Universality of human microbial dynamics

Abstract

Human-associated microbial communities have a crucial role in determining our health and well-being, and this has led to the continuing development of microbiome-based therapies such as faecal microbiota transplantation. These microbial communities are very complex, dynamic and highly personalized ecosystems, exhibiting a high degree of inter-individual variability in both species assemblages and abundance profiles. It is not known whether the underlying ecological dynamics of these communities, which can be parameterized by growth rates, and intra- and inter-species interactions in population dynamics models, are largely host-independent (that is, universal) or host-specific. If the inter-individual variability reflects host-specific dynamics due to differences in host lifestyle, physiology or genetics, then generic microbiome manipulations may have unintended consequences, rendering them ineffective or even detrimental. Alternatively, microbial ecosystems of different subjects may exhibit universal dynamics, with the inter-individual variability mainly originating from differences in the sets of colonizing species. Here we develop a new computational method to characterize human microbial dynamics. By applying this method to cross-sectional data from two large-scale metagenomic studies--the Human Microbiome Project and the Student Microbiome Project--we show that gut and mouth microbiomes display pronounced universal dynamics, whereas communities associated with certain skin sites are probably shaped by differences in the host environment. Notably, the universality of gut microbial dynamics is not observed in subjects with recurrent Clostridium difficile infection but is observed in the same set of subjects after faecal microbiota transplantation. These results fundamentally improve our understanding of the processes that shape human microbial ecosystems, and pave the way to designing general microbiome-based therapies.

Extended Data Figure 1. Displacement of normalized N-dimensional random walks

a, Trajectory of a 2-dimensional random-walk represents the absolute abundance of two species x_1, x₂. The initial state is marked by a red circle and the first 100 steps are shown. The solid black line is the 1-dimensional simplex upon which the locations are projected to obtain the relative abundances x̃₁, x̃₂. The dotted lines starting at the origin represent the projection process: all the points in a dotted line have the same relative abundances and they are all projected to the intersection of the dotted line and the simplex (e.g. the solid red and green circles are projected to the red and green open circles, respectively). We define a new coordinate z̃(t) ≡ x̃₂(t)− x̃₁(t) for the location of normalized relative abundance on the simplex. The displacement of the normalized random walk after t steps is then z̃(t) − z̃(0), where z̃(0) is the projected location of the initial state (see, as an example, the distance between the green and the red open circles in a). b, Distributions of displacement of an ensemble of 1,000 random walks after t steps (t=1, 5, 10, 100, 1000). For small t, the displacement distributions depend on t, while for large t (t=100, 1000) the distributions are the same. c, Symbols represent the average displacement of 1,000 N-dimensional normalized random walks (here we set N=50), measured as D_rJSD, and the error-bars represent the standard deviation. Each random walk is forced to stay on the positive orthant, i.e. if $x_i^{(t)}<0$ we set $x_i^{(t)}=0$ . The D_rJSD was calculated using all N coordinates, setting $x_i^{(t)}={10}^{-4}$ as a pseudo count for $x_i^{(t)}=0$. Where t is small, the distance grows with increasing t, however, the distance saturates for large t. The dashed red and green lines represent the average distance between two random locations (green) and between the final locations (x^(t=1,000)) of the random walks (red).

