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Probabilistic Multivariate Early Warning Signals

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Computational Methods in Systems Biology (CMSB 2022)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 13447))

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Abstract

A broad range of natural and social systems from human microbiome to financial markets can go through critical transitions, where the system suddenly collapses to another stable configuration. Anticipating such transition early and accurately can facilitate controlled system manipulation and mitigation of undesired outcomes. Generic data-driven indicators, such as autocorrelation and variance, have been shown to increase in the vicinity of an approaching tipping point, and statistical early warning signals have been reported across a range of systems. In practice, obtaining reliable predictions has proven to challenging, as the available methods deal with simplified one-dimensional representations of complex systems, and rely on the availability of large amounts of data. Here, we demonstrate that a probabilistic data aggregation strategy can provide new ways to improve early warning detection by more efficiently utilizing the available information from multivariate time series. In particular, we consider a probabilistic variant of a vector autoregression model as a novel early warning indicator and argue that it has certain advantages in model regularization, treatment of uncertainties, and parameter interpretation. We evaluate the performance against alternatives in a simulation benchmark and show improved sensitivity in warning signal detection in a common ecological model encompassing multiple interacting species.

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Code Availability.

R source code for the experiments is available at 10.5281/zenodo.6472720.

References

  1. Arani, B.M.S., Carpenter, S.R., Lahti, L., van Nes, E.H., Scheffer, M.: Exit time as a measure of ecological resilience. Science 372(6547), eaay4895 (2021). https://doi.org/10.1126/science.aay4895

  2. Arkilanian, A.A., Clements, C.F., Ozgul, A., Baruah, G.: Effect of time series length and resolution on abundance- and trait-based early warning signals of population declines. Ecology 101(7), e03040 (2020). https://doi.org/10.1002/ecy.3040

  3. Auger-Méthé, M., et al.: State-space models’ dirty little secrets: even simple linear Gaussian models can have estimation problems. Sci. Rep. 6(1), 26677 (2016). https://doi.org/10.1038/srep26677

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  4. Belizário, J.E., Faintuch, J.: Microbiome and gut dysbiosis. In: Silvestre, R., Torrado, E. (eds.) Metabolic Interaction in Infection. ES, vol. 109, pp. 459–476. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-74932-7_13

    Chapter  Google Scholar 

  5. Bury, T.M., et al.: Deep learning for early warning signals of tipping points. Proc. Natl. Acad. Sci. 118(39), e2106140118 (2021). https://doi.org/10.1073/pnas.2106140118

  6. Chen, L., Liu, R., Liu, Z.P., Li, M., Aihara, K.: Detecting early-warning signals for sudden deterioration of complex diseases by dynamical network biomarkers. Sci. Rep. 2, 342 (2012). https://doi.org/10.1038/srep00342

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Chen, S., O’Dea, E., Drake, J., Epureanu, B.: Eigenvalues of the covariance matrix as early warning signals for critical transitions in ecological systems. Sci. Rep. 9, 2572 (2019). https://doi.org/10.1038/s41598-019-38961-5

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  8. Clements, C.F., Drake, J.M., Griffiths, J.I., Ozgul, A.: Factors influencing the detectability of early warning signals of population collapse. Am. Nat. 186(1), 50–58 (2015). https://doi.org/10.1086/681573

    Article  PubMed  Google Scholar 

  9. Clements, C.F., Ozgul, A.: Indicators of transitions in biological systems. Ecol. Lett. 21(6), 905–919 (2018). https://doi.org/10.1111/ele.12948

    Article  PubMed  Google Scholar 

  10. Dakos, V.: Identifying best-indicator species for abrupt transitions in multispecies communities. Ecol. Ind. 94, 494–502 (2018). https://doi.org/10.1016/j.ecolind.2017.10.024

    Article  Google Scholar 

  11. Dakos, V., Bascompte, J.: Critical slowing down as early warning for the onset of collapse in mutualistic communities. Proc. Natl. Acad. Sci. 111(49), 17546–17551 (2014). https://doi.org/10.1073/pnas.1406326111

