1. Introduction

The microbiome and health status are related. In fact, techniques are emerging to treat diseases through the microbiome, such as fecal microbiota transplantation [1], probiotic supplementation [1], nutrition-based approaches or the use of the microbiome as a biomarker [2]. In addition, the microbiome has the potential to revolutionize the future of pharmacology due to the interactions between the microbiome and drugs [3]. As a result it is paramount to know more about microbiome dynamics. Microbiota stability over time is related to health status [4]. This fact highlights the importance of studying microbiome time series. The initial approaches to analyzing longitudinal microbiome data included MDSINE [5], which represents an early methodological example in this domain. Table 1 shows the R packages designed to analyse microbiome cross-sectional and longitudinal data. In addition, microbiome data is compositional due to limitations of the techniques used to collect the data [6]. Compositional data carries relative information and for this reason, the compositions are usually expressed in terms of percentages and the sum of the data is subject to a constant constraint [7]. Correlations between compositional data are spurious [8] and as a result, specific methodology is needed to analyze compositional data [9].

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Table 1. R packages designed to analyze microbiome datasets.

https://doi.org/10.1371/journal.pcbi.1014328.t001

In the CoDaLoMic package, we implemented three models specifically designed to analyze microbiome compositional and longitudinal data, accounting not only for pairwise interactions but also for interactions among groups of bacteria. This approach provides a robust framework for investigating microbial interactions at a group level, extending beyond the pairwise focus of most existing methods. Furthermore, CoDaLoMic facilitates the analysis of microbiome variability in relation to host health status and enables the clustering of taxa that exhibit similar temporal dynamics. However, the package does not support population-level analyses involving comparisons across multiple individuals within a single dataset. In this case, each individual’s time series is modeled independently, although the results can be compared post hoc. CoDaLoMic enables multi-subject comparisons across datasets. As presented in [22], our proposal is successful in comparing treated and control microbial populations, revealing distinct behavioral patterns. It also provides insights into the contribution of the entire microbial community to the abundance of individual genera and identifies specific groups of genera that influence particular taxa.

Unlike approaches such as state-space models (SSM) or dynamic Bayesian networks (DBN) the models implemented in CoDaLoMic—namely Dirich-gLV, FBM, and BPBM—are specifically formulated within the framework of compositional data, which is methodologically more appropriate for microbiome analysis. These models explicitly employ the Dirichlet distribution and log-ratio transformations such as alr or principal balances, thereby respecting the relative structure of the data and avoiding the spurious inferences that may arise when modeling abundances on an absolute scale. Furthermore, the models implemented in CoDaLoMic directly capture the temporal self-dependence of each taxon, as well as taxon interactions and community-level effects, through parameters with clear ecological interpretations—such as persistence, competition, or facilitation. The BPBM model, in turn, incorporates Selected Principal Balances (SPBals) to summarize the main ecological gradients of the microbial community, enabling a dimensionality reduction without sacrificing biological interpretability. In contrast, SSMs and DBNs often include latent components or conditional dependency structures which, although powerful from a statistical perspective, can be difficult to interpret ecologically—especially in highly diverse microbiomes with hundreds of taxa. Moreover, these approaches are not always designed to handle compositional data directly, which may require additional transformations or assumptions that are less suitable for this data type. Overall, the models implemented in CoDaLoMic offer alternatives that are better aligned with the nature of microbiome data, provide transparent ecological interpretation, and are more practical and scalable for a wide range of applications in the longitudinal analysis of microbial communities. Our proposal offers a unique approach for the analysis of longitudinal microbiome data by combining Bayesian autoregressive modeling with compositional transformations (log-ratios and principal balances), which is not implemented in the other packages reviewed. Unlike tools such as phyloseq, microbiome, or microViz, which are primarily designed for data handling, visualization, and exploratory analysis, CoDaLoMic explicitly models the temporal dynamics of microbial communities while respecting their compositional nature through time-dependent Dirichlet distributions. Compared to packages such as SplinectomeR or q2-longitudinal, which analyze temporal trajectories without generative modeling, CoDaLoMic enables the inference of causal relationships between groups of taxa (balances) and allows short-term prediction of future community compositions. Even when compared to coda4microbiome, which also operates within the log-ratio framework, CoDaLoMic stands out for its ability to estimate microbial interactions through hierarchical Bayesian models and the use of principal balances, thus reducing dimensionality while maintaining biological interpretability. In summary, CoDaLoMic complements the existing ecosystem of microbiome tools by providing a robust framework for compositional, longitudinal, and inferential modeling.