Extended Data Figure 2. Detection of group dynamics using ordination technique

In each raw, 500 synthetic samples were generated. Samples in the same group were taken from the steady states of the same GLV model of 100 species. The initial species assemblages were determined in two scenarios: at random (columns a–d) or based on the group (e–h). In the latter scenario, in each group the species were first randomly ordered and then in each of the samples the first f species were selected and the other been removed (f is randomly chosen from a uniform distribution 𝕆(20,100)). In columns a and e, a standard ordination technique, i.e. the principal coordinate analysis (PCoA), was applied. All 500 samples were shown in the plane of the first two principal coordinates (using rJSD as the distance metric) and coloured according to their group. In columns b and f only the samples that have high overlap (>0.95) with at least one other sample were shown. Columns c and g show the dissimilarity distributions P(rJSD) between the high-overlap sample pairs. Columns d and h show the DOCs. The ordination technique successfully detects the existence of group dynamics (especially when the number of groups is small). We anticipate that the group dynamics can also be detected by classical clustering analysis. In the scenario of random collections, the PCoA of high-overlap samples, i.e. samples that have high overlap (>0.95) with at least one other sample, is doing better than the PCoA of all samples to detect group dynamics, especially for a small number (2~10) of groups. Moreover, for a small number of groups, the dissimilarity distributions P(rJSD) can distinguish between the two scenarios of initial assemblage selection: random or group-based. The ordination technique cannot distinguish between the cases of 500 groups (“individual dynamics”) and single group (“Universal dynamics”). Those cases can be distinguished by the DOC analysis.

Extended Data Figure 3. Detecting universality in population dynamics models

Synthetic microbial samples were calculated as steady states of Generalized Lotka-Volterra (GLV) models (see Methods section). The GLV models are generated as “cohorts” (100 models in each cohort) with different levels of i) inter-species interaction strength; and ii) universality, tuned by the parameters σ̃ and δ̃, respectively (see Methods section). In each of the 100 models, a random fraction f of the species (f ~ 𝕆(0,0.8)) was initially removed, and the remaining species were initiated with random abundance (x ~ 𝕆(0,1)). The Dissimilarity-Overlap points of sample pairs in each cohort and of the corresponding randomized samples are shown in light blue and yellow respectively. The solid curves represent the DOCs calculated using the robust LOWESS method. The DOC of “cohorts” generated by GLV models without inter-species interactions (a1, a4, a7) is flat even in the high-overlap region. This is because, without inter-species interactions, for any sample pair the presence or absence of unique (i.e. non-shared) species has no effect on the shared ones. A flat DOC is also observed in the case of individual dynamics (a7, a8, a9), where a higher overlap between sample pairs does not lead to more similar abundance profiles. However, in the case of universal dynamics with strong inter-species interactions (e.g. a3), the DOC displays a clear negative slope in the high-overlap region.

Extended Data Figure 4. DOC analysis of gut microbiome samples from longitudinal studies

In plots a–d, sample pairs are selected from four different subjects, with number of samples: M_a = 299, M_b = 180, M_c = 336, M_d = 131, respectively. The mean DOCs (calculated from 100 bootstrap realizations using the robust LOWESS method) of each subject and the corresponding randomized samples are shown in dark blue and yellow, respectively. The shaded area indicates the range of the 94% confidence intervals. The overlap distributions are shown in red. For all the four subjects, a clear negative slope of the DOC is observed at the high-overlap region, indicating a largely time-invariant or universal dynamics for each subject throughout the measurement period. This is in marked contrast with the flat DOC of the null model (See SISec. 1.3). The secondary peak of lower overlap samples in b (overlap ≈ 0.8) is of sample pairs from two different periods, before and after a Salmonella infection, which represent two distinct microbial steady states and thus exhibit a flat DOC. This is consistent with our assumption of time-invariant microbial dynamics for a given healthy individual.

Extended Data Figure 5. DOC analysis of gut microbiome samples is consistent across different studies and different dissimilarity measures

For two microbiome samples, the dissimilarity of their abundance profiles over shared species can be evaluated by different measures. Weighted measures, such as root Jensen-Shannon Divergence (rJSD), Bray-Curtis (BC) dissimilarity and Yue-Clayton (YC) dissimilarity should be applied to the renormalized abundance profiles, to ensure mathematical independency between the overlap and the dissimilarity measures. Rank-based dissimilarity measures, e.g. negative Spearman Correlation (nSC), can be directly applied without renormalization. We used the four dissimilarity measures (rJSD, BC, YC and nSC) to calculate the DOC (using robust LOWESS)of gut microbiome samples from two studies: the HMP and SMP. In all cases, we observed a pronounced negative slope in the DOC (dark-blue curve) of real sample pairs (light-blue points) and a flat DOC (orange curve) for the pairs of randomized samples (yellow points).

