Animal breeding procedures historically focus on improving the phenotype through genotype. With the relatively recent discovery of the role of microbes on phenotype, and its interplay with genotype, the design of breeding procedure has become more complex. Moreover, such procedures also comes with constraints, such as limited population and a limited access to genotypes. This calls for new tools accounting for holobiont reality to help in the design of such procedures.

As part of the scientific committee of the French JOBIM’25 conference, I accepted the role of recommender of the paper by Pety et al. [1] as it triggered my interest on how make a simple and exploitable model from such complex phenomena involving host genomics, microbial population and environmental forcing.

I have been particularly interested by the mechanistic/explicit modeling and interpretability of the model as thanks to its simplicity, many internal variables can be quantitatively interpreted, for instance in terms of explained variance, or effects of variables.

The current manuscript indeed proposes a method (RITHMS) for simulating hologenomic data -- namely the joint information of an host genotype and its associated microbiome -- over several generations subject to selection. The current tool extends previous simulators in multiple directions, either by including the microbial compartment or by including more realistic features.

RITHMS encompasses more realistic aspects compared to previous methods, in particular taxa-dependent heritability, data-sourced initialization, possibility of modulation of environmental parameters overtime. RITHMS is versatile in its parametrization, with proven transgenerational stability of target values, and can adapt to many scenario depending on the user’s need.

The downside of keeping RITHMS interpretable and avoiding too much complexity, is that several strong - but widespread - assumptions underlie the current model, such as general linearity of the responses, but also absence of complex genomic and microbial realities such as epistasis and taxa interaction respectively.

Nevertheless, the authors propose several examples of use cases of concrete interest, some of which have been added thanks to the constructive criticisms of the reviewers.

One should finally underline that RITHMS is implemented as a functional R package. The full potential of RITHMS will be revealed by the concrete use cases in which the simplifications assumed in the model does not hinder the general conclusions provided by the simulations.

References

[1] Solène Pety, Ingrid David, Andrea Rau, Mahendra Mariadassou (2025) Simulating transgenerational hologenomes under selection with RITHMS. arXiv, ver.4 peer-reviewed and recommended by PCI Mathematical and Computational Biology https://doi.org/10.48550/arXiv.2502.07366

Stochastic reaction networks are a general framework to model the dynamics of a population of non-identical particles. Each particle belongs to a species (in reference to chemical species), of which there is a fixed, finite number, and the model is a continuous-time Markov chain tracking the abundance of each species. The transitions of this chain correspond to chemical reactions that instantly transform groups of particles called complexes into other particles. Under the assumption that there is a finite number of reactions, the model can be conveniently described by a directed graph whose vertices correspond to complexes and whose edges correspond to chemical reactions. In its most general form, this framework is very broadly applicable: there does not have to be conservation of mass (particles can be created and destroyed, irrespective of an underlying notion of mass — thus, this covers, e.g., multitype branching processes); and the kinetics do not have to obey the law of mass action (the rate at which each reaction occurs can be an arbitrary function of the state of the system, i.e. of the abundances of the species). As a result, its use goes beyond chemistry and includes, e.g., compartmental models in epidemiology.

One of the main goals in the study of stochastic reaction networks is to understand how the structure of the graph parameterizing the model affects its dynamics — in other words, what dynamical properties of the Markov chain can be read directly from the graph. Much of the existing research focuses on stationary distributions and, in this context, the notion of complex-balanced distribution is relevant. This notion parallels the notion of complex-balanced equilibrium for deterministic reaction networks; loosely speaking, a stationary distribution is complex-balanced if, for every state and every complex, the probability flux out of the state through the complex equals the probability flux into the state through that same complex. In the deterministic setting, the existence of a positive complex-balanced equilibrium is a non-trivial question that can be studied using deficiency theory (in particular the celebrated deficiency zero theorem of [3]). However, in stochastic reaction networks, despite some results [2], the existence and characterization of complex-balanced distributions was largely an open question.

In this recommended paper [1], the authors obtain a deficiency theorem for stochastic reaction networks. More specifically, they characterize complex-balanced distributions in terms of the cycles of its graph, and provide a sufficient (and, assuming additional conditions are met, necessary) condition for the existence of a complex-balanced distribution. This paper therefore marks an important step in the extension of deficiency theory to stochastic reaction networks. Moreover, for their proof the authors introduce a method they call "reaction cleaving" — an operation that preserves complex-balancedness and can be used iteratively to decompose the reaction graph into disjoint cycles. This method is elegant and of independent interest, and it might be used to tackle other questions.