2. Design and Implementation

2.3. Model selection criteria

CoDaLoMic provides implementations of three models: Dirich-gLV [26], FBM [27], and BPBM [28]. A detailed description of these models is available in the GitHub repository (https://github.com/Creus-Marti/CoDaLoMic-Tutorial.git) and in S2 Appendix. Table 2 summarizes the key considerations for selecting one model over another, in relation to the specific objectives intended to be achieved through its application.

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Table 2. Comparison of microbial community models based on biological relevance and practical considerations.

https://doi.org/10.1371/journal.pcbi.1014328.t002

For further detail, Figs 1 and 2 illustrate the research questions addressed by each model and the corresponding outputs generated to answer them. Specifically, Fig 1 presents the outputs and questions related to dataset description while Fig 2 extends this by including both descriptive and predictive analyses. Interpretation of the output is explained in the model tutorials available in the GitHub repository (https://github.com/Creus-Marti/CoDaLoMic-Tutorial.git).

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Fig 1. Describing microbiome dynamics.

CoDaLoMic is able to describe microbiome dynamics. A: Data structure. B: Estimated parameters obtained with the Dirich-gLV model. C: Estimated parameters obtained with the FBM model. D: PCA of the estimated parameters (obtained with FBM model). E: Estimated parameters obtained with the BPBM model. F: Dendogram with the principal balances. G: Value of the Selected Principal Balances (SPBal) during all time points. Panels B, C and E are also available (in LATEX format) in S1 Text.

https://doi.org/10.1371/journal.pcbi.1014328.g001

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Fig 2. Describing and predicting microbiome dynamics.

CoDaLoMic describes and predicts microbiome dynamics. Panels A, B, and C show the expected values generated by each model; panels D, E, and F display the corresponding variances. The vertical line indicates the point at which prediction begins. Panel G presents a graphical overview of the dataset, which is identical across all three models. Panel H shows the mean value of the RMSD, NSC, RSS and MAPE for the three models. Panel H is also available in LATEX format in S1 Text.

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Note that part A in Fig 1 illustrates the structure of the input data required by the package; part B, C and E in Fig 1 interpret the estimated parameters obtained for each model; and part D in Fig 1 presents the estimated parameters of the FBM model in a graphical format. Fig 1 appears the concept of Principal Balances and Selected Principal Balances (SPBal), they denote a log-ratio contrast between groups of taxa selected for their capacity to account for the majority of variance in compositional data. A higher absolute value of the SPBal indicates a greater difference between the groups. The SPBal are the PB for which the sum of the percentage of variance is higher than 80%. More detail can be found in S2 Appendix or in the GitHub repository (https://github.com/Creus-Marti/CoDaLoMic-Tutorial.git). As a result, part F in Fig 1 shows a dendrogram that groups together the taxa whose relationships maximize the variance and part G in Fig 1 shows the degree of similarity or dissimilarity between the groups that maximize the variance across all time points. In addition, part A, B and C in Fig 2 show the expected values generated by each model, serving as a graphical assessment of model fit; part D, E and F in Fig 2 present the variance analysis; part G in Fig 2 describes the dataset; and part H in Fig 2 displays the quality indices.

In summary, the choice of model depends on the specific analytical focus: Dirich-gLV is most appropriate when investigating pairwise interactions; FBM should be selected when both taxa-level and community-level effects are of interest; and BPBM is recommended for analyses centered on community structure. All three methods require that the time sampling frequency be equidistant across all time points. This interval may be daily, weekly, monthly or any other consistent temporal lag, but the distance between consecutive time points must remain uniform. If any time point is missing, imputation methods must be employed for estimation.

3. Results

In this section, a comparative performance analysis of CoDaLoMic will be conducted against all methods presented in Table 1 that are specifically designed for longitudinal data. These methods include: q2-longitudinal, coda4microbiome, SplinectomeR, BiomeHorizon and seqtime. Table 3 shows the results of the comparion.