Extended Data Figure 6

a, The fraction of data for which a negative slope is observed in Fig. 3. Note that for overlap values close to zero (e.g., Fig. 5 d, f1–4, g1–3) a positive slope occur as the artifact of dissimilarity between relative abundance profiles with small number of species (See SI Sec. 1.1.3). For gut and mouth, a negative slope of DOC is observed in the two data sets for a broad range of overlap, indicating a significant universality of microbial dynamics in those habitats. In contrast, the negative slope of DOC in the hand’s skin microbiome is observed only for small part of the sample pairs. b, Box plot of the slope of DOC calculated from 200 bootstrap realizations. The slope is calculated by fitting a linear mixed-effects model for data points with overlap larger than the median. The one-tailed p-value is then calculated as the fraction of bootstrap realizations with a non-negative slope. The Benjamini-Hochberg procedure was used to calculate the false discovery rate (FDR) for multiple comparisons. The null hypothesis of non-negative slope is rejected for all body sites (p < 10⁻²) except four skin sites: forehead (p = 0.099), palm (p = 0.377) in the SMP study and left/right antecubital fossa in the HMP study (p = 0.099 and p = 0.495).

Extended Data Figure 7. Effects of various host factors on the DOC analysis

a, The effect of body mass index (BMI) on the DOC analysis. a1, DOC analysis of all gut microbiome sample pairs among 190 subjects from the HMP study. Red points represent samples pairs associated with at least one obese subject (with BMI > 30). a2, Same as shown in a, but 13 obese subjects with BMI > 30 were excluded. a3, blue points represent the gut microbiome samples’ overlap and ΔBMI. The red curve is the average (error bars represent the s.e.m.). a4, dissimilarity versus ΔBMI. a5, distribution of ΔBMI values, divided to four groups of equal number of pairs. a6–a9, DOC analysis of the sample pairs in each group. b, The effect of diet on the DOC analysis. b1, Diet difference (ΔDiet)between two subjects is defined as the Euclidean distance between their associated diet scores in the two leading principal components PC₁ and PC₂. In total there are M = 97 healthy subjects in the Cross-sectional Study of Diet and Stool Microbiome Composition (COMBO) study. b2, overlap versus ΔDiet. Blue points represent the overlap and ΔDiet of all gut microbiome pairs among the 97 subjects from the COMBO study. The red curve is the average (error bars represent the s.e.m.). b3, dissimilarity versus ΔDiet. b4, distribution of ΔDiet values, divided to four groups of equal number of pairs. b5–b8, DOC analysis of the pairs in each group. c, The effect of age on the DOC analysis. c1, overlap versus ΔDiet. Blue points represent the overlap and ΔAge of all gut microbiome samples pairs between the 190 subjects from the HMP study. The red curve is the average (error bars represent the s.e.m.). c2, dissimilarity versus ΔAge. c3, distribution of ΔAge values, divided to four groups of equal number of pairs. c4–c7, DOC analysis of the pairs in each group. d, The effect of stool consistency on the DOC analysis. d1, DOC analysis of all sample pairs. In this dataset the subjects have BSS values between 1 and 6. The points (sample pairs) associated with subjects with BSS = 6 (at least one subject has BSS = 6)are colored in red. The black line is the DOC. d2, DOC analysis of all subjects with BSS < 6. d3–d4, among all subjects with 1 ≤ BSS ≤ 5, the overlap and the dissimilarity are independent on ΔBSS. d5, Distribution of ΔBSS values for the 46 subjects with 1 ≤ BSS ≤ 5. d6, DOC analysis of the pairs with similar BSS values, 0 ≤ ΔBSS ≤ 1 and (d7) pairs with more different BSS values, 2 ≤ ΔBSS ≤ 4. In both cases, a clear negative slope of the DOC isobserved. e, The effect of race on the DOC analysis. e1, All subjects (M = 190), e2, White subjects (M = 153) and e3, Asian (M = 25). Note that in the HMP study, stool samples were collected from 153 White, 10 Black, 25 Asian, and 2 subjects with other races.

