# Macroecological dynamics of gut microbiota

## Abstract

The gut microbiota is now widely recognized as a dynamic ecosystem that plays an important role in health and disease. Although current sequencing technologies make it possible to explore how relative abundances of host-associated bacteria change over time, the biological processes governing microbial dynamics remain poorly understood. Therefore, as in other ecological systems, it is important to identify quantitative relationships describing various aspects of gut microbiota dynamics. In the present study, we use multiple high-resolution time series data obtained from humans and mice to demonstrate that, despite their inherent complexity, gut microbiota dynamics can be characterized by several robust scaling relationships. Interestingly, the observed patterns are highly similar to those previously identified across diverse ecological communities and economic systems, including the temporal fluctuations of animal and plant populations and the performance of publicly traded companies. Specifically, we find power-law relationships describing short- and long-term changes in gut microbiota abundances, species residence and return times, and the correlation between the mean and the temporal variance of species abundances. The observed scaling laws are altered in mice receiving different diets and are affected by context-specific perturbations in humans. We use the macroecological relationships to reveal specific bacterial taxa, the dynamics of which are substantially perturbed by dietary and environmental changes. Overall, our results suggest that a quantitative macroecological framework will be important for characterizing and understanding the complex dynamics of diverse microbial communities.

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## Data availability

All sequencing data used in the present study can be downloaded from the European Nucleotide Archive (accession no. PRJEB6518 for humans A and B; see ref. 4 for metadata) and MG-RAST databases (4457768.34459735.3 (https://www.mg-rast.org/linkin.cgi?project=mgp93) for humans M3 and F4 (ref. 3); 4597621.34599933.3 (https://www.mg-rast.org/linkin.cgi?project=mgp11172) for mice8). These data were used to generate all figures in the main text, Supplementary information and Extended Data, with the exception of Extended Data Fig. 3, for which the figures were adapted from the original references16,17,22,23,24,63; figures from the original references were digitized and the resulting data points re-plotted.

## Code availability

All MATLAB scripts used to perform data analysis and generate figures are available on GitHub (https://github.com/brianwji/Macroecological-Relationships).

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## Acknowledgements

We thank G. Plata, H. Wang, E. Alm, J. Sonnenburg and E. Sonnenburg for very helpful scientific discussions. D.V. acknowledges funding from the National Institutes of Health (NIH; grant nos. R01GM079759, R35GM131884 and R01DK118044). B.W.J. was supported in part under a Ruth L. Kirschstein National Research Service Award Institutional Research Training grant (no. T32GM007367), and by the MD–PhD programme at Columbia University. R.U.S. was supported by a Fannie and John Hertz Foundation Fellowship and a National Science Foundation Graduate Research Fellowship (no. DGE-1644869).

## Author information

Authors

### Contributions

D.V. conceived the study, and oversaw the project, data analysis and interpretation. B.W.J., R.U.S. and K.T. performed the data analysis, interpretation and modelling. P.D.D. contributed to the data interpretation and analysis. All the authors wrote the manuscript.

### Corresponding author

Correspondence to Dennis Vitkup.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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

## Extended data

### Extended Data Fig. 1 Distribution of daily abundance changes for human and mouse gut microbiota.

Daily abundance changes for an OTU were calculated as the logarithm of the ratio of successive abundances, $$\mu = {\mathrm{log}}(X\left( {t + 1} \right)/X\left( t \right))$$, where X(t) is the relative abundance of the OTU on day t. The distributions of abundance changes for the analyzed bacterial communities closely follow the Laplace distribution: $$p\left( \mu \right) = (1/2b){\mathrm{exp}}( - |\mu |/b)$$ in a, humans (b = 0.83 ± 0.1, 0.67 ± 0.1, 0.71 ± 0.07, 0.73 ± 0.05, human A, B, M3, F4, respectively; mean ± s.d., across n = 6 equal subsamples of the data, see Methods) and b, mice (b = 0.82 ± 0.1, 0.67 ± 0.03, mice on the LFPP and HFHS diets, respectively; mean ± s.d., across n = 3 individual mice). c, Daily abundance changes of gut microbiota calculated at different taxonomic resolutions. Microbiota abundance changes were calculated as the logarithm of the ratio of successive abundances, $$\mu = {\mathrm{log}}(X\left( {t + 1} \right)/X\left( t \right))$$, where X(t) corresponds to the sum of abundances on day t for all OTUs within the same taxonomic group. OTUs were defined at the level of 97% sequence similarity of 16S rRNA. d, Distribution of normalized daily abundance changes in the human gut microbiota. To obtain the distribution, daily abundance changes for individual OTUs were first normalized by their corresponding standard deviations. The distributions of resulting normalized abundance changes were then combined across all OTUs and across humans A, B, M3, and F4. Barplot shows the Akaike Information Criterion (AIC) calculated based on the maximum likelihood estimate (MLE) fits to the data using the Gaussian and Laplace distributions. The bars show the mean AIC calculated across 10,000 bootstrap samples of the abundance changes data, errors represent the standard deviation, and the triple asterisk *** represents p<10-4; across the 104 bootstrap samples, the AIC were always smaller for the Laplace distributions, indicating better fits to the data. In all panels, solid lines show MLE fits to the data.