References

[1] Linard Hoessly, Carsten Wiuf, Panqiu Xia (2025) Reaction cleaving and complex-balanced distributions for chemical reaction networks with general kinetics. arXiv, ver.4 peer-reviewed and recommended by PCI Mathematical and Computational Biology https://doi.org/10.48550/arXiv.2301.04091

[2] Hong, H., Hernandez, B. S., Kim, J., Kim, J. K.  (2023) Computational translation framework identifies biochemical reaction networks with special topologies and their long-term dynamics. SIAM J. Appl. Math. 83, 3, 1025–1048. https://doi.org/10.1137/22M150469X

[3] Fritz Horn and Roy Jackson (1972) General mass action kinetics, Arch. Ration. Mech. Anal., 47, pp. 81–116. https://doi.org/10.1007/BF00251225

Accurately inferring phylogenetic relationships among different species is a fundamental challenge in evolutionary biology. This task becomes particularly complex when dealing with species that have experienced extensive horizontal gene transfer (HGT), as is common in microbial evolution [1]. Such gene transfer events can obscure true evolutionary histories, making traditional methods less reliable.

In this context, Weiner et al. [2] conducted a comprehensive study evaluating the performance of four prominent methods—SpeciesRax [3], ASTRAL-Pro 2 [4], PhyloGTP [5], and AleRax [6]—designed to infer species trees while accounting for/mitigating the effects of HGT.

These four methods were tested across a diverse array of simulated datasets, varying key parameters such as sequence length, number of genes, and levels of evolutionary divergence. Additionally, their performance was evaluated on two empirical biological datasets.

On simulated datasets, the two most computationally demanding tools, AleRax and PhyloGTP, underperform compared to the others. AleRax demonstrates comparable accuracy to PhyloGTP on error-free gene trees but significantly outperforms PhyloGTP when using estimated—thus error-prone— gene trees. When comparing PhyloGTP and SpeciesRax, the authors observe that PhyloGTP tends to outperform SpeciesRax when the number of input gene trees is limited or when duplication, transfer, and loss (DTL) rates are high. Conversely, SpeciesRax generally yields better results on datasets characterized by low DTL rates. Additionally, ASTRAL-Pro 2 exhibits lower accuracy across nearly all tested scenarios relative to the other methods.

In the analysis of empirical datasets, the four methods show similar performance on the Frankiales dataset, ASTRAL-Pro 2 being extremely fast. However, on the more complex Archaeal dataset, AleRax produces a species tree that differs markedly from previously supported Archaeal trees. This divergence may stem from AleRax's limited performance on highly divergent, complex datasets, or could suggest that the AleRax tree is right and can more accurately captures the true evolutionary history of the group—a question that warrants further investigation.

A preliminary version of this work, focusing primarily on PhyloGTP's evaluation, was previously presented at the RECOMB Comparative Genomics 2024 conference [5]. This extended version offers valuable insights and perspectives for practitioners interested in microbial phylogenomics. 

References

[1] Lapierre, P., Lasek-Nesselquist, E., & Gogarten, J. P. (2014). The impact of HGT on phylogenomic reconstruction methods. Briefings in bioinformatics, 15(1), 79-90. https://doi.org/10.1093/bib/bbs050 

[2] Weiner, S., Feng, Y., Gogarten, J. P., Bansal, M. S. (2025) A systematic assessment of phylogenomic approaches for microbial species tree reconstruction. bioRxiv, ver.4 peer-reviewed and recommended by PCI Mathematical and Computational Biology https://doi.org/10.1101/2024.11.20.624597

[3] Morel, B., Schade, P., Lutteropp, S., Williams, T. A., Szöllősi, G. J., & Stamatakis, A. (2022). SpeciesRax: a tool for maximum likelihood species tree inference from gene family trees under duplication, transfer, and loss. Molecular biology and evolution, 39(2), msab365. https://doi.org/10.1093/molbev/msab365

[4] Zhang, C., & Mirarab, S. (2022). ASTRAL-Pro 2: ultrafast species tree reconstruction from multi-copy gene family trees. Bioinformatics, 38(21), 4949-4950. https://doi.org/10.1093/bioinformatics/btac620

[5] Weiner, S., Feng, Y., Gogarten, J. P., & Bansal, M. S. (2024, April). Assessing the potential of gene tree parsimony for microbial phylogenomics. In RECOMB International Workshop on Comparative Genomics (pp. 129-149). Cham: Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-58072-7_7

[6] Morel, B., Williams, T. A., Stamatakis, A., & Szöllősi, G. J. (2024). AleRax: a tool for gene and species tree co-estimation and reconciliation under a probabilistic model of gene duplication, transfer, and loss. Bioinformatics, 40(4), btae162. https://doi.org/10.1093/bioinformatics/btae162

