- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Stochastic spatiotemporal growth model reproducing the universal statistical laws of the gut microbiome

Rie Maskawa1,*, Hideki Takayasu1,2, Lena Takayasu3,2, Wataru Suda2, and Misako Takayasu1,†

  • *Contact author: masukawa.r.a34a@m.isct.ac.jp
  • †Contact author: takayasu@comp.isct.ac.jp
PDF

Phys. Rev. Research 7, 013269 – Published 13 March, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.013269

Abstract

Although gut microbiomes exhibit host-specific complexity, it is becoming clear that their dynamics are governed by common rules. In this paper, we empirically show that three key statistical laws—the fat-tailed species abundance distribution, the scaling law of fluctuations, and the tent-shaped log growth rate distribution—are quantitatively universal across humans and mice. We further propose a simple stochastic model that comprehensively reproduces these statistical laws. The model is based on a microscopic model representing the dynamics of each species at local sites on the gut wall, modeled as a random multiplicative process. By introducing coarse-grained time and spatial scales that reflect real-world sampling processes, the model provides a physical interpretation of the dynamic properties of the empirical data, including timescales and temporal stochasticity. Furthermore, incorporation of diffusion effects predicts a heterogeneous spatial distribution on the gut wall. This model serves as a fundamental framework for the unified analysis of the spatiotemporal patterns of the gut microbiome.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (52)

