr. 123, 104123 (2025).

    Google Scholar 

  48. Xu, M., Deng, W., Zhu, Y. & LÜ, L. Assessing and improving the structural robustness of global liner shipping system: a motif-based network science approach. Reliab. Eng. Syst. Saf. 240, 109576 (2023).

    Google Scholar 

  49. Wei, X. et al. Resilience analysis of container port networks based on motif dynamics. In 2023 7th International Conference on Transportation Information and Safety (ICTIS), 263–266 (IEEE, 2023).

  50. Akaike, H. Information theory and an extension of the maximum likelihood principle. In Selected papers of hirotugu akaike, 199–213 (Springer, 1998).

  51. Neath, A. A. & Cavanaugh, J. E. The bayesian information criterion: background, derivation, and applications. Wiley Interdiscip. Rev. Comput. Stat. 4, 199–203 (2012).

    Google Scholar 

  52. Wilks, S. S. The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Stat. 9, 60–62 (1938).

    Google Scholar 

  53. Ferrari, S. & Cribari-Neto, F. Beta regression for modelling rates and proportions. J. Appl. Stat. 31, 799–815 (2004).

    Google Scholar 

  54. Geissinger, E. A., Khoo, C. L., Richmond, I. C., Faulkner, S. J. & Schneider, D. C. A case for beta regression in the natural sciences. Ecosphere 13, e3940 (2022).

    Google Scholar 

  55. Proctor, J. L. & Eckhoff, P. A. Discovering dynamic patterns from infectious disease data using dynamic mode decomposition. Int. Health 7, 139–145 (2015).

    Google Scholar 

  56. Griffith, T. D. & Hubbard Jr, J. E. System identification methods for dynamic models of brain activity. Biomed. Signal Process. Control 68, 102765 (2021).

    Google Scholar 

  57. Brunton, B. W., Johnson, L. A., Ojemann, J. G. & Kutz, J. N. Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition. J. Neurosci. Methods 258, 1–15 (2016).

    Google Scholar 

  58. Demo, N., Tezzele, M. & Rozza, G. Pydmd: Python dynamic mode decomposition. J. Open Source Softw. 3, 530 (2018).

    Google Scholar 

  59. Ichinaga, S. M. et al. Pydmd: a Python package for robust dynamic mode decomposition. J. Mach. Learn. Res. 25, 1–9 (2024).

    Google Scholar 

  60. Vaart, A. W. v. d. Relative Efficiency of Tests. Cambridge Series in Statistical and Probabilistic Mathematics (Cambridge University Press, 1998).

Download references

Acknowledgements

K.T. acknowledges the PhD studentship support from Northeastern University.

Author information

Authors and Affiliations

  1. Network Science Institute, Northeastern University London, London, UK

    Kevin Teo, Naomi Arnold & István Z. Kiss

  2. School of Engineering, Mathematics & Physics, University of Kent, Canterbury, UK

    Andrew Hone

  3. AlphaOcean.ai Ltd, Brighton, East Sussex, UK

    Michael Coulon & Martin Ireland

  4. Machine Intelligence Group for the Betterment of Health and the Environment, Network Science Institute, Northeastern University, Boston, MA, USA

    Mauricio Santillana

  5. Department of Mathematics, Northeastern University, Boston, MA, USA

    István Z. Kiss

Authors
  1. Kevin Teo
    View author publications

    Search author on:PubMed Google Scholar

  2. Naomi Arnold
    View author publications

    Search author on:PubMed Google Scholar

  3. Andrew Hone
    View author publications

    Search author on:PubMed Google Scholar

  4. Michael Coulon
    View author publications

    Search author on:PubMed Google Scholar

  5. Martin Ireland
    View author publications

    Search author on:PubMed Google Scholar

  6. Mauricio Santillana
    View author publications

    Search author on:PubMed Google Scholar

  7. István Z. Kiss
    View author publications

    Search author on:PubMed Google Scholar

Contributions

K.T., N.A., M.C., M.I., and I.Z.K. designed research; K.T. and N.A. performed research; M.S. contributed analytic tools; K.T., N.A., A.H., M.C., M.S., and I.Z.K. analyzed data; K.T., N.A., A.H., M.C., M.S., and I.Z.K. wrote the paper.

Corresponding authors

Correspondence to Kevin Teo or István Z. Kiss.

Ethics declarations

Competing interests

K.T., N.A., A.H., and M.S. declare no competing interests. M.I. and M.C. are employees of a shipping-related company, AlphaOcean.ai. M.I., M.C., and I.Z.K. own shares in AlphaOcean.ai. The start-up company’s core product is building optimization models to assist shipowners with refueling strategies, which are not related to the research in this paper.

Peer review

Peer review information

Nature Communications thanks Shaobo Wang, Wen-Long Shang, and the other anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information (download PDF )

Reporting Summary (download PDF )

Transparent Peer Review file (download PDF )

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, 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 you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. 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-nc-nd/4.0/.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Teo, K., Arnold, N., Hone, A. et al. Unveiling individual and collective temporal patterns in the tanker shipping network. Nat Commun (2026). https://doi.org/10.1038/s41467-026-70013-1

Download citation

  • Received: 30 January 2025

  • Accepted: 16 February 2026

  • Published: 27 February 2026

  • DOI: https://doi.org/10.1038/s41467-026-70013-1

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Download PDF

Advertisement

Explore content

  • Research articles
  • Reviews & Analysis
  • News & Comment
  • Videos
  • Collections
  • Subjects
  • Follow us on Facebook
  • Follow us on X
  • Sign up for alerts
  • RSS feed

About the journal

  • Aims & Scope
  • Editors
  • Journal Information
  • Open Access Fees and Funding
  • Calls for Papers
  • Editorial Values Statement
  • Journal Metrics
  • Editors' Highlights
  • Contact
  • Editorial policies
  • Top Articles

Publish with us

  • For authors
  • For Reviewers
  • Language editing services
  • Open access funding
  • Submit manuscript

Search

Advanced search

Quick links

  • Explore articles by subject
  • Find a job
  • Guide to authors
  • Editorial policies

Nature Communications (Nat Commun)

ISSN 2041-1723 (online)

nature.com footer links

About Nature Portfolio

  • About us
  • Press releases
  • Press office
  • Contact us

Discover content

  • Journals A-Z
  • Articles by subject
  • protocols.io
  • Nature Index

Publishing policies

  • Nature portfolio policies
  • Open access

Author & Researcher services

  • Reprints & permissions
  • Research data
  • Language editing
  • Scientific editing
  • Nature Masterclasses
  • Research Solutions

Libraries & institutions

  • Librarian service & tools
  • Librarian portal
  • Open research
  • Recommend to library

Advertising & partnerships

  • Advertising
  • Partnerships & Services
  • Media kits
  • Branded content

Professional development

  • Nature Awards
  • Nature Careers
  • Nature Conferences

Regional websites

  • Nature Africa
  • Nature China
  • Nature India
  • Nature Japan
  • Nature Middle East
  • Privacy Policy
  • Use of cookies
  • Legal notice
  • Accessibility statement
  • Terms & Conditions
  • Your US state privacy rights
Springer Nature

© 2026 Springer Nature Limited

Nature Briefing AI and Robotics

Sign up for the Nature Briefing: AI and Robotics newsletter — what matters in AI and robotics research, free to your inbox weekly.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing: AI and Robotics