Metabolism is the driving force of life and thereby plays a key role in understanding microbial functioning in monoculture and in ecosystems, from natural habitats to biotechnological applications, from microbiomes related to human health to food production. However, the complexity of metabolic networks poses a major challenge for understanding how they are shaped by evolution and how we can manipulate them. Therefore, many network-based methods have been developed to study metabolism.
With the vast increase of genomic data, genome-scale metabolic networks have become popular use. For these stoichiometric models, metabolic enzymes are predicted using genome data and subsequently algorithms are used to add reactions to construct a complete (biomass producing) metabolic network (e.g., Henry et al., 2010; Machado et al., 2018; see for an overview Mendoza et al., 2019). Many tools are being developed to make predictions with these models, usually variations of FBA (Orth et al., 2010), but also methods for community predictions (Scott Jr et al., 2023) and simulations in time and space (Bauer et al., 2017; Dukovski et al., 2021). The vast amount of sequencing data combined with the high-throughput possibilities of this method make it appealing, but there is a drawback: Namely that the automated construction of networks lacks accuracy and often curation is necessary before these models produce realistic and useful results. This is exemplified by recent studies of microbial metabolism that are better predicted by genome content only than by actual metabolic models (Gralka et al., 2023; Li et al., 2023).

On the other end are well-curated small-scale models of metabolic pathways. For those, knowledge of the enzymes of a pathway, their kinetic properties and (optionally) regulation by metabolites is incorporated in usually a differential equation model. Standard methods for systems of differential equations can be used to study steady-states and the dynamics of these models, which can lead to accurate predictions (Flamholz et al., 2013; van Heerden et al., 2014). However, the downside is that the methods are difficult to scale up and, for many enzymes, the detailed information necessary for these models is not available. Combined with computational challenges, these models are limited to specific pathways and cannot be used for whole cells, nor even communities. Therefore, there is still a need for both methods and models to make accurate predictions on a scale beyond single pathways.

Corrao et al. (2025) aim for an intermediate size model that is both accurate and predictive, does not need an extensive set of enzyme parameters, but also encompasses most of the cell’s metabolic pathways. As they phrase it: a model in the ‘Goldilocks’ zone. Curation can improve genome-scale models substantially but requires additional experimental data. However, as the authors show, even the well-curated model of Escherichia coli can sometimes show unrealistic metabolic flux patterns. A smaller model can be better curated and therefore more predictive, and more methods can be applied, as for example EFM based approaches. The authors show an extensive set of methodologies that can be applied to this model and yield interpretable results. Additionally, the model contains a wealth of standardized annotation that could set a standard for the field.

This is a first model of its kind, and it is not surprising that E. coli is used as its metabolism is very well-studied. However, this could set the basis for similar models for other well-studied organisms. Because the model is well-annotated and characterized, it is very suitable for testing new methods that make predictions with such an intermediate-sized model and that can later be extended for larger models. In the future, such models for different species could aid the creation of methods for studying and predicting metabolism in communities, for which there is a large need for applications (e.g. bioremediation and human health).

The different layers of annotation and the available code with clear documentation make this model an ideal resource as teaching material as well. Methods can be explained on this model, which can still be visualized and interpreted because of its reduced size, while it is large enough to show the differences between methods.

Although it might be too much to expect models of this type for all species, the different layers of annotation can be used to inspire better annotation of genome-scale models and enhance their accuracy and predictability. Thus, this paper sets a standard that could benefit research on metabolic pathways from individual strains to natural communities to communities for biotechnology, bioremediation and human health.

References

Bauer, E., Zimmermann, J., Baldini, F., Thiele, I., Kaleta, C., 2017. BacArena: Individual-based metabolic modeling of heterogeneous microbes in complex communities. PLOS Comput. Biol. 13, e1005544. https://doi.org/10.1371/journal.pcbi.1005544

Corrao, M., He, H., Liebermeister, W., Noor, E., Bar-Even, A., 2025. A compact model of Escherichia coli core and biosynthetic metabolism. arXiv, ver.4, peer-reviewed and recommended by PCI Mathematical and Computational Biology. https://doi.org/10.48550/arXiv.2406.16596

Dukovski, I., Bajić, D., Chacón, J.M., Quintin, M., Vila, J.C.C., Sulheim, S., Pacheco, A.R., Bernstein, D.B., Riehl, W.J., Korolev, K.S., Sanchez, A., Harcombe, W.R., Segrè, D., 2021. A metabolic modeling platform for the computation of microbial ecosystems in time and space (COMETS). Nat. Protoc. 16, 5030–5082. https://doi.org/10.1038/s41596-021-00593-3