  1. A. Bashan, T. E. Gibson, J. Friedman, V. J. Carey, S. T. Weiss, E. L. Hohmann, and Y.-Y. Liu, Universality of human microbial dynamics, Nature (London) 534, 259 (2016).
  2. B. W. Ji, R. U. Sheth, P. D. Dixit, K. Tchourine, and D. Vitkup, Macroecological dynamics of gut microbiota, Nat. Microbiol. 5, 768 (2020).
  3. J. Grilli, Macroecological laws describe variation and diversity in microbial communities, Nat. Commun. 11, 4743 (2020).
  4. J. E. Goldford, N. Lu, D. Bajić, S. Estrela, M. Tikhonov, A. Sanchez-Gorostiaga, D. Segrè, P. Mehta, and A. Sanchez, Emergent simplicity in microbial community assembly, Science 361, 469 (2018).
  5. S. Pueyo, Diversity: Between neutrality and structure, Oikos 112, 392 (2006).
  6. B. J. McGill, R. S. Etienne, J. S. Gray, D. Alonso, M. J. Anderson, H. K. Benecha, M. Dornelas, B. J. Enquist, J. L. Green, F. He et al., Species abundance distributions: Moving beyond single prediction theories to integration within an ecological framework, Ecol. Lett. 10, 995 (2007).
  7. S. Wu, G. Wang, E. R. Angert, W. Wang, W. Li, and H. Zou, Composition, diversity, and origin of the bacterial community in grass carp intestine, PLoS ONE 7, e30440 (2012).
  8. E. Ser-Giacomi, L. Zinger, S. Malviya, C. De Vargas, E. Karsenti, C. Bowler, and S. De Monte, Ubiquitous abundance distribution of non-dominant plankton across the global ocean, Nat. Ecol. Evol. 2, 1243 (2018).
  9. V. M. Eguíluz, G. Salazar, J. Fernández-Gracia, J. K. Pearman, J. M. Gasol, S. G. Acinas, S. Sunagawa, X. Irigoien, and C. M. Duarte, Scaling of species distribution explains the vast potential marine prokaryote diversity, Sci. Rep. 9, 18710 (2019).
  10. L. Takayasu, W. Suda, E. Watanabe, S. Fukuda, K. Takanashi, H. Ohno, M. Takayasu, H. Takayasu, and M. Hattori, A 3-dimensional mathematical model of microbial proliferation that generates the characteristic cumulative relative abundance distributions in gut microbiomes, PLoS ONE 12, e0180863 (2017).
  11. L. Descheemaeker and S. de Buyl, Stochastic logistic models reproduce experimental time series of microbial communities, Elife 9, e55650 (2020).
  12. L. Descheemaeker, J. Grilli, and S. de Buyl, Heavy-tailed abundance distributions from stochastic Lotka-Volterra models, Phys. Rev. E 104, 034404 (2021).
  13. L. R. Taylor, Aggregation, variance and the mean, Nature (London) 189, 732 (1961).
  14. Z. S. Ma, Power law analysis of the human microbiome, Mol. Ecol. 24, 5428 (2015).
  15. R. M. Anderson, D. M. Gordon, M. J. Crawley, and M. P. Hassell, Variability in the abundance of animal and plant species, Nature (London) 296, 245 (1982).
  16. G. Titmus, Are animal populations really aggregated? Oikos 40, 64 (1983).
  17. M. J. Keeling, Simple stochastic models and their power-law type behaviour, Theor. Popul. Biol. 58, 21 (2000).
  18. A. M. Kilpatrick and A. R. Ives, Species interactions can explain Taylor's power law for ecological time series, Nature (London) 422, 65 (2003).
  19. W. S. Kendal, Taylor's ecological power law as a consequence of scale invariant exponential dispersion models, Ecol. Complex. 1, 193 (2004).
  20. S. Azaele, S. Pigolotti, J. R. Banavar, and A. Maritan, Dynamical evolution of ecosystems, Nature (London) 444, 926 (2006).
  21. J. Sun, S. P. Cornelius, J. Janssen, K. A. Gray, and A. E. Motter, Regularity underlies erratic population abundances in marine ecosystems, J. R. Soc. Interface 12, 20150235 (2015).
  22. T. H. Keitt and H. E. Stanley, Dynamics of North American breeding bird populations, Nature (London) 393, 257 (1998).
  23. M. H. R. Stanley, L. A. N. Amaral, S. V. Buldyrev, S. Havlin, H. Leschhorn, P. Maass, M. A. Salinger, and H. E. Stanley, Scaling behaviour in the growth of companies, Nature (London) 379, 804 (1996).
  24. A. B. George and J. O'Dwyer, Universal abundance fluctuations across microbial communities, tropical forests, and urban populations, Proc. Natl. Acad. Sci. USA 120, e2215832120 (2023).
  25. K. Faust, F. Bauchinger, B. Laroche, S. de Buyl, L. Lahti, A. D. Washburne, D. Gonze, and S. Widder, Signatures of ecological processes in microbial community time series, Microbiome 6, 120 (2018).
  26. X.-W. Wang and Y.-Y. Liu, Origins of scaling laws in microbial dynamics, Phys. Rev. Res. 5, 013004 (2023).
  27. S. P. Hubbell, The Unified Neutral Theory of Biodiversity and Biogeography (Princeton University Press, Princeton, NJ, 2001).
  28. C. M. Mutshinda, R. B. O'Hara, and I. P. Woiwod, Species abundance dynamics under neutral assumptions: A Bayesian approach to the controversy, Funct. Ecol. 22, 340 (2008).
