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

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

In the hereby recommended paper [1], Delaney, Letten and Engelstädter study the appearance of antibiotic resistance(s) in a bacterial population subject to a combination of two antibiotics \( A \) and \( B \), in concentrations \( C_A \) and \( C_B \) respectively. Their goal was to find optimal values of \( C_A \) and \( C_B \) that minimize the risk of evolutionary rescue, under the unusual assumption that resistance mutations to either antibiotic are not equally likely.

The authors introduce a stochastic model assuming that the susceptible population grows like a supercritical birth-death process which becomes subcritical in the presence of antibiotics (and exactly critical for a certain concentration c of a single antibiotic): the effect of each antibiotic is either to reduce division rate (bacteriostatic drug) or to enhance death rate (bacteriocidal drug) by a factor which has a sigmoid functional dependence on antibiotic concentration. 

Now at each division, a resistance mutation can arise, with probability \( \mu_A \) for a resistance to antibiotic \( A \) and with probability \( \mu_B \) for a resistance to antibiotic \( B \).

The goal of the paper is to find the optimal ratio of drug concentrations \( C_A \) and \( C_B \) when these are subject to a constrain \( C_A + C_B = c \), depending on the ratio of mutation rates. Assuming total resistance and no cross resistance, the authors show that the optimal concentrations are given by \( C_A = c/(1+\sqrt{\mu_A/\mu_B }) \) and \( C_B = c/(1+\sqrt{\mu_B/\mu_A}) \), which leads to the beautiful result that the optimal ratio \( C_A/C_B \) is equal to the square root of \( \mu_B/\mu_A \).

The authors have made a great job completing their initial submission by simulations of model extensions, relaxing assumptions like single antibiotic mode, absence of competition, absence of cost of resistance, sharp cutoff in toxicity… and comparing the results obtained by simulation to their mathematical result.

The paper is very clearly written and any reader interested in antibiotic resistance, stochastic modeling of bacterial populations and/or evolutionary rescue will enjoy reading it. Let me thank the authors for their patience and for their constant willingness to comply with the reviewers’ and recommender’s demands during the reviewing process. 

Reference

Oscar Delaney, Andrew D. Letten, Jan Engelstaedter (2025) Optimal antimicrobial dosing combinations when drug-resistance mutation rates differ. bioRxiv, ver.3 peer-reviewed and recommended by PCI Mathematical and Computational Biology https://doi.org/10.1101/2024.05.04.592498

VDJ recombination is a crucial process in the immune system, where a V (variable) gene, a D (diversity) gene, and a J (joining) gene are randomly combined to create unique antigen receptor genes. This process generates a vast diversity of antibodies and T-cell receptors, essential for recognizing and combating a wide array of pathogens. By identifying and quantifying these VDJ recombinations, we can gain a deeper and more precise understanding of the immune response, enhancing our ability to monitor and manage immune-related conditions.

It is therefore important to develop efficient methods to identify and extract VDJ recombinations from large sequences (e.g., several millions/billions of nucleotides). The work by Borée, Giraud, and Salson [2] contributes one such algorithm. As in previous work, the proposed algorithm employs the Aho-Corasick automaton to simultaneously match several patterns against a string but, differently from other methods, it also combines the efficiency of spaced seeds. Working with seeds rather than the original string has the net benefit of speeding up the algorithm and reducing its memory usage, sometimes at the price of a modest loss in accuracy. Experiments conducted on five different datasets demonstrate that these features grant the proposed method excellent practical performance compared to the best previous methods, like Vidjil [3] (up to 5X faster) and MiXCR [1] (up to 30X faster), with no quality loss.

The method can also be considered an excellent example of a more general trend in scalable algorithmic design: adapt "classic" algorithms (in this case, the Aho-Corasick pattern matching algorithm) to work in sketch space (e.g., the spaced seeds used here), trading accuracy for efficiency. Sometimes, this compromise is necessary for the sake of scaling to very large datasets using modest computing power.

References

[1] D. A. Bolotin, S. Poslavsky, I. Mitrophanov, M. Shugay, I. Z. Mamedov, E. V. Putintseva, and D. M. Chudakov (2015). "MiXCR: software for comprehensive adaptive immunity profiling." Nature Methods 12, 380–381. ISSN: 1548-7091. https://doi.org/10.1038/nmeth.3364

[2] C. Borée, M. Giraud, M. Salson (2024) "Alignment-free detection and seed-based identification of multi-loci V(D)J recombinations in Vidjil-algo". https://hal.science/hal-04361907v2, version 2, peer-reviewed and recommended by Peer Community In Mathematical and Computational Biology.

[3] M. Giraud, M. Salson, M. Duez, C. Villenet, S. Quief, A. Caillault, N. Grardel, C. Roumier, C. Preudhomme, and M. Figeac (2014). "Fast multiclonal clusterization of V(D)J recombinations from high-throughput sequencing". BMC Genomics 15, 409. https://doi.org/10.1186/1471-2164-15-409. 

As part of many bioinformatics tools, one encodes a k-mer, which is a string, into an integer. The natural encoding uses a bijective function to map the k-mers onto the interval [0, s^k - ], where s is the alphabet size. This encoding is minimal, in the sense that the encoded integer ranges from 0 to the number of represented k-mers minus 1. 

However, often one is only interested in encoding canonical k-mers. One common definition is that a k-mer is canonical if it is lexicographically not larger than its reverse complement. In this case, only about half the k-mers from the universe of k-mers are canonical, and the natural encoding is no longer minimal. For the special case of a DNA alphabet and odd k, there exists a "parity-based" encoding for canonical k-mers which is minimal. 

In [1], the author presents a minimal encoding for canonical k-mers that works for general alphabets and both odd and even k. They also give an efficient bit-based representation for the DNA alphabet. 

This paper fills a theoretically interesting and often overlooked gap in how to encode k-mers as integers. It is not yet clear what practical applications this encoding will have, as the author readily acknowledges in the manuscript. Neither the author nor the reviewers are aware of any practical situations where the lack of a minimal encoding "leads to serious limitations." However, even in an applied field like bioinformatics, it would be short-sighted to only value theoretical work that has an immediate application; often, the application is several hops away and not apparent at the time of the original work. 

In fact, I would speculate that there may be significant benefits reaped if there was more theoretical attention paid to the fact that k-mers are often restricted to be canonical. Many papers in the field sweep under the rug the fact that k-mers are made canonical, leaving it as an implementation detail. This may indicate that the theory to describe and analyze this situation is underdeveloped. This paper makes a step forward to develop this theory, and I am hopeful that it may lead to substantial practical impact in the future. 

References

[1] Roland Wittler (2023) "General encoding of canonical k-mers. bioRxiv, ver.2, peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology https://doi.org/10.1101/2023.03.09.531845