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Dakos, V., et al.: Methods for detecting early warnings of critical transitions in time series illustrated using simulated ecological data. PLoS ONE 7(7), 1–20 (2012). https://doi.org/10.1371/journal.pone.0041010

    Article  CAS  Google Scholar 

  13. Dakos, V., van Nes, E.H., D’Odorico, P., Scheffer, M.: Robustness of variance and autocorrelation as indicators of critical slowing down. Ecology 93(2), 264–271 (2012). https://doi.org/10.1890/11-0889.1

    Article  PubMed  Google Scholar 

  14. Gelman, A., Carlin, J., Stern, H., Dunson, D., Vehtari, A., Rubin, D.: Bayesian Data Analysis, 3rd edn. Chapman and Hall/CRC (2013). https://doi.org/10.1201/b16018

  15. Gelman, A., Rubin, D.B.: Inference from iterative simulation using multiple sequences. Stat. Sci. 7(4), 457–472 (1992). https://doi.org/10.1214/ss/1177011136

    Article  Google Scholar 

  16. Hastings, A., Wysham, D.B.: Regime shifts in ecological systems can occur with no warning. Ecol. Lett. 13(4), 464–472 (2010). https://doi.org/10.1111/j.1461-0248.2010.01439.x

    Article  PubMed  Google Scholar 

  17. Held, H., Kleinen, T.: Detection of climate system bifurcations by degenerate fingerprinting. Geophys. Res. Lett. 312, L23207 (2004). https://doi.org/10.1029/2004GL020972

  18. Ives, A.R., Dakos, V.: Detecting dynamical changes in nonlinear time series using locally linear state-space models. Ecosphere 3(6), 58 (2012). https://doi.org/10.1890/ES11-00347.1

  19. Khalighi, M., Sommeria-Klein, G., Faust, K., Gonze, D., Lahti, L.: Quantifying the impact of ecological memory on the dynamics of interacting communities. PLOS Comput. Biol. (2022)

    Google Scholar 

  20. Kuss, M., Rasmussen, C.E.: Assessing approximate inference for binary Gaussian process classification. J. Mach. Learn. Res. 6(Oct), 1679–1704 (2005)

    Google Scholar 

  21. Lahti, L., Salojärvi, J., Salonen, A., Scheffer, M., de Vos, W.M.: Tipping elements in the human intestinal ecosystem. Nat. Commun. 5, 4344 (2014). https://doi.org/10.1038/ncomms5344

    Article  CAS  PubMed  Google Scholar 

  22. Laitinen, V., Dakos, V., Lahti, L.: Probabilistic early warning signals. Ecol. Evol. 11(20), 14101–14114 (2021). https://doi.org/10.1002/ece3.8123

    Article  PubMed  PubMed Central  Google Scholar 

  23. Lenton, T.M.: Tipping positive change. Philos. Trans. R. Soc. B: Biol. Sci. 375(1794), 20190123 (2020). https://doi.org/10.1098/rstb.2019.0123

  24. Lenton, T.M., et al.: Tipping elements in the earth’s climate system. Proc. Natl. Acad. Sci. 105(6), 1786–1793 (2008). https://doi.org/10.1073/pnas.0705414105

    Article  PubMed  PubMed Central  Google Scholar 

  25. Lever, J.J., Nes, E., Scheffer, M., Bascompte, J.: The sudden collapse of pollinator communities. Ecol. Lett. 17, 350–359 (2014). https://doi.org/10.1111/ele.12236

    Article  PubMed  Google Scholar 

  26. Liu, R., Chen, P., Aihara, K., Chen, L.: Identifying early-warning signals of critical transitions with strong noise by dynamical network markers. Sci. Rep. 5(1), 17501 (2015). https://doi.org/10.1038/srep17501

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  27. Proverbio, D., Kemp, F., Magni, S., Gonçalves, J.: Performance of early warning signals for disease re-emergence: a case study on Covid-19 data. PLoS Comput. Biol. 18(3), 1–22 (2022). https://doi.org/10.1371/journal.pcbi.1009958