Extended Data Figure 8. DOC analysis under special conditions

a, The effect of strongly interacting species. A comparison of two GLV models of 100 species with random inter-species interactions. The system parameters were fixed for all the simulated samples (M = 100), representing maximal universality. In a1, all species have the same characteristic interaction strength, while in a2, the inter-species interactions of one species are significantly stronger than all other species, representing a strongly interacting species. The presence/absence of the strongly interacting species dramatically affect (either directly or indirectly) the abundance profile of many other species leading to a pronounced secondary cloud of points in the Dissimilarity-Overlap plane (a4). The effect is the most pronounced in the region of high overlap (top 5%) pairs, and can be detected by looking at their dissimilarity distributions (a5–a6). b, DOC behaves the same for samples with uniform or skewed abundance distribution. b1, b2, Samples were generated from the steady states of the GLV model with largely uniform abundance distribution (determined mainly by the species growth rates). In the case of interacting species (b1), a negative slope of the DOC is observed but not in the case of noninteracting species (b2). b3, Real samples from the gut (from the HMP study, genus level) exhibit a high level of alpha-diversity and a very skewed abundance distribution. A negative slope of the DOC in the high-overlap region is observed. b4, The randomized samples preserve the abundance distribution of the real samples but the effect of inter-species interactions is removed, leading to a flat DOC. c, Effect of core species and non-interacting periphery species. c1, Samples were generated as steady states of the GLV model with N = 100 species. The parameters of the GLV model were fixed for all the samples, representing maximal universality. The initial species assemblages were chosen as follows: 30 species were present in all the samples, representing a set of “core species”, and the other 70 “peripheral” species were present with lower probability (mean 0.18, min 0.12, and max 0.24). c2, Presence probability of real gut microbial samples, from the HMP at the genus level. Only one genus (Bacterioides) is present in all the samples. c3, Species presence probability in a GLV model where all species are present with average probability 0.6. c4, The effect of the interactions of the peripheral species. In the GLV model, the inter-species interactions among the core species (“core-core”) has a characteristic strength σ_core = 0.15, and both the “periphery-periphery” and the “periphery-core” interactions have a characteristic strength σ_p. When σ_p = 0, i.e. the peripheral species do not interact with the core species, the DOC is flat. When σ_p > 0, the DOC has a negative slope. c5–c6, In the case of real gut microbiome samples as well as the GLV model without core species, the DOC has a negative slope in the high-overlap region. d, The effect of sequencing depth on the DOC analysis. d1, Richness (number of present OTUs) vs. sequencing depth of 190 HMP gut samples. 12 subjects with less than 1,300 reads/sample were excluded and the remaining 178 were assigned into two groups of n = 89 subjects, with average sequencing depth 3,019 and 8,640 reads/sample, respectively. d2, d3, The characteristic overlap between samples of Group 1 is smaller than between samples of Group 2. However, DOC analysis of each group shows a clear negative slope. d4–d6, Samples of each group were rarefied prior to analysis with minimal community size of 1,317 and 4,333 in Group 1 and Group 2 respectively, as represented by the black dashed lines in d4. d7–d9, Samples of both groups were rarefied prior to analysis with the same minimal community size of 1,317, as represented by the black dashed line in d7.

Extended Data Figure 9. DOC analysis of longitudinal microbiome data from six lakes in Germany

(Data downloaded from http://qiita.microbio.me, Study ID: 945). a. ‘Stechlin’ (M = 440); b. ‘Haus’ (M = 26); c. ‘Tiefwaren’ (M = 164); d. ‘Melzer’ (M = 68); e. ‘Breiter Luzin’ (M = 89); f. ‘Fuchskuhle’ (M = 355). Blue points represent the dissimilarity-overlap values of sample pairs from the same lake. The DOCs of real samples from each lake and that from the corresponding randomized samples are calculated using robust LOWESS and shown in red and yellow, respectively. For all the six lakes, a clear negative slope is observed for the DOCs of real samples, suggesting universal or time-invariant microbial dynamics for each lake. Differences in the DOC shapes (e.g. the moderate DOC slope in b, c and d, in contrast with the steep DOC in a, e and f) deserve a systematic study of those microbial ecosystems. This example clear demonstrates the applicability of DOC analysis to general microbial ecosystems, e.g. soil, ocean, rizosphere/phyllosphere, fermenters, etc.

