|Id||Title||Authors||Abstract||Picture||Thematic fields||Recommender||Reviewers||Submission date|
02 May 2023
Population genetics: coalescence rate and demographic parameters inferenceOlivier Mazet, Camille Noûs https://doi.org/10.48550/arXiv.2207.02111
Estimates of Effective Population Size in Subdivided PopulationsRecommended by Alan Rogers based on reviews by 2 anonymous reviewers
We often use genetic data from a single site, or even a single individual, to estimate the history of effective population size, Ne, over time scales in excess of a million years. Mazet and Noûs  emphasize that such estimates may not mean what they seem to mean. The ups and downs of Ne may reflect changes in gene flow or selection, rather than changes in census population size. In fact, gene flow may cause Ne to decline even if the rate of gene flow has remained constant.
Consider for example the estimates of archaic population size in Fig. 1, which show an apparent decline in population size between roughly 700 kya and 300 kya. It is tempting to interpret this as evidence of a declining number of individuals, but that is not the only plausible interpretation.
Each of these estimates is based on the genome of a single diploid individual. As we trace the ancestry of that individual backwards into the past, the ancestors are likely to remain in the same locale for at least a generation or two. Being neighbors, there’s a chance they will mate. This implies that in the recent past, the ancestors of a sampled individual lived in a population of small effective size.
As we continue backwards into the past, there is more and more time for the ancestors to move around on the landscape. The farther back we go, the less likely they are to be neighbors, and the less likely they are to mate. In this more remote past, the ancestors of our sample lived in a population of larger effective size, even if neither the number of individuals nor the rate of gene flow has changed.
For awhile then, Ne should increase as we move backwards into the past. This process does not continue forever, because eventually the ancestors will be randomly distributed across the population as a whole. We therefore expect Ne to increase towards an asymptote, which represents the effective size of the entire population.
This simple story gets more complex if there is change in either the census size or the rate of gene flow. Mazet and Noûs  have shown that one can mimic real estimates of population history using models in which the rate of gene flow varies, but census size does not. This implies that the curves in Fig. 1 are ambiguous. The observed changes in Ne could reflect changes in census size, gene flow, or both.
For this reason, Mazet and Noûs  would like to replace the term “effective population size” with an alternative, the “inverse instantaneous coalescent rate,” or IIRC. I don’t share this preference, because the same critique could be made of all definitions of Ne. For example, Wright [3, p. 108] showed in 1931 that Ne varies in response to the sex ratio, and this implies that changes in Ne need not involve any change in census size. This is also true when populations are geographically structured, as Mazet and Noûs  have emphasized, but this does not seem to require a new vocabulary.
Figure 1: PSMC estimates of the history of population size based on three archaic genomes: two Neanderthals and a Denisovan .
Mazet and Noûs  also show that estimates of Ne can vary in response to selection. It is not hard to see why such an effect might exist. In genomic regions affected by directional or purifying selection, heterozygosity is low, and common ancestors tend to be recent. Such regions may contribute to small estimates of recent Ne. In regions under balancing selection, heterozygosity is high, and common ancestors tend to be ancient. Such regions may contribute to large estimates of ancient Ne. The magnitude of this effect presumably depends on the fraction of the genome under selection and the rate of recombination.
In summary, this article describes several processes that can affect estimates of the history of effective population size. This makes existing estimates ambiguous. For example, should we interpret Fig. 1 as evidence of a declining number of archaic individuals, or in terms of gene flow among archaic subpopulations? But these questions also present research opportunities. If the observed decline reflects gene flow, what does this imply about the geographic structure of archaic populations? Can we resolve the ambiguity by integrating samples from different locales, or using archaeological estimates of population density or interregional trade?
 Fabrizio Mafessoni et al. “A high-coverage Neandertal genome from Chagyrskaya Cave”. Proceedings of the National Academy of Sciences, USA 117.26 (2020), pp. 15132–15136. https://doi.org/10.1073/pnas.2004944117.