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Table 3. Comparison between the proposed methods and existing approaches across various aspects: input characteristics, research questions addressed and computational characteristics and performance. Only two methods accept the same input type (Seqtime and BiomeHorizon). These are compared methodologically based on the types of problems they address. Computational characteristics and performance are evaluated against Seqtime, as BiomeHorizon is designed for visualization rather than dynamic estimation and does not support RMSD calculation. The table reports RMSD for estimation and prediction, as well as computation time equired to estimate the model.’tp’ denotes time point, “s” seconds, “d” days, ‘–’ indicates model failure and * indicates models implemented in CoDaLoMic.

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First, Table 3 details the characteristics of the input data required by the different methods. Notably, q2-longitudinal, coda4microbiome and SplinectomeR are suitable for analyzing multiple individuals and necessitate metadata to distinguish between subjects. Conversely, CoDaLoMic, BiomeHorizon, and seqtime are not designed for this type of input data. Consequently, a direct comparison of the performance of CoDaLoMic with q2-longitudinal, coda4microbiome and SplinectomeR is not feasible, as these methods address fundamentally different research questions.

Secondly, Table 3 illustrates the distinctions among the research questions addressed by CoDaLoMic, BiomeHorizon and seqtime. We can observe that several research questions are addressed exclusively by CoDaLoMic, which immediately demonstrates the utility of CoDaLoMic regardless of the other proposed methods. Thirdly, we will compare the performance and computational efficiency of CoDaLoMic and seqtime in describing and predicting microbiome dynamics across datasets varying in the number of taxa. Notably, BiomeHorizon is excluded from this comparison, as its primary design objective is visualization rather than dynamic description or prediction.

Table 3 presents the Root Mean Square Deviation (RMSD) values calculated for both the descriptive and predictive capacity of the different methods in datasets of different lengths. Additionally, the table details the computational time required for the estimation process across datasets of varying sizes. The compilations were performed on an HPC cluster running Rocky Linux 8.10, consisting of 13 compute nodes with a total of 608 CPU cores (1216 threads with hyper-threading) and 15 TB of RAM. The system is equipped with a distributed Ceph storage architecture incorporating SSD/NVMe drives and an internal network bandwidth of 20 Gb/s. The peak performance of the cluster, as measured by HPLinpack 2.3, is 7 Tflops/s. In order to simulate the datasets of different lengths, we first constructed the interaction matrix by drawing its entries randomly from a uniform distribution [23]. We then generated the initial bacterial abundances using a Poisson distribution [24]. Combining these components, we simulated the community dynamics under a generalized Lotka–Volterra framework. All simulations were performed using the R package seqtime [24].

Table 3 shows that BPBM achieves the highest accuracy in both description and prediction, although it is also the most computationally demanding method. FBM attains results comparable to BPBM while requiring substantially less computation time. Seqtime is the fastest approach, but it yields the lowest accuracy. In addition, seqtime is unable to produce results for the largest datasets because, during the prediction step, it is not possible to solve de Lotka Volterra equations. A similar issue arises with the Dirichlet‑gLV model, it often fails to produce stable results because it is highly sensitive to atypical values. In estimating the Dirichlet parameter, an exponential transformation is applied; however, this transformation may diverge to infinity, which prevents the computation of the predicted values. This sensitivity to outliers can also hinder the estimation of the expected values, not only the predicted ones.

We will now address the comparison of research questions using a case study based on the cockroach dataset (see a description of the dataset in part A of S1 Fig), with particular emphasis on interpreting the outputs of CoDaLoMic. Part A in Table 4 indicates that the Dirich-gLV model provides the poorest fit to the cockroach data, as it exhibits the highest values for RMSD, RSS and MAPE. Furthermore, its NSC value is the furthest from one. Seqtime improves upon Dirich-gLV, however, its performance is further enhanced by FBM and BPBM. FBM and BPBM produce similar results, but BPBM enhances all values, except for RMSD, which remains the same for both models. Note that BiomeHorizon is designed for visualization rather than calculation and do not support the calculation of these indexes. Considering this information, we will analyze the results obtained with seqtime (see part A, B, C and D of S2 Fig), BiomeHorizon (see S3 Fig), FBM and BPBM when estimating the cockroach dataset.