    Article  CAS  Google Scholar 

  28. Quax, R., Apolloni, A., Sloot, P.: The diminishing role of hubs in dynamical processes on complex networks. J. R. Soc. Interface 10, 20130568 (2013)

    Google Scholar 

  29. Quax, R., Kandhai, D., Sloot, P.M.A.: Information dissipation as an early-warning signal for the Lehman brothers collapse in financial time series. Sci. Rep. 3(1), 1898 (2013). https://doi.org/10.1038/srep01898

    Article  PubMed  PubMed Central  Google Scholar 

  30. Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. The MIT Press (2006). https://doi.org/10.7551/mitpress/3206.001.0001

  31. Salosensaari, A., et al.: Taxonomic signatures of cause-specific mortality risk in human gut microbiome. Nat. Commun. 12, 2671 (2021). https://doi.org/10.1038/s41467-021-22962-y

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Scheffer, M.: Critical Transitions in Nature and Society. Princeton University Press, New Jersey (2009). https://doi.org/10.1515/9781400833276

  33. Scheffer, M., et al.: Early-warning signals for critical transitions. Nature 461(7260), 53–59 (2009)

    Article  CAS  Google Scholar 

  34. Scheffer, M., Carpenter, S., Foley, J.A., Folke, C., Walker, B.: Catastrophic shifts in ecosystems. Nature 413(6856), 591–596 (2001). https://doi.org/10.1038/35098000

    Article  CAS  PubMed  Google Scholar 

  35. Southall, E., Brett, T.S., Tildesley, M.J., Dyson, L.: Early warning signals of infectious disease transitions: a review. J. R. Soc. Interface 18(182), 20210555 (2021). https://doi.org/10.1098/rsif.2021.0555

  36. Stan Development Team: RStan: the R interface to Stan (2020). R package version 2.21.2

    Google Scholar 

  37. Stein, M.L.: Interpolation of Spatial Data: Some Theory for Kriging. Springer Series in Statistics, Springer, New York (1999). https://doi.org/10.1007/978-1-4612-1494-6

    Book  Google Scholar 

  38. Tipping, M.E., Bishop, C.M.: Probabilistic principal component analysis. J. R. Stat. Soc.: Ser. B (Stat. Methodol.) 61(3), 611–622 (1999). https://doi.org/10.1111/1467-9868.00196

    Article  Google Scholar 

  39. Weinans, E., et al.: Finding the direction of lowest resilience in multivariate complex systems. J. R. Soc. Interface 16, 20190629 (2019). https://doi.org/10.1098/rsif.2019.0629

  40. Weinans, E., Quax, R., van Nes, E.H., van de Leemput, I.A.: Evaluating the performance of multivariate indicators of resilience loss. Sci. Rep. 11(1), 9148 (2021). https://doi.org/10.1038/s41598-021-87839-y

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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Acknowledgements

This work has been supported by Academy of Finland (decisions 295741, 330887) and by Turku university graduate school (UTUGS). The authors wish to acknowledge CSC - IT Center for Science, Finland, for computational resources. The authors declare no conflict of interest.

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Authors and Affiliations

  1. Department of Computing, University of Turku, Turku, Finland

    Ville Laitinen & Leo Lahti

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  1. Ville Laitinen
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  2. Leo Lahti
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Correspondence to Ville Laitinen .

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Editors and Affiliations

  1. University of Turku, Turku, Finland

    Ion Petre

  2. University of Bucharest, Bucharest, Romania

    Andrei Păun

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Laitinen, V., Lahti, L. (2022). Probabilistic Multivariate Early Warning Signals. In: Petre, I., Păun, A. (eds) Computational Methods in Systems Biology. CMSB 2022. Lecture Notes in Computer Science(), vol 13447. Springer, Cham. https://doi.org/10.1007/978-3-031-15034-0_13

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  • DOI: https://doi.org/10.1007/978-3-031-15034-0_13

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