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

Antimicrobial resistance (AMR) arises due to two main reasons: pathogens are either intrinsically resistant to the antimicrobials, or they can develop new resistance mechanisms in a continuous fashion over time and space. The latter has been referred to as within-host evolution of antimicrobial resistance and studied in infectious disease settings such as Tuberculosis [1]. During antibiotic treatment for example within-host evolutionary AMR dynamics plays an important role [2] and presents significant challenges in terms of optimizing treatment dosage. The study by Djidjou-Demasse et al. [3] contributes to addressing such challenges by developing a modelling approach that utilizes integro-differential equations to mathematically capture continuity in the space of the bacterial resistance levels.

Given its importance as a major public health concern with enormous societal consequences around the world, the evolution of drug resistance in the context of various pathogens has been extensively studied using population genetics approaches [4]. This problem has been also addressed using mathematical modelling approaches including Ordinary Differential Equations (ODE)-based [5. 6] and more recently Stochastic Differential Equations (SDE)-based models [7]. In [3] the authors propose a model of within-host AMR evolution in the absence and presence of drug treatment. The advantage of the proposed modelling approach is that it allows for AMR to be represented as a continuous quantitative trait, describing the level of resistance of the bacterial population termed quantitative AMR (qAMR) in [3]. Moreover, consistent with recent experimental evidence [2] integro-differential equations take into account both, the dynamics of the bacterial population density, referred to as “bottleneck size” in [2] as well as the evolution of its level of resistance due to drug-induced selection. 

The model proposed in [3] has been extensively and rigorously analysed to address various scenarios including the significance of host immune response in drug efficiency, treatment failure and preventive strategies. The drug treatment chosen to be investigated in this study, namely chemotherapy, has been characterised in terms of the level of evolved resistance by the bacterial population in presence of antimicrobial pressure at equilibrium.

Furthermore, the minimal duration of drug administration on bacterial growth and the emergence of AMR has been probed in the model by changing the initial population size and average resistance levels. A potential limitation of the proposed model is the assumption that mutations occur frequently (i.e. during growth), which may not be necessarily the case in certain experimental and/or clinical situations.

References

[1] Castro RAD, Borrell S, Gagneux S (2021) The within-host evolution of antimicrobial resistance in Mycobacterium tuberculosis. FEMS Microbiology Reviews, 45, fuaa071. https://doi.org/10.1093/femsre/fuaa071

[2] Mahrt N, Tietze A, Künzel S, Franzenburg S, Barbosa C, Jansen G, Schulenburg H (2021) Bottleneck size and selection level reproducibly impact evolution of antibiotic resistance. Nature Ecology & Evolution, 5, 1233–1242. https://doi.org/10.1038/s41559-021-01511-2

[3] Djidjou-Demasse R, Sofonea MT, Choisy M, Alizon S (2021) Within-host evolutionary dynamics of antimicrobial quantitative resistance. HAL, hal-03194023, ver. 4 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://hal.archives-ouvertes.fr/hal-03194023

[4] Wilson BA, Garud NR, Feder AF, Assaf ZJ, Pennings PS (2016) The population genetics of drug resistance evolution in natural populations of viral, bacterial and eukaryotic pathogens. Molecular Ecology, 25, 42–66. https://doi.org/10.1111/mec.13474

[5] Blanquart F, Lehtinen S, Lipsitch M, Fraser C (2018) The evolution of antibiotic resistance in a structured host population. Journal of The Royal Society Interface, 15, 20180040. https://doi.org/10.1098/rsif.2018.0040

[6] Jacopin E, Lehtinen S, Débarre F, Blanquart F (2020) Factors favouring the evolution of multidrug resistance in bacteria. Journal of The Royal Society Interface, 17, 20200105. https://doi.org/10.1098/rsif.2020.0105

[7] Igler C, Rolff J, Regoes R (2021) Multi-step vs. single-step resistance evolution under different drugs, pharmacokinetics, and treatment regimens (BS Cooper, PJ Wittkopp, Eds,). eLife, 10, e64116. https://doi.org/10.7554/eLife.64116

This article by Clenet et al. [1] tackles a fundamental mathematical model in ecology to understand the impact of the architecture of interactions on the equilibrium of the system.

The authors consider the classical Lotka-Volterra model, depicting the effect of interactions between species on their abundances. They focus on the case whenever there are numerous species, and where their interactions are compartmentalized in a block structure. Each block has a strength coefficient, applied to a random Gaussian matrix. This model aims at capturing the structure of interacting communities, with blocks describing the interactions within a community, and other blocks the interactions between communities.

In this general mathematical framework, the authors demonstrate sufficient conditions for the existence and uniqueness of a stable equilibrium, and conditions for which the equilibrium is feasible. Moreover, they derive statistical heuristics for the proportion, mean, and distribution of abundance of surviving species.
While the main text focuses on the case of two interacting communities, the authors provide generalizations to an arbitrary number of blocks in the appendix.

Overall, the article constitutes an original and solid contribution to the study of mathematical models in ecology. It combines mathematical analysis, dynamical system theory, numerical simulations, grounded with relevant hypothesis for the modeling of ecological systems.
The obtained results pave the way to further research, both towards further mathematical proofs on the model analysis, and towards additional model features relevant for ecology, such as spatial aspects.

References

[1] Maxime Clenet, François Massol, Jamal Najim (2023) Impact of a block structure on the Lotka-Volterra model. arXiv, ver.3 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://doi.org/10.48550/arXiv.2311.09470

​​​Determining if genes are orthologous (i.e. homologous genes whose most common ancestor represents a speciation) or paralogous (homologous genes whose most common ancestor represents a duplication) is a foundational problem in bioinformatics. For instance, the input to almost all phylogenetic methods is a sequence alignment of genes assumed to be orthologous.  Understanding if genes are paralogs or orthologs can also be important for assigning function, for example genes that have diverged following duplication may be more likely to have neofunctionalised or subfunctionalised compared to genes that have diverged following speciation, which may be more likely to have continued in a similar role.

This paper by Jones et al (2022) contributes to a wide range of literature addressing the inference of orthology/paralogy relations but takes a different approach to explaining inconsistency between an assumed species phylogeny and a relation graph (a graph where nodes represent genes and edges represent that the two genes are orthologs). Rather than assuming that inconsistencies are the result of incorrect assessment of orthology (i.e. incorrect edges in the relation graph) they ask if the relation graph could be consistent with a species tree combined with some amount of lateral (horizontal) gene transfer.

The two main questions addressed in this paper are (1) if a network N and a relation graph R are consistent, and (2) if – given a species tree S and a relation graph R – transfer arcs can be added to S in such a way that it becomes consistent with R? 

The first question hinges on the concept of a reconciliation between a gene tree and a network (section 2.1) and amounts to asking if a gene tree can be found that can both be reconciled with the network and consistent with the relation graph. The authors show that the problem is NP hard. Furthermore, the related problem of attempting to find a solution using k or fewer transfers is NP-hard, and also W[1] hard implying that it is in a class of problems for which fixed parameter tractable solutions have not been found. The proof of NP hardness is by reduction to the k-multi-coloured clique problem via an intermediate problem dubbed “antichain on trees” (Section 3). The “antichain on trees” construction may be of interest to others working on algorithmic complexity with phylogenetic networks.

In the second question the possible locations of transfers are not specified (or to put it differently any time consistent transfer arc is considered possible) and it is shown that it generally will be possible to add transfer edges to S in such a way that it can be consistent with R. However, the natural extension to this question of asking if it can be done with k or fewer added arcs is also NP hard.

Many of the proofs in the paper are quite technical, but the authors have relegated a lot of this detail to the appendix thus ensuring that the main ideas and results are clear to follow in the main text. I am grateful to both reviewers for their detailed reviews and through checking of the proofs.

References

Jones M, Lafond M, Scornavacca C (2022) Consistency of orthology and paralogy constraints in the presence of gene transfers. arXiv:1705.01240 [cs], ver. 6 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://arxiv.org/abs/1705.01240

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