Flamholz, A., Noor, E., Bar-Even, A., Liebermeister, W., Milo, R., 2013. Glycolytic strategy as a tradeoff between energy yield and protein cost. Proc. Natl. Acad. Sci. 110, 10039–10044. https://doi.org/10.1073/pnas.1215283110

Gralka, M., Pollak, S., Cordero, O.X., 2023. Genome content predicts the carbon catabolic preferences of heterotrophic bacteria. Nat. Microbiol. 8, 1799–1808. https://doi.org/10.1038/s41564-023-01458-z

Henry, C.S., DeJongh, M., Best, A.A., Frybarger, P.M., Linsay, B., Stevens, R.L., 2010. High-throughput generation, optimization and analysis of genome-scale metabolic models. Nat. Biotechnol. 28, 977–982. https://doi.org/10.1038/nbt.1672

Li, Z., Selim, A., Kuehn, S., 2023. Statistical prediction of microbial metabolic traits from genomes. PLOS Comput. Biol. 19, e1011705. https://doi.org/10.1371/journal.pcbi.1011705

Machado, D., Andrejev, S., Tramontano, M., Patil, K.R., 2018. Fast automated reconstruction of genome-scale metabolic models for microbial species and communities. Nucleic Acids Res. 46, 7542–7553. https://doi.org/10.1093/nar/gky537

Mendoza, S.N., Olivier, B.G., Molenaar, D., Teusink, B., 2019. A systematic assessment of current genome-scale metabolic reconstruction tools. Genome Biol. 20, 158. https://doi.org/10.1186/s13059-019-1769-1

Orth, J.D., Thiele, I., Palsson, B.Ø., 2010. What is flux balance analysis? Nat. Biotechnol. 28, 245–248. https://doi.org/10.1038/nbt.1614

Scott Jr, W.T., Benito-Vaquerizo, S., Zimmermann, J., Bajić, D., Heinken, A., Suarez-Diez, M., Schaap, P.J., 2023. A structured evaluation of genome-scale constraint-based modeling tools for microbial consortia. PLOS Comput. Biol. 19, e1011363. https://doi.org/10.1371/journal.pcbi.1011363

van Heerden, J.H., Wortel, M.T., Bruggeman, F.J., Heijnen, J.J., Bollen, Y.J.M., Planqué, R., Hulshof, J., O’Toole, T.G., Wahl, S.A., Teusink, B., 2014. Lost in Transition: Start-Up of Glycolysis Yields Subpopulations of Nongrowing Cells. Science 343, 1245114. https://doi.org/10.1126/science.1245114

The article by Bez et al [1] addresses an important issue for statisticians and ecological modellers: the impact of modelling choices when considering state-space models to represent time series with hidden regimes.

The authors present an empirical study of the impact of model misspecification for models in the HMM and HSMM family. The misspecification can be at the level of the hidden chain (Markovian or semi-Markovian assumption) or at the level of the observed chain (AR0 or AR1 assumption). 

The study uses data on the movements of fishing vessels. Vessels can exert pressure on fish stocks when they are fishing, and the aim is to identify the periods during which fishing vessels are fishing or not fishing, based on GPS tracking data. Two sets of data are available, from two vessels with contrasting fishing behaviour. The empirical study combines experiments on the two real datasets and on data simulated from models whose parameters are estimated on the real datasets. In both cases, the actual sequence of activities is available. The impact of a model misspecification is mainly evaluated on the restored hidden chain (decoding task), which is very relevant since in many applications we are more interested in the quality of decoding than in the accuracy of parameters estimation. Results on parameter estimation are also presented and metrics are developed to help interpret the results. The study is conducted in a rigorous manner and extensive experiments are carried out, making the results robust.

The main conclusion of the study is that choosing the wrong AR model at the observed sequence level has more impact than choosing the wrong model at the hidden chain level.

The article ends with an interesting discussion of this finding, in particular the impact of resolution on the quality of the decoding results. As the authors point out in this discussion, the results of this study are not limited to the application of GPS data to the activities of fishing vessels Beyond ecology, H(S)MMs are also widely used epidemiology, seismology, speech recognition, human activity recognition ... The conclusion of this study will therefore be useful in a wide range of applications. It is a warning that should encourage modellers to design their hidden Markov models carefully or to interpret their results cautiously.

References

[1] Nicolas Bez, Pierre Gloaguen, Marie-Pierre Etienne, Rocio Joo, Sophie Lanco, Etienne Rivot, Emily Walker, Mathieu Woillez, Stéphanie Mahévas (2024) Proper account of auto-correlations improves decoding performances of state-space (semi) Markov models. HAL, ver.3 peer-reviewed and recommended by PCI Math Comp Biol https://hal.science/hal-04547315v3