### Extended Data Fig. 2 Compositional effects on the distribution of daily abundance changes for bacterial communities with various diversities.

Simulations of bacterial community dynamics (with N=65 OTUs) were performed using the Ornstein-Uhlenbeck process. Black dots represent the resulting distributions of daily absolute abundance changes, while hollow dots represent the distributions of daily relative abundance changes. In panels (a-c), steady-state OTU abundances in each community were sampled from a power law, where the power law exponent was selected to generate bacterial communities with different diversities; community diversities were quantified by the effective number of species (ENS = eH, where H is the Shannon diversity). In (d), the simulated steady-state OTU abundances were equal to those in the real data. In all panels, solid lines represent Gaussian distribution fits to the simulated data.

### Extended Data Fig. 3 Growth rate distributions in diverse ecological communities and economic systems.

a, Annual growth rate distributions of North American bird populations16, marine species abundances22, publicly-traded company sales23 and university R&D expenditures24. Figures were adapted from their original text. Distributions of company sales and R&D expenditures were re-plotted for companies with initial dollar sales of more than one billion dollars and universities with large R&D expenditures (see refs. 23,24 for details). Lines are provided for visual purposes only. b, Residence time distributions of species from diverse ecosystems. Figures were adapted from ref. 63, with original data describing North American breeding bird species, estuarine fish species, and plant species collected from both prairie and forest ecosystems. Lines are provided for visual purposes only. c, Long-term drift of bird species abundances16 and North Atlantic fish stock abundances17. Figures were adapted from their original text.

### Extended Data Fig. 4 Variability in daily abundance changes for human gut microbiota.

a-d, Black data points show the standard deviation of daily OTU abundance changes as a function of average daily OTU abundances $$x_m = \frac{1}{2}\left[ {\log \left( {X_k(t + 1)} \right) + {\mathrm{log}}(X_k(t))} \right]$$ in humans. Gray data points were generated by simulating time series data in which OTU abundance changes originated exclusively from Poissonian sampling noise. The simulations were performed by sampling sequencing read counts from the underlying OTU abundance distributions empirically observed in humans A, B, M3, and F4 (Methods). Random zero counts were added for each OTU to match the frequency of its zero counts in the real data. Sequencing reads were sampled to the same depths as in the real data. The simulations demonstrate that the observed decrease in the variability of OTU abundance changes as a function of the average daily OTU abundances is not a result of simple Poissonian sampling effects.

### Extended Data Fig. 5 Standard deviations of daily abundance changes decrease with increasing average daily abundances for individual OTUs.

Standard deviations of changes in daily OTU abundance as a function of the average OTU abundance; the standard deviations were calculated, for each OTU separately, across bins of various daily OTU abundances. The abundance bins were selected to have an equal number of time points in each bin. Panel a shows the relationships for each OTU in Human A. Dotted lines represent regression fits to the data for each OTU. Panels are sorted according to the p-value of the regression fits, and the slopes of the fits are shown in the top right corner of each panel (n=7). The 48 out of the total of 65 OTUs shown here are significant, based on the FDR cutoff of 10% (the Benjamini-Hochberg method). b, Distribution of slopes of the linear regression fits across 154 OTUs and the four human datasets. Only the OTUs with regression p-values significant based on the FDR cutoff of 10% are shown.

### Extended Data Fig. 6 Long-term drift of gut microbiota abundances in humans and mice.

a,b, Mean-squared displacements of log-relative OTU abundances 2t)> as a function of time Δt. Dashed lines represent regression fits to the data using the equation of abnormal diffusion 2t)>Δt2H, where H is the Hurst exponent characterizing the diffusion process. The diffusion Hurst exponents are H = 0.07 ± 0.03, 0.10 ± 0.04, 0.08 ± 0.02, 0.1 ± 0.07 for humans A, B, M3, and F4, respectively, and H = 0.08 ± 0.02, 0.19 ± 0.02 for the LFPP and HFHS mice (mean ± s.d., n = 6 equal subsamples of the data for humans and n = 3 animals for mice, see Methods).

