Linking complex microbial interactions and dysbiosis through a disordered Lotka–Volterra model
- Dipartimento di Fisica “G. Galilei” e INFN sezione di Padova, Università di Padova, Italy
- Dipartimento di Ingegneria Civile, Edile e Ambientale (ICEA), Università di Padova, Italy
- École Polytechnique Fédérale de Lausanne, Switzerland
- Dipartimento di Scienze Chirurgiche, Oncologiche e Gastroenterologiche (DiSCOG), Università di Padova, Italy
- Laboratoire Matière et Systèmes Complexes (MSC), Université Paris Cité, CNRS, France
- Padova Neuroscience Center, University of Padova, Italy
Figures
Figure 1
The inference protocol of the dgLV generative model is performed by a moment matching optimization procedure.
We aim to infer the free parameters – shown on the right – so that to match the mean abundance, higher-order correlations between species abundances, and the average carrying capacity for the two cohorts, that is, – on the left. This procedure enables us to extract relevant information about the ecological dynamics from cross-sectional data of healthy (blue) and diseased (red) microbiomes, which are treated as independent disordered realizations.
Figure 2
Order parameters inferred from the data using Equation 4.
(a) shows , (b) , and (c) in healthy (blue) and unhealthy (red) cohorts. Circles denote the mean value of each order parameter, and error bars indicate the standard deviation across bootstrap realizations. Bootstrap estimates were obtained from 5000 iterations, each retaining 90% of samples within each cohort. Gray symbols show the corresponding null-model values obtained by randomizing cohort labels prior to estimation.
Figure 3
Distinct ecological organization in healthy vs diseased microbiomes.
(a) Inferred (demographic noise strength) and (interactions heterogeneity) for healthy (blue) and diseased (red) microbiomes are clustered. Darker dots correspond to better solutions (i.e., solutions with a lower value of the cost function ), while the two points with hexagonal markers correspond to the best two (healthy and diseased, respectively) solutions. In the first panel inset, we also show (in log–log scale) the species abundance distributions (SADs) corresponding to each solution. To have a more concise representation, we present each SAD fixing the disorder to its average . (b) The probability density function of the inferred interactions for healthy (blue) and diseased (red) microbiomes. Dysbiosis reduces the heterogeneity of the interaction strengths. The quantities reported in the legend are the average and standard deviation of . They are calculated as and , where is the species pool size, estimated as the set of all observed species in a dataset, can denote healthy () or diseased () individuals.
Figure 4
Stability of healthy vs diseased microbiomes.
(a) The replicon eigenvalue corresponding to each solution of our optimization procedure (shaded dots). The solid hexagon represents the replicon corresponding to the best solutions that minimize the error in predicting the order parameters of the theory (minimum ). The two investigated microbiome phenotypes (healthy in blue, diseased in red) are significantly different. In particular, diseased microbiomes are closer to the marginal stability of replica-symmetric ansatz (gray horizontal line). (b) Solutions of the moment-matching objective function are shown as a function of and , which in turn depend on the species abundance distribution (SAD) parameters (see main text). Healthy (blue) and diseased (red) microbiomes appear to be clustered. Therefore, distinct ecological organization scenarios (strong neutrality/emergent neutrality) take place. Darker dots correspond to solutions with lower values of the cost function, while hexagonal markers correspond to the two best solutions.
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Linking complex microbial interactions and dysbiosis through a disordered Lotka–Volterra model
eLife 14:RP105948.
https://doi.org/10.7554/eLife.105948.3