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Table 4. Table with the information of the cockroach dataset. A: mean values of RMSD, NSC, RSS and MAPE for all models. B: Parameter information and its interpretation when using FBM. C: Information and interpretation obtained with the estimation of BPBM, we assign a number to each bacterium for easier identification: 1 is g_Dysgonomonas, 2 is g_Bacteroides, 3 is f_Lachnospiraceae, 4 is g_Desulfovibrio, 5 is gSoleaferrea, 6 is g_Alistipes, 7 is f_Ruminococcaceae, 8 is c_Bacteroidia, 9 is g_Breznakia, 10 is f_Tannerellaceae, 11 is gR-7_group, 12 is f_Dysgonomonadaceae, 13 is c_vadinHA49, 14 is g_Desulfatiferula, 15 is Other.

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Part B in Table 4 taxa versus community dynamics as explained by FBM. For the taxa g__Dysgonomonas, g__Bacteroides, f__Ruminococcaceae, g__Breznakia, f__Dysgonomonadaceae, and c__vadinHA49, the community weight is higher than the self-weight in defining their abundance at the subsequent time point (we call them group C). Conversely, g__Candidatus_Soleaferrea is unique in exhibiting similar influence from both the bacterium itself and the rest of the community. For all remaining bacteria, the self-influence predominates over the community influence in determining future abundance (we call them group B). These dynamics are also observable in the PCA present in part B of S1 Fig, where groups C and B exhibit clear separation.

Part C in Table 4 details the inter-taxa dynamics explained by BPBM. Within Group B, 8,10,3 (c_Bacteroidia, f_Tannerellaceae, f_Lachnospiraceae) and 11 (gR-7_group) exhibit similar behavior, and their combined relationship exerts the primary influence across the majority of the dataset.Taxa within Group C interact cooperatively with Group B members. Specifically, 13,14,9 (c_vadinHA49, g_Desulfatiferula, g_Breznakia) and 12 (f_Dysgonomonadaceae) share similar behavior and chiefly influence the bacteria in Group B. Furthermore, the combined set of taxa 5,7,6,2 (gSoleaferrea, f_Ruminococcaceae, g_Alistipes, g_Dysgonomonas) and 8,10,3,11 (c_Bacteroidia, f_Tannerellaceae, f_Lachnospiraceae, gR-7_group) display divergent behavior, with their relationships collectively impacting nearly the entire dataset. Finally, the collection of taxa 13,14,9,12 (c_vadinHA49, g_Desulfatiferula, g_Breznakia, f_Dysgonomonadaceae) exhibits behavior distinct from the rest of the dataset (a separation also depicted in part B of S4 Fig) and its interaction primarily influences genera 1,2,4,15 (g__Dysgonomonas, g__Bacteroides, g__Desulfovibrio, Other).

It must be noted that S5 and S6 Figs presents the expected values obtained from the FBM and BPBM models, and visually confirms the goodness-of-fit of the models to the observed data. Before concluding, note that both the BPBM and FBM methods allow variance analysis (see part C of S1 Fig and part C of S4 Fig) and that BPBM additionally produces a dendogram showing the groups of bacteria whose relationships exhibit the maximum variability (see part A of S4 Fig).

In S2 Fig we observe the network visualization provided by seqtime. Specifically, we observe a closed-loop dynamic wherein taxon 1 benefits from taxon 2, which in turn is sequentially benefited by taxa 11, 7, 5, 9, 13, and 10, completing the cycle back to taxon 1.Conversely, S3 Fig presents the results obtained using BiomeHorizon. It is observed that while most taxa exhibit alternating periods of high and low abundance, taxa 2, 14, and 15 display a distinct pattern: they are highly abundant initially but subsequently experience a marked decrease in abundance.

The analysis of the cockroach dataset, utilizing the various methods, unequivocally demonstrates that each approach is tailored to address distinct research objectives. The innovation inherent in the FBM and BPBM lies specifically in their capacity to describe microbiome dynamics taking into account the relationships between groups of bacteria.

4. Availability and future directions

A deeper understanding of microbiome dynamics is crucial, as microbial stability over time is directly associated with host health status [4]. This necessitates the study of microbiome time series to facilitate the development of effective, mechanism-based clinical treatments.