  29. M. Kalyuzhny, R. Kadmon, and N. M. Shnerb, A neutral theory with environmental stochasticity explains static and dynamic properties of ecological communities, Ecol. Lett. 18, 572 (2015).
  30. P.-Y. Ho, B. H. Good, and K. C. Huang, Competition for fluctuating resources reproduces statistics of species abundance over time across wide-ranging microbiotas, elife 11, e75168 (2022).
  31. G. G. Lorenzana, A. Altieri, and G. Biroli, Interactions and migration rescuing ecological diversity, PRX Life 2, 013014 (2024).
  32. L. Takayasu, E. Watanabe, T. Umeyama, R. Kurokawa, R. Maskawa, S. Basu, Y. Ogata, Y. Kiguchi, H. Masuoka, M. Umezaki, H. Takayasu, M. Takayasu, M. Hattori, and W. Suda, High-resolution temporal profiling of the gut microbiome through the whole life of mice, https://doi.org/10.1101/2022.11.07.515511.
  33. L. A. David, A. C. Materna, J. Friedman, M. I. Campos-Baptista, M. C. Blackburn, A. Perrotta, S. E. Erdman, and E. J. Alm, Host lifestyle affects human microbiota on daily timescales, Genome Biol. 15, R89 (2014).
  34. J. G. Caporaso, C. L. Lauber, E. K. Costello, D. Berg-Lyons, A. Gonzalez, J. Stombaugh, D. Knights, P. Gajer, J. Ravel, N. Fierer, J. I. Gordon, and R. Knight, Moving pictures of the human microbiome, Genome Biol. 12, R50 (2011).
  35. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.013269 for additional tables and figures.
  36. P. J. den Boer, Dispersal power and survial, Carabids in a cultivated countryside. Misc. Papers LH Wageningen 14 (1977).
  37. A. Giometto, M. Formentin, A. Rinaldo, J. E. Cohen, and A. Maritan, Sample and population exponents of generalized Taylor's law, Proc. Natl. Acad. Sci. USA 112, 7755 (2015).
  38. J. J. Jiang, K. Yamada, H. Takayasu, and M. Takayasu, Scale-dependent power law properties in hashtag usage time series of Weibo, Sci. Rep. 13, 22298 (2023).
  39. H. Kesten, Random difference equations and Renewal theory for products of random matrices, Acta Math. 131, 207 (1973).
  40. H. Takayasu, A.-H. Sato, and M. Takayasu, Stable infinite variance fluctuations in randomly amplified Langevin systems, Phys. Rev. Lett. 79, 966 (1997).
  41. M. Takayasu, H. Watanabe, and H. Takayasu, Generalised central limit theorems for growth rate distribution of complex systems, J. Stat. Phys. 155, 47 (2014).
  42. W. Feller, An Introduction to Probability Theory and Its Applications, 2nd ed., Wiley Series in Probability and Statistics Vol. 2 (John Wiley & Sons, Nashville, TN, 1971).
  43. A. Amir, An elementary renormalization-group approach to the generalized central limit theorem and extreme value distributions, J. Stat. Mech. (2020) 013214.
  44. A. Sousa, H. Takayasu, D. Sornette, and M. Takayasu, Power-law distributions from Sigma-Pi structure of sums of random multiplicative processes, Entropy 19, 417 (2017).
  45. T. Mizuno, M. Katori, H. Takayasu, and M. Takayasu, Statistical laws in the income of japanese companies, in Empirical Science of Financial Fluctuations (Springer Japan, Tokyo, 2002), pp. 321–330.
  46. R. Sender, S. Fuchs, and R. Milo, Revised estimates for the number of human and bacteria cells in the body, PLoS Biol. 14, e1002533 (2016).
  47. Y. Y. Lee, A. Erdogan, and S. S. C. Rao, How to assess regional and whole gut transit time with wireless motility capsule, J. Neurogastroenterol. Motil. 20, 265 (2014).
  48. J. J. Lim, C. Diener, J. Wilson, J. J. Valenzuela, N. S. Baliga, and S. M. Gibbons, Growth phase estimation for abundant bacterial populations sampled longitudinally from human stool metagenomes, Nat. Commun. 14, 5682 (2023).
  49. Y. Yoshino, T. Galla, and K. Tokita, Rank abundance relations in evolutionary dynamics of random replicators, Phys. Rev. E 78, 031924 (2008).
  50. F. Roy, G. Biroli, G. Bunin, and C. Cammarota, Numerical implementation of dynamical mean field theory for disordered systems: Application to the Lotka–Volterra model of ecosystems, J. Phys. A: Math. Theor. 52, 484001 (2019).
  51. E. Mallmin, A. Traulsen, and S. De Monte, Chaotic turnover of rare and abundant species in a strongly interacting model community, Proc. Natl. Acad. Sci. USA 121, e2312822121 (2024).
  52. https://github.com/rie-maskawa/stochastic_spatiotemporal_growth_model.

Outline

Information

Phys. Rev. Research 7, 013269– Published 13 March, 2025
  • Received 26 August 2024
  • Accepted 17 February 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation