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

Unlike a species tree, a gene tree results not only from speciation events, but also from events acting at the gene level, such as duplications and losses of gene copies, and gene transfer events [1]. The reconciliation of phylogenetic trees consists in embedding a given gene tree into a known species tree and, doing so, determining the location of these gene-level events on the gene tree [2]. Reconciled gene trees can be seen as phylogenetic trees where internal node labels are used to discriminate between different gene-level events. Comparing them is of foremost importance in order to assess the performance of various reconciliation methods (e.g. [3]).
A paper describing an extension of the widely used Robinson-Foulds (RF) distance [4] to trees with labeled internal nodes was presented earlier this year [5]. This distance, called ELRF, is based on edge edits and coincides with the RF distance when all internal labels are identical; unfortunately, the ELRF distance is very costly to compute. In the present paper [6], the authors introduce a distance called LRF, which is inspired by the TED (Tree Edit Distance [7]) and is based on node edits. As the ELRF, the new distance coincides with the RF distance for identically-labeled internal nodes, but has the additional desirable features of being computable in linear time. Also, in the ELRF distance, an edge can be deleted if only it connects nodes with the same label. The new formulation does not have this restriction, and this is, in my opinion, an improvement since the restriction makes little sense in the comparison of reconciled gene trees.
The authors show the pertinence of this new distance by studying the impact of taxon sampling on reconciled gene trees when internal labels are computed via a method based on species overlap. The linear algorithm to compute the LRF distance presented in the paper has been implemented and the software —written in Python— is freely available for the community to use it. I bet that the LRF distance will be widely used in the coming years!

References

[1] Maddison, W. P. (1997). Gene trees in species trees. Systematic biology, 46(3), 523-536. doi: https://doi.org/10.1093/sysbio/46.3.523
[2] Boussau, B., and Scornavacca, C. (2020). Reconciling gene trees with species trees. Phylogenetics in the Genomic Era, p. 3.2:1–3.2:23. [3] Doyon, J. P., Chauve, C., and Hamel, S. (2009). Space of gene/species trees reconciliations and parsimonious models. Journal of Computational Biology, 16(10), 1399-1418. doi: https://doi.org/10.1089/cmb.2009.0095
[4] Robinson, D. F., and Foulds, L. R. (1981). Comparison of phylogenetic trees. Mathematical biosciences, 53(1-2), 131-147. doi: https://doi.org/10.1016/0025-5564(81)90043-2
[5] Briand, B., Dessimoz, C., El-Mabrouk, N., Lafond, M. and Lobinska, G. (2020). A generalized Robinson-Foulds distance for labeled trees. BMC Genomics 21, 779. doi: https://doi.org/10.1186/s12864-020-07011-0
[6] Briand, S., Dessimoz, C., El-Mabrouk, N. and Nevers, Y. (2020) A linear time solution to the labeled Robinson-Foulds distance problem. bioRxiv, 2020.09.14.293522, ver. 4 peer-reviewed and recommended by PCI Mathematical and Computational Biology. doi: https://doi.org/10.1101/2020.09.14.293522
[7] Zhang, K., and Shasha, D. (1989). Simple fast algorithms for the editing distance between trees and related problems. SIAM journal on computing, 18(6), 1245-1262. doi: https://doi.org/10.1137/0218082

Galtier [1] introduces “Aphid,” a new statistical method that estimates the contributions of gene flow (GF) and incomplete lineage sorting (ILS) to phylogenetic conflict.  Aphid is based on the observation that GF tends to make gene genealogies shorter, whereas ILS makes them longer.  Rather than fitting the full likelihood, it models the distribution of gene genealogies as a mixture of several canonical gene genealogies in which coalescence times are set equal to their expectations under different models. This simplification makes Aphid far faster than competing methods. In addition, it deals gracefully with bidirectional gene flow—an impossibility under competing models. Because of these advantages, Aphid represents an important addition to the toolkit of evolutionary genetics.

In the interest of speed, Aphid makes several simplifying assumptions. Yet even when these were violated, Aphid did well at estimating parameters from simulated data. It seems to be reasonably robust.

Aphid studies phylogenetic conflict, which occurs when some loci imply one phylogenetic tree and other loci imply another. This happens when the interval between successive speciation events is fairly short. If this interval is too short,  however,  Aphid’s approximations break down, and its estimates are biased. Galtier suggests caution when the fraction of discordant phylogenetic trees exceeds 50–55%. Thus, Aphids will be most useful when the interval between speciation events is short, but not too short.

Galtier applies the new method to three sets of primate data. In two of these data sets  (baboons and African apes), Aphid detects gene flow that would likely be missed by competing methods. These competing methods are primarily sensitive to gene flow that is asymmetric in two senses: (1) greater flow in one direction than the other, and (2) unequal gene flow connecting an outgroup to two sister species.  Aphid finds evidence of symmetric gene flow in the ancestry of baboons and also in that of African apes. The data suggest that ancestral humans and chimpanzees both interbred with ancestral gorillas, and at about the same rate.  Aphid’s ability to detect this signature sets it apart from competing methods.

References

[1]   Nicolas Galtier (2023) “An approximate likelihood method reveals ancient gene flow between human, chimpanzee and gorilla”. bioRxiv, ver. 3 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology.  https://doi.org/10.1101/2023.07.06.547897

It is often the case that scientific knowledge exists but is scattered across numerous experimental studies. Because of this dispersion in different formats, it remains difficult to access, extract, reproduce, confirm or generalise. This is the case in crop science, where Mahmoud et al [1] propose to collect and assemble data from numerous field experiments on intercropping.