Extended Data Figure 10. Average dissimilarity between two normalized random vectors

Two indepdent vectors x, y of n elements randomly choosen from uniform distribution u (0,1) were generated and then normalized ${\widehat{x}}_i\equiv \frac{x_i}{{\sum }_{j=1}^n{x}_j}$ and ${\widehat{y}}_i\equiv \frac{y_i}{{\sum }_{j=1}^n{y}_j}$ . (Note that in practice all n elements are always shared in x and y, since zeros are very unlikely). The dissimilarity D(x̂, ŷ) is then calculated using the five dissimilarity measures (D_JSD, D_rJSD, D_BC, D_YC and D_nSC). Average dissimilarity and standard deviations of 1,000 pairs are shown in a1, b1, c1, d1 and e1, for the different measures. The horizontal black dashed line represents the average dissimilarity for n = 100. For all the measures here, the dissimilarity displays no n-dependence for n > 15, while D_nSC is n-independent for any n > 0. Similar analysis was performed for vectors whose elements were chosen from power-law distributions P(x)~x^−α with α = 3 (a2, b2,c2,d2ande2)and P(x)~x^−α with α = 2 (a3, b3, c3, d3 and e3).

Figure 1. Alternative scenarios of microbial dynamics across different healthy subjects

Microbial dynamics captured by (1) is simply characterized by an ecological network, where nodes represent species (with node sizes proportional to growth rates) and edges represent inter-species interactions (with green/red arrows represent excitatory/inhibitory interactions, respectively). Different subjects typically have different species assemblages, represented by colored circles near each subject. a, The underlying dynamics/network is unique for each subject. b, Subjects within the same group share the same dynamics/network that is significantly different from that of other groups. c, Different subjects have the same underlying dynamics/network.

Figure 2. Higher overlap of microbial communities is associated with lower dissimilarity

a, Four gut microbial sample pairs (i–iv)represented by stacked bars at the genus level. For each sample pair, their shared genera are colored while non-shared genera are shown in gray. b, DOC(in dark blue) of gut microbial sample pairs from the HMP study (M = 190 samples). Gray dots represent all the 17,955 sample pairs. c, DOC (in dark red) of the randomized samples is flat. In (b) and (c), and throughout the paper, shaded area indicates the range of the 94% confidence intervals (see Methods section).

Figure 3. Detecting universality of microbial dynamics in different body sites

We calculated DOCs for real (dark blue) and randomized samples (dark red) of two datasets: (1) SMP- a, gut, b, tongue, c1, forehead skin, c2, palm skin; (2) HMP – d, gut, e1, tongue dorsam, e2, attached keratinized gingiva, e3, buccal mucosa, e4, hard palate, e5, palatine tonsils, e6, subgingival plaque, e7, supergingival plaque, e8, throat, e9, saliva, f1,2, left/right antecubital fossa, f3,4, left/right retroauricular crease, g1, vaginal introitus, g2, mid vagina, g3, posterior fornix, h, anterior nares. The vertical green line represents the “change point” (see Methods section).

Figure 4. DOC analysis of human subjects with rCDI

a, Before FMT, the DOC (dark green line) of the rCDI subjects is nearly flat. b, After FMT, the DOC (dark blue line) displays a pronounced negative slope in the high-overlap region. We denoted a subject pair as a solid (or hollow) circle if the two subjects received FMT from the same donor (or two different donors), respectively. Interestingly, solid circles spread over a wide range of overlap values, suggesting that even if two subjects share the same donor, their post-FMT microbiomes may still display strong inter-individual variability.