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

Paleoproteomics is a rapidly growing field with numerous challenges, many of which are due to the highly fragmented, modified, and degraded nature of ancient proteins. Though there are established standards for analysis, it is unclear how different software tools affect the identification and quantification of peptides, proteins, and post-translational modifications. To address this knowledge gap, Rodriguez Palomo et al. design a controlled system by experimentally degrading and purifying bovine beta-lactoglobulin, and then systematically compare the performance of many commonly used tools in its analysis.

They present comprehensive investigations of false discovery rates, open and narrow searches, de novo sequencing coverage bias and accuracy, and peptide chemical properties and bias. In each investigation, they explore wide ranges of appropriate tools and parameters, providing guidelines and recommendations for best practices. Based on their findings, Rodriguez Palomo et al. develop a proposed pipeline that is tailored for the analysis of ancient proteins. This pipeline is an important contribution to paleoproteomics and is likely to be of great value to the research community, as it is designed to enhance power, accuracy, and consistency in studies of ancient proteins.

References

Ismael Rodriguez-Palomo, Bharath Nair, Yun Chiang, Joannes Dekker, Benjamin Dartigues, Meaghan Mackie, Miranda Evans, Ruairidh Macleod, Jesper V. Olsen, Matthew J. Collins (2023) Benchmarking the identification of a single degraded protein to explore optimal search strategies for ancient proteins. bioRxiv, ver.3 peer-reviewed and recommended by PCI Math Comp Biol https://doi.org/10.1101/2023.12.15.571577

Insecticides are used to control crop pests and prevent severe crop losses. They are also a major cause of the current decline in biodiversity, contribute to climate change, and pollute soil and water, with consequences for human and environmental health [1]. The rationale behind the work of Malou et al [2] is that some pesticide application protocols can be improved by a better knowledge of the insects, their biology, their ecology and their real-time infestation dynamics in the fields. Thanks to a network of pheromone sensors and a mathematical method to derive the spatio-temporal distribution of pest populations from the signals, it is theoretically possible to adjust the time, dose and area of treatment and to use less pesticide with greater efficiency than an uninformed protocol.

Malou et al [2] focus on the mathematical problem, recognising that its real role in pest control would require work on its implementation and on a benefit-harm analysis. The problem is an "inverse problem" [3] in that it consists of inferring the presence of insects from the trail left by the pheromones, given a model of pheromone diffusion by insects. The main contribution of this work is the formulation and comparison of different regularisation terms in the optimisation inference scheme, in order to guide the optimisation by biological knowledge of specific pests, such as some parameters of population dynamics.

The accuracy and precision of the results are tested and compared on a simple toy example to test the ability of the model and algorithm to detect the source of the pheromones and the efficiency of the data assimilation principle. A further simulation is then carried out on a real plot with realistic parameters and rules based on knowledge of a maize pest. A repositioning of the sensors (informed by the results from the initial positions) is carried out during the test phase to allow better detection.

The work of Malou et al [2] is large, deep and complete. Its includes a detailed study of the numerical solutions of different data assimilation methods, as well as a theoretical reflection on how this work could contribute to agricultural and environmental issues.

References

[1] IPBES (2024). Thematic Assessment Report on the Underlying Causes of Biodiversity Loss and the Determinants of Transformative Change and Options for Achieving the 2050 Vision for Biodiversity of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services. O’Brien, K., Garibaldi, L., and Agrawal, A. (eds.). IPBES secretariat, Bonn, Germany. https://doi.org/10.5281/zenodo.11382215

[2] Thibault Malou, Nicolas Parisey, Katarzyna Adamczyk-Chauvat, Elisabeta Vergu, Béatrice Laroche, Paul-Andre Calatayud, Philippe Lucas, Simon Labarthe (2025) Biology-Informed inverse problems for insect pests detection using pheromone sensors. HAL, ver.2 peer-reviewed and recommended by PCI Math Comp Biol https://hal.inrae.fr/hal-04572831v2

[3] Isakov V (2017). Inverse Problems for Partial Differential Equations. Vol. 127. Applied Mathematical Sciences. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-51658-5.

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