### Extended Data Fig. 7 Long-term drift of individual OTU abundances.

a, Mean-squared displacements of log-relative abundance for individual OTUs <δ2t)> as a function of time Δt. Dashed lines represent regression fits to data, using the abnormal diffusion equation <δ2t)>Δt2H, where H is the Hurst exponent characterizing the diffusion process. Panels correspond to individual OTUs from human A. The Hurst exponents were determined using least squared regression fits to n = 100 data points for each OTU (see Methods). b, Distributions of Hurst exponents across individual OTUs in humans A, B, M3, F4. The Hurst exponents describing the abundance drift of the entire bacterial communites in each human are indicated by dashed lines.

### Extended Data Fig. 8 Distributions of residence and return times of gut microbiota in humans and mice.

Distributions of residence and return times for a, human and b, mouse gut microbiota. Solid lines represent fits to the data using power laws with exponential tails of the form p(t)t−αeλt. In humans, the power law exponents are αres = 2.3 ± 0.04, 2.2 ± 0.05, 2.2 ± 0.07, and 2.14 ± 0.08 for the residence times and αret = 1.1 ± 0.02, 0.15 ± 0.03, 1.2 ± 0.05, and 1.09 ± 0.07 for the return times (A, B, M3, F4 respectively; mean ± s.d., n = 6 equal subsamples of the data, see Methods). In mice, αres = 2.2 ± 0.04, 2.2 ± 0.03 and αret = 0.72 ± 0.03,0.67 ± 0.06 for the LFPP and HFHS diet groups, respectively (mean ± s.d., across n = 3 mice).

### Extended Data Fig. 9 Taylor’s power law relationships in human and mouse gut microbiota.

Temporal abundance variances $$\sigma _X^2$$ as a function of average species abundances X in (a) human and (b) mouse gut microbiota. Dashed lines represent least-squares fits to the data using Taylor’s power law of the form $$\sigma _X^2 \propto X^\beta$$. Each dot represents the mean and temporal abundance variance for a single OTU. a, The power law exponents in humans are β = 1.66 ± 0.09, 1.60 ± 0.08, 1.71 ± 0.07, 1.71 ± 0.07 for humans A, B, M3, and F4, respectively (mean ± s.d., n = 6 equal subsamples of the data, see Methods). Colored dots denote specific OTUs whose abundances on any day exceeded the average abundance over all other days by more than 25-fold (Supplementary Table 1). b, The power law exponents in mice are β = 1.49 ± 0.02 and 1.86 ± 0.07 for the LFPP and HFHS diets, respectively (mean ± s.d., across n = 3 mice). c, The temporal profile of relative abundances of spiking OTUs identified in (a) for the two humans (A and B), whose lifestyles were documented over the time series. Major events affecting the gut microbiota of these individuals included travel of individual A to a developing country near day 100, and an enteric infection in individual B near day 150.

### Extended Data Fig. 10 Effects of the compositional nature of microbiota data on Taylor’s law exponents.

To investigate possible effects of the compositional nature of microbiota data on Taylor’s law exponents, simulations were carried out in absolute abundances using a model identical to the one used by Kilpatrick and Ives35; in the model, Taylor’s law exponents of 2 were expected. After converting absolute bacterial abundances, obtained in the simulations, to relative abundances, Taylor’s law exponents were recalculated to assess the effects of data compositionality. a, Steady-state OTU abundances for each simulated community were drawn from a power law, with the power law exponents selected to generate a range of community diversities; the community diversities were quantified by the effective number of species (ENS = eH, where H is the Shannon diversity). Across ENS values (x axis), the resulting Taylor’s exponents (y axis), calculated using absolute and relative abundances, are shown by solid and dashed black lines, respectively. Error bars represent the standard deviation across n = 20 independent simulations. The colored semi-dotted lines represent the Taylor’s exponents observed in real data in the four human datasets analyzed in our study. b, A representative simulation in which steady-state OTU abundances were equal to the mean abundances in Human A.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1 and 2 and Tables 1 and 2.

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Ji, B.W., Sheth, R.U., Dixit, P.D. et al. Macroecological dynamics of gut microbiota. Nat Microbiol 5, 768–775 (2020). https://doi.org/10.1038/s41564-020-0685-1

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