 Olivier Mazet and Camille Noûs. “Population genetics: coalescence rate and demographic parameters inference”. arXiv, ver. 2 peer-reviewed and recommended by Peer Community In Mathematical and Computational Biology (2023). https://doi.org/10.48550/ARXIV.2207.02111.
 Sewall Wright. “Evolution in mendelian populations”. Genetics 16 (1931), pp. 97–159. https://doi.org/10.48550/ARXIV.2207.0211110.1093/genetics/16.2.97.
|Population genetics: coalescence rate and demographic parameters inference||Olivier Mazet, Camille Noûs||<p style="text-align: justify;">We propose in this article a brief description of the work, over almost a decade, resulting from a collaboration between mathematicians and biologists from four different research laboratories, identifiable as the c...||Genetics and population Genetics, Probability and statistics||Alan Rogers||Joseph Lachance, Anonymous||2022-07-11 14:03:04||View|
18 Apr 2023
Cancer phylogenetic tree inference at scale from 1000s of single cell genomesSohrab Salehi, Fatemeh Dorri, Kevin Chern, Farhia Kabeer, Nicole Rusk, Tyler Funnell, Marc J Williams, Daniel Lai, Mirela Andronescu, Kieran R. Campbell, Andrew McPherson, Samuel Aparicio, Andrew Roth, Sohrab Shah, and Alexandre Bouchard-Côté https://doi.org/10.1101/2020.05.06.058180
Phylogenetic reconstruction from copy number aberration in large scale, low-depth genome-wide single-cell data.Recommended by Amaury Lambert based on reviews by 3 anonymous reviewers
The paper  presents and applies a new Bayesian inference method of phylogenetic reconstruction for multiple sequence alignments in the case of low sequencing coverage but diverse copy number aberrations (CNA), with applications to single cell sequencing of tumors.
The idea is to take advantage of CNA to reconstruct the topology of the phylogenetic tree of sequenced cells in a first step (the `sitka' method), and in a second step to assign single nucleotide variants (SNV) to tree edges (and then calibrate their lengths) (the `sitka-snv' method).
The data are summarized into a binary-valued CxL matrix Y, where C is the number of cells and L is the number of loci (here, loci are segments of prescribed length called `bins'). The entry of Y at row i and column j is 1 (otherwise 0) iff in the ancestral lineage of cell i, at least one genomic rearrangement has occurred, and more specifically the gain or loss of a segment with at least one endpoint in locus j or in locus j+1. The authors expect the infinite-allele assumption to approximately hold (i.e., that at most one mutation occurs at any given marker and that 0 is the ancestral state). They refer to this assumption as the `perfect phylogeny assumption'. By only recording from CNA events the endpoints at which they occur, the authors lose the information on copy number, but they gain the assumption of independence of the mutational processes occurring at different sites, which approximately holds for CNA endpoints.
The goal of sitka is to produce a posterior distribution on phylogenetic trees conditional on the matrix Y , where here a phylogenetic tree is understood as containing the information on 1) the topology of the tree but not its edge lengths, and 2) for each edge, the identity of markers having undergone a mutation, in the sense of the previous paragraph.
The results of the method are tested against synthetic datasets simulated under various assumptions, including conditions violating the perfect phylogeny assumption and compared to results obtained under other baseline methods. The method is extended to assign SNV to edges of the tree inferred by sitka. It is also applied to real datasets of single cell genomes of tumors.
The manuscript is very well-written, with a high degree of detail. The method is novel, scalable, fast and appears to perform favorably compared to other approaches. It has been applied in independent publications, for example to multi-year time-series single-cell whole-genome sequencing of tumors, in order to infer the fitness landscape and its dynamics through time, see .
The reviewing process has taken too long, mainly because of other commitments I had during the period and to the difficulty of finding reviewers. Let me apologize to the authors and thank them for their patience as well as for the scientific rigor they brought to their revisions and answers to reviewers, who I also warmly thank for their quality work.
 Sohrab Salehi, Fatemeh Dorri, Kevin Chern, Farhia Kabeer, Nicole Rusk, Tyler Funnell, Marc J Williams, Daniel Lai, Mirela Andronescu, Kieran R. Campbell, Andrew McPherson, Samuel Aparicio, Andrew Roth, Sohrab Shah, and Alexandre Bouchard-Côté. Cancer phylogenetic tree inference at scale from 1000s of single cell genomes (2023). bioRxiv, 2020.05.06.058180, ver. 4 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology.