It happens that the construction of the global dataset requires a lot of time, attention and a well thought-out method, inspired by the literature on data science [2] and adapted to the specificities of crop science. This activity also leads to new possibilities that were not available in individual datasets, such as the detection of full factorial designs using graph theory tools developed on top of the global dataset.

The study by Mahmoud et al [1] has thus multiple dimensions:

• The description of the solutions given to this data assembly challenge.
• The illustration of the usefulness of such procedure in a case study of 37 field experiments on cereal-legume associations. The dataset is publicly available [3], while some results obtained from it have been independently published elsewhere [e.g. 4].
• The description of an algorithm able to detect complete factorial designs.
• An informed discussion of the merits of global datasets compared to alternatives, in particular meta-analyses
• A documented reflection on scientific practices in the era of big data, guided by the principles of open science.

I was particularly interested in the promotion of the FAIR principles, perhaps used a little too uncritically in my view, as an obvious solution to data sharing. On the one hand, I am admiring and grateful for the availability of these data, some of which have never been published, nor associated with published results. This approach is likely to unearth buried treasures. On the other hand, I can understand the reluctance of some data producers to commit to total, definitive sharing, facilitating automatic reading, without having thought about a certain reciprocity on the part of users and use by artificial intelligence. Reciprocity in terms of recognition, as is discussed by Mahmoud et al [1], but also in terms of contribution to the commons [5] or reading conditions for machine learning.
But this is another subject, to be dealt with in the years to come, and for which, perhaps, the contribution recommended here will be enlightening.

References

[1] Mahmoud R., Casadebaig P., Hilgert N., Gaudio N. A workflow for processing global datasets: application to intercropping. 2024. ⟨hal-04145269v2⟩ ver. 2 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://hal.science/hal-04145269

[2] Wickham, H. 2014. Tidy data. Journal of Statistical Software 59(10) https://doi.org/10.18637/jss.v059.i10

[3] Gaudio, N., R. Mahmoud, L. Bedoussac, E. Justes, E.-P. Journet, et al. 2023. A global dataset gathering 37 field experiments involving cereal-legume intercrops and their corresponding sole crops. https://doi.org/10.5281/zenodo.8081577

[4] Mahmoud, R., Casadebaig, P., Hilgert, N. et al. Species choice and N fertilization influence yield gains through complementarity and selection effects in cereal-legume intercrops. Agron. Sustain. Dev. 42, 12 (2022). https://doi.org/10.1007/s13593-022-00754-y

[5] Bernault, C. « Licences réciproques » et droit d'auteur : l'économie collaborative au service des biens communs ?. Mélanges en l'honneur de François Collart Dutilleul, Dalloz, pp.91-102, 2017, 978-2-247-17057-9. https://shs.hal.science/halshs-01562241

The article, "Bayesian Joint-Regression Analysis of Unbalanced Series of On-Farm Trials," presents a Bayesian statistical framework tailored for analyzing highly unbalanced datasets from participatory plant breeding (PPB) trials, specifically wheat trials. The key goal of this research is to address the challenges of genotype-environment (G×E) interactions in on-farm trials, which often have limited replication and varied testing conditions across farms.

The study applies a hierarchical Bayesian model with Finlay-Wilkinson regression, which improves the estimation of G×E effects despite substantial data imbalance. By incorporating a Student’s t-distribution for residuals, the model is more robust to extreme values, which are common in on-farm trials due to variable environments.  Note that the model allows a detailed breakdown of variance, identifying environment effects as the most significant contributors, thus highlighting areas for future breeding focus. Using Hamiltonian Monte Carlo methods, the study achieves reasonable computation times, even for large datasets. 

Obviously, the limitation of the methods comes from the level of data balance and replication. The method requires a minimum level of data balance and replication, which can be a challenge in very decentralized breeding networks Moreover, the Bayesian framework, though computationally feasible, may still be complex for widespread adoption without computational resources or statistical expertise.

The paper presents a sophisticated Bayesian framework specifically designed to tackle the challenges of unbalanced data in participatory plant breeding (PPB). It showcases a novel way to manage the variability in on-farm trials, a common issue in decentralized breeding programs. 

This study's methods accommodate the inconsistencies inherent in on-farm trials, such as extreme values and minimal replication. By using a hierarchical Bayesian approach with a Student’s t-distribution for robustness, it provides a model that maintains precision despite these real-world challenges. This makes it especially relevant for those working in unpredictable agricultural settings or decentralized trials. From a more general perspective, this paper’s findings support breeding methods that prioritize specific adaptation to local conditions. It is particularly useful for researchers and practitioners interested in breeding for agroecological or organic farming systems, where G×E interactions are critical but hard to capture in traditional trial setups.

Beyond agriculture, the paper serves as an excellent example of advanced statistical modeling in highly variable datasets. Its applications extend to any field where data is incomplete or irregular, offering a clear case for hierarchical Bayesian methods to achieve reliable results.

Finally, although begin quite methodological, the paper provides practical insights into how breeders and researchers can work with farmers to achieve meaningful varietal evaluations.  

References

Michel Turbet Delof , Pierre Rivière , Julie C Dawson, Arnaud Gauffreteau , Isabelle Goldringer , Gaëlle van Frank , Olivier David (2024) Bayesian joint-regression analysis of unbalanced series of on-farm trials. HAL, ver.2 peer-reviewed and recommended by PCI Math Comp Biol https://hal.science/hal-04380787