Fig 1.
Example phase spaces and trajectories for compositional Lotka-Volterra.
The top row displays examples using the additive log-ratio transformation for three taxa. The bottom row displays examples in relative-abundance space corresponding to the examples in the top row. Arrows display the direction of the gradient, while the colors display its magnitude (lighter is smaller). A) Phase space where dynamics depend on relative growth rates alone. B) Phase space where dynamics depend on growth rates and interactions. The black dot denotes a fixed point. The solid line depicts a simulated trajectory, where an external perturbation (red line) moves the system away from the fixed point. C) Alternate view of the example in B. The red arrow denotes an external perturbation causing the system to move away from the fixed point. D) Phase space in the simplex corresponding to A. Black dots denote fixed points and only occur on the corners. E) Phase space in the simplex corresponding to B. Black dots denote six possible fixed points. The line displays the same simulated trajectory as B. F) Simulation example corresponding to B depicted as relative abundances. An external perturbation at time point 50 causes the system to move away from the fixed point in the interior of the simplex toward one at the boundary.
Fig 2.
Comparison of performance between ridge regression and elastic net.
Performance was evaluated on simulated ground truth using three metrics: root-mean-square error (RMSE) between true and estimated interactions, RMSE between true and estimated growth rates, and RMSE between true and estimated hold out trajectories for 5 samples per simulation replicate. Box plots describe the distribution in RMSE over 50 simulation replications. Significance is computed using the Wilcoxon signed-rank test (****: p < 10−4; ***:p < 10−3; **: p < 10−2; *: p < 0.05; ns: not significant).
Table 1.
Description of the three real datasets investigated.
Fig 3.
Correspondence between relative parameters estimated using gLV and cLV on three datasets.
Each box plot displays the distribution of observed community size (i.e. N(t)) across all samples, rescaled such that . Scatter plots display the relative parameters estimated by cLV (y-axis), and the corresponding difference in parameters of gLV (x-axis). cLV better approximates interactions inferred using gLV when the variability in concentrations is low, matching theoretical expectations. A strong correspondence is observed between external perturbations across all datasets.
Table 2.
Number of parameters of each model.
Fig 4.
Comparing predicted trajectories from initial conditions across models.
RMSE (y-axis) between true and estimated trajectories per sample across three datasets (panels) and six models. RMSE is computed on held out data using leave-one-out cross-validation: one sample is held out at time and the models are trained on the remaining data. Trajectories are predicted on the held out sample from initial conditions. Significance is computed relative using the one-sided Wilcoxon signed rank test (**: p < 0.01; *: p < 0.05; ns: not significant).
Fig 5.
cLV recapitulates absolute interactions.
Estimated effect of external perturbations (A) and interactions (B) inferred by cLV. Parameters are computed with respect to uncl. Lachnospiraceae in the denominator for interactions, and und. uncl. Mollicutes for perturbations. Estimated parameters recapitulate the interaction network with C. difficle (C) proposed by Stein et al. [7].