 Sohrab Salehi, Farhia Kabeer, Nicholas Ceglia, Mirela Andronescu, Marc J. Williams, Kieran R. Campbell, Tehmina Masud, Beixi Wang, Justina Biele, Jazmine Brimhall, David Gee, Hakwoo Lee, Jerome Ting, Allen W. Zhang, Hoa Tran, Ciara O’Flanagan, Fatemeh Dorri, Nicole Rusk, Teresa Ruiz de Algara, So Ra Lee, Brian Yu Chieh Cheng, Peter Eirew, Takako Kono, Jenifer Pham, Diljot Grewal, Daniel Lai, Richard Moore, Andrew J. Mungall, Marco A. Marra, IMAXT Consortium, Andrew McPherson, Alexandre Bouchard-Côté, Samuel Aparicio & Sohrab P. Shah. Clonal fitness inferred from time-series modelling of single-cell cancer genomes (2021). Nature 595, 585–590. https://doi.org/10.1038/s41586-021-03648-3
|Cancer phylogenetic tree inference at scale from 1000s of single cell genomes||Sohrab Salehi, Fatemeh Dorri, Kevin Chern, Farhia Kabeer, Nicole Rusk, Tyler Funnell, Marc J Williams, Daniel Lai, Mirela Andronescu, Kieran R. Campbell, Andrew McPherson, Samuel Aparicio, Andrew Roth, Sohrab Shah, and Alexandre Bouchard-Côté||<p style="text-align: justify;">A new generation of scalable single cell whole genome sequencing (scWGS) methods allows unprecedented high resolution measurement of the evolutionary dynamics of cancer cell populations. Phylogenetic reconstruction ...||Evolutionary Biology, Genetics and population Genetics, Genomics and Transcriptomics, Machine learning, Probability and statistics||Amaury Lambert||2021-12-10 17:08:04||View|
14 Mar 2023
Marker and source-marker reprogramming of Most Permissive Boolean networks and ensembles with BoNesisLoïc Paulevé https://doi.org/10.48550/arXiv.2207.13307
Reprogramming of locally-monotone Boolean networks with BoNesisRecommended by Sergiu Ivanov based on reviews by Ismail Belgacem and 1 anonymous reviewer
Reprogramming of cellular networks is a well known challenge in computational biology consisting first of all in properly representing an ensemble of networks having a role in a phenomenon of interest, and secondly in designing strategies to alter the functioning of this ensemble in the desired direction. Important applications involve disease study: a therapy can be seen as a reprogramming strategy, and the disease itself can be considered a result of a series of adversarial reprogramming actions. The origins of this domain go back to the seminal paper by Barabási et al.  which formalized the concept of network medicine.
An abstract tool which has gathered considerable success in network medicine and network biology are Boolean networks: sets of Boolean variables, each equipped with a Boolean update function describing how to compute the next value of the variable from the values of the other variables. Despite apparent dissimilarity with the biological systems which involve varying quantities and continuous processes, Boolean networks have been very effective in representing biological networks whose entities are typically seen as being on or off. Particular examples are protein signalling networks as well as gene regulatory networks.
The paper  by Loïc Paulevé presents a versatile tool for tackling reprogramming of Boolean networks seen as models of biological networks. The problem of reprogramming is often formulated as the problem of finding a set of perturbations which guarantee some properties on the attractors. The work  relies on the most permissive semantics , which together with the modelling assumption allows for considerable speed-up in the practically relevant subclass of locally-monotone Boolean networks.
The paper is structured as a tutorial. It starts by introducing the formalism, defining 4 different general variants of reprogramming under the most permissive semantics, and presenting evaluations of their complexity in terms of the polynomial hierarchy. The author then describes the software tool BoNesis which can handle different problems related to Boolean networks, and in particular the 4 reprogramming variants. The presentation includes concrete code examples with their output, which should be very helpful for future users.