CoDaLoMic is a comprehensive R package (available on CRAN: https://CRAN.R-project.org/package=CoDaLoMic)designed to model and predict the dynamics of microbiome communities over time. It leverages advanced models such as Dirich-gLV, FBM, and BPBM to examine microbial abundance and the intricate relationships between various bacterial groups at different time points. What sets CoDaLoMic apart is its ability to predict future microbial abundances based on the interactions between bacterial taxa, providing a more nuanced understanding of how changes in one group can directly or indirectly affect others. The package allows for the estimation of these relationships using maximum likelihood estimation (for Dirich-gLV and FBM models) and MCMC (for BPBM), enabling researchers to analyze complex microbiome data over extended periods.

The focus of CoDaLoMic on prediction and its capacity to model microbial interactions over time makes it particularly valuable for longitudinal microbiome studies. It addresses the challenge of understanding not only the current state of the microbiome but also how it will evolve based on existing patterns and relationships. In contrast to other R packages, such as coda4microbiome, q2-longitudinal, or SplinectomeR, which focus on different aspects of microbiome analysis—such as community composition, diversity metrics, or statistical associations—CoDaLoMic goes beyond just descriptive analysis. It emphasizes predictive modeling, making it especially useful for research aiming to understand the long-term dynamics of microbiome populations, such as in studies of health interventions, environmental changes, or disease progression.

Additionally, CoDaLoMic incorporates the concept of principal balances (SPBal), offering a unique approach capturing the interactions between bacterial groups and their collective influence on microbiome composition. This allows for a more precise and actionable understanding of microbial community behavior and has the potential to inform clinical or therapeutic decisions based on microbiome data. The package also provides detailed outputs in LaTeX format, facilitating the inclusion of results in scientific publications.

However, the package also has limitations. As the size of the dataset increases, the computation time required for model estimation grows significantly. In cases where the dataset is particularly large, these computational demands may exceed the capacity of standard desktop computers, necessitating the use of more powerful external servers or cloud-based systems to perform the necessary calculations efficiently. This issue is especially relevant for large-scale microbiome studies where computational resources can become a bottleneck. Furthermore, the current models implemented in CoDaLoMic are primarily designed to analyze the microbiome dynamics of a single subject at a time. The package does not currently support population-level analyses involving simultaneous modeling across multiple individuals within a single dataset. Instead, each individual’s time series is modeled independently, with results compared post hoc. While CoDaLoMic enables multi-subject comparisons across separate datasets, integrated multi-subject modeling within the same dataset remains a future development goal. Additionally, the current models do not yet incorporate external covariates such as dietary factors, host health status, medication use, or other environmental variables. These factors, together with batch effects, are well-recognized sources of variability in microbiome studies and can significantly influence microbial composition and dynamics. Therefore, it is crucial to apply appropriate preprocessing corrections prior to using CoDaLoMic to avoid confounding effects. We recommend performing batch correction on data transformed by log-ratio methods (e.g., clr or alr transformations) to preserve the intrinsic compositional structure of the data. In contrast, preprocessing techniques such as rarefaction or total sum scaling normalization can distort compositional relationships and compromise the validity of downstream modeling results; thus, these approaches are discouraged. Using CoDaLoMic, subjects should be analyzed on an individual basis, enabling post hoc analysis to explore associations between the longitudinal data behavior and health status, treatment type, or other relevant clinical variables. Looking forward, future versions of CoDaLoMic will explicitly incorporate external covariates and batch effects within the modeling framework. This enhancement will enable more direct and robust analyses of their impact on microbiome dynamics, particularly benefiting clinical or dietary intervention studies by improving the models’ ability to capture complex, context-dependent microbial community behaviors. Integrating these covariates is expected to improve both the accuracy and interpretability of predictions derived from longitudinal microbiome data. Looking ahead, there are several key areas for future development. A major objective is to extend the models to handle data from multiple subjects simultaneously within the same dataset, enabling more comprehensive population-level analyses. This advancement will facilitate comparative studies across individuals or groups exposed to different treatments or environmental factors. Additionally, ongoing optimization of the code will focus on improving computational efficiency and reducing runtime, ensuring the package remains scalable and efficient when applied to very large datasets.

Supporting information

Acknowledgments

The computations were performed on the Garnatxa HPC cluster at the Institute for Integrative Systems Biology (I2SysBio), I2SysBio is a mixed research center of the University of Valencia (UV) and the Spanish National Research Council (CSIC).