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.

​​​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

In “Estimating dates of origin and end of COVID-19 epidemics”, Bénéteau et al. develop and apply a mathematical modeling approach to estimate the date of the origin of the SARS-CoV-2 epidemic in France. They also assess how long strict control measures need to last to ensure that the prevalence of the virus remains below key public health thresholds. This problem is challenging because the numbers of infected individuals in both tails of the epidemic are low, which can lead to errors when deterministic models are used. To achieve their goals, the authors developed a discrete stochastic model. The model is non-Markovian, meaning that individual infection histories influence the dynamics. The model also accounts for heterogeneity in the timing between infection and transmission and includes stochasticity as well as consideration of superspreader events. By comparing the outputs of their model with several alternative models, Bénéteau et al. were able to assess the importance of stochasticity, individual heterogeneity, and non-Markovian effects on the estimates of the dates of origin and end of the epidemic, using France as a test case. Some limitations of the study, which the authors acknowledge, are that the time from infection to death remains largely unknown, a lack of data on the heterogeneity of transmission among individuals, and the assumption that only a single infected individual caused the epidemic. Despite the acknowledged limitations of the work, the results suggest that cases may be detected long before the detection of an epidemic wave. Also, the approach may be helpful for informing public health decisions such as the necessary duration of strict lockdowns and for assessing the risks of epidemic rebound as restrictions are lifted. In particular, the authors found that estimates of the end of the epidemic following lockdowns are more sensitive to the assumptions of the models used than estimates of its beginning. In summary, this model adds to a valuable suite of tools to support decision-making in response to disease epidemics.

References

Bénéteau T, Elie B, Sofonea MT, Alizon S (2021) Estimating dates of origin and end of COVID-19 epidemics. medRxiv, 2021.01.19.21250080, ver. 3 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://doi.org/10.1101/2021.01.19.21250080

Published PSMC estimates of Neanderthal effective population size (𝑁e) show an approximately five-fold decline over the past 20,000 years [1]. This observation may be attributed to a true decline in Neanderthal 𝑁e, statistical error that is notorious with PSMC estimation, or geographic subdivision and gene flow that has been hypothesized to occur within the Neanderthal population. Determining which of these factors contributes to the observed decline in Neanderthal 𝑁e is an important question that can provide insight into human evolutionary history.

Though it is widely believed that the decline in Neanderthal 𝑁e is due to geographic subdivision and gene flow, no prior studies have theoretically examined whether these evolutionary processes can yield the observed pattern. In this paper [2], Rogers tackles this problem by employing two mathematical models to explore the roles of geographic subdivision and gene flow in the Neanderthal population. Results from both models show that geographic subdivision and gene flow can indeed result in a decline in 𝑁e that mirrors the observed decline estimated from empirical data. In contrast, Rogers argues that neither statistical error in PSMC estimates nor a true decline in 𝑁e are expected to produce the consistent decline in estimated 𝑁e observed across three distinct Neanderthal fossils. Statistical error would likely result in variation among these curves, whereas a true decline in 𝑁e would produce shifted curves due to the different ages of the three Neanderthal fossils.

In summary, Rogers provides convincing evidence that the most reasonable explanation for the observed decline in Neanderthal 𝑁e is geographic subdivision and gene flow. Rogers also provides a basis for understanding this observation, suggesting that 𝑁e declines over time because coalescence times are shorter between more recent ancestors, as they are more likely to be geographic neighbors. Hence, Rogers’ theoretical findings shed light on an interesting aspect of human evolutionary history.

References

[1] Fabrizio Mafessoni, Steffi Grote, Cesare de Filippo, Svante Pääbo (2020) “A high-coverage Neandertal genome from Chagyrskaya Cave”. Proceedings of the National Academy of Sciences USA 117: 15132- 15136. https://doi.org/10.1073/pnas.2004944117

[2] Alan Rogers (2024) “Genetic evidence for geographic structure within the Neanderthal population”. bioRxiv, version 4 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://doi.org/10.1101/2023.07.28.551046

Soraggi et al. [2] describe HMMploidy, a statistical method that takes DNA sequencing data as input and uses a hidden Markov model to estimate ploidy. The method allows ploidy to vary not only between individuals, but also between and even within chromosomes. This allows the method to detect aneuploidy and also chromosomal regions in which multiple paralogous loci have been mistakenly assembled on top of one another. 

HMMploidy estimates genotypes and ploidy simultaneously, with a separate estimate for each genome. The genome is divided into a series of non-overlapping windows (typically 100), and HMMploidy provides a separate estimate of ploidy within each window of each genome. The method is thus estimating a large number of parameters, and one might assume that this would reduce its accuracy. However, it benefits from large samples of genomes. Large samples increase the accuracy of internal allele frequency estimates, and this improves the accuracy of genotype and ploidy estimates. In large samples of low-coverage genomes, HMMploidy outperforms all other estimators. It does not require a reference genome of known ploidy. The power of the method increases with coverage and sample size but decreases with ploidy. Consequently, high coverage or large samples may be needed if ploidy is high. 

The method is slower than some alternative methods, but run time is not excessive. Run time increases with number of windows but isn't otherwise affected by genome size. It should be feasible even with large genomes, provided that the number of windows is not too large. The authors apply their method and several alternatives to isolates of a pathogenic yeast, Cryptococcus neoformans, obtained from HIV-infected patients. With these data, HMMploidy replicated previous findings of polyploidy and aneuploidy. There were several surprises. For example, HMMploidy estimates the same ploidy in two isolates taken on different days from a single patient, even though sequencing coverage was three times as high on the later day as on the earlier one. These findings were replicated in data that were down-sampled to mimic low coverage. 

Three alternative methods (ploidyNGS [1], nQuire, and nQuire.Den [3]) estimated the highest ploidy considered in all samples from each patient. The present authors suggest that these results are artifactual and reflect the wide variation in allele frequencies. Because of this variation, these methods seem to have preferred the model with the largest number of parameters. HMMploidy represents a new and potentially useful tool for studying variation in ploidy. It will be of most use in studying the genetics of asexual organisms and cancers, where aneuploidy imposes little or no penalty on reproduction. It should also be useful for detecting assembly errors in de novo genome sequences from non-model organisms.

References

[1] Augusto Corrêa dos Santos R, Goldman GH, Riaño-Pachón DM (2017) ploidyNGS: visually exploring ploidy with Next Generation Sequencing data. Bioinformatics, 33, 2575–2576. https://doi.org/10.1093/bioinformatics/btx204

[2] Soraggi S, Rhodes J, Altinkaya I, Tarrant O, Balloux F, Fisher MC, Fumagalli M (2022) HMMploidy: inference of ploidy levels from short-read sequencing data. bioRxiv, 2021.06.29.450340, ver. 6 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://doi.org/10.1101/2021.06.29.450340

[3] Weiß CL, Pais M, Cano LM, Kamoun S, Burbano HA (2018) nQuire: a statistical framework for ploidy estimation using next generation sequencing. BMC Bioinformatics, 19, 122. https://doi.org/10.1186/s12859-018-2128-z