The paper  introduces a novel scenario: reprogramming of ensembles of Boolean networks delineated by some properties, including for example the property of having a given interaction graph. Ensemble reprogramming looks particularly promising in situations in which the biological knowledge is insufficient to fully determine all the update functions, i.e. in the majority of modelling situations. Finally, the author also shows how BoNesis can be used to deal with sequential reprogramming, which is another promising direction in computational controllability, potentially enabling more efficient therapies [4,5].
|Marker and source-marker reprogramming of Most Permissive Boolean networks and ensembles with BoNesis||Loïc Paulevé||<p style="text-align: justify;">Boolean networks (BNs) are discrete dynamical systems with applications to the modeling of cellular behaviors. In this paper, we demonstrate how the software BoNesis can be employed to exhaustively identify combinat...||Combinatorics, Computational complexity, Dynamical systems, Molecular Biology, Systems biology||Sergiu Ivanov||Ismail Belgacem, Anonymous||2022-08-31 15:00:21||View|
19 Sep 2022
HMMploidy: inference of ploidy levels from short-read sequencing dataSamuele Soraggi, Johanna Rhodes, Isin Altinkaya, Oliver Tarrant, Francois Balloux, Matthew C Fisher, Matteo Fumagalli https://doi.org/10.1101/2021.06.29.450340
Detecting variation in ploidy within and between genomesRecommended by Alan Rogers based on reviews by Barbara Holland, Benjamin Peter and Nicolas Galtier
Soraggi et al.  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 , nQuire, and nQuire.Den ) 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.
 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
 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
 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
|HMMploidy: inference of ploidy levels from short-read sequencing data||Samuele Soraggi, Johanna Rhodes, Isin Altinkaya, Oliver Tarrant, Francois Balloux, Matthew C Fisher, Matteo Fumagalli||<p>The inference of ploidy levels from genomic data is important to understand molecular mechanisms underpinning genome evolution. However, current methods based on allele frequency and sequencing depth variation do not have power to infer ploidy ...||Design and analysis of algorithms, Evolutionary Biology, Genetics and population Genetics, Probability and statistics||Alan Rogers||2021-07-01 05:26:31||View|
21 Feb 2022
Consistency of orthology and paralogy constraints in the presence of gene transfersMark Jones, Manuel Lafond, Celine Scornavacca https://arxiv.org/abs/1705.01240
Allowing gene transfers doesn't make life easier for inferring orthology and paralogyRecommended by Barbara Holland based on reviews by 2 anonymous reviewers
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 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.
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
|Consistency of orthology and paralogy constraints in the presence of gene transfers||Mark Jones, Manuel Lafond, Celine Scornavacca||<p style="text-align: justify;">Orthology and paralogy relations are often inferred by methods based on gene sequence similarity that yield a graph depicting the relationships between gene pairs. Such relation graphs frequently contain errors, as ...||Computational complexity, Design and analysis of algorithms, Evolutionary Biology, Graph theory||Barbara Holland||2021-06-30 15:01:44||View|
04 Feb 2022
Non-Markovian modelling highlights the importance of age structure on Covid-19 epidemiological dynamicsBastien Reyné, Quentin Richard, Camille Noûs, Christian Selinger, Mircea T. Sofonea, Ramsès Djidjou-Demasse, Samuel Alizon https://doi.org/10.1101/2021.09.30.21264339
Importance of age structure on modeling COVID-19 epidemiological dynamicsRecommended by Chen Liao based on reviews by Facundo Muñoz, Kevin Bonham and 1 anonymous reviewer
COVID-19 spread around the globe in early 2020 and has deeply changed our everyday life . Mathematical models allow us to estimate R0 (basic reproduction number), understand the progression of viral infection, explore the impacts of quarantine on the epidemic, and most importantly, predict the future outbreak . The most classical model is SIR, which describes time evolution of three variables, i.e., number of susceptible people (S), number of people infected (I), and number of people who have recovered (R), based on their transition rates . Despite the simplicity, SIR model produces several general predictions that have important implications for public health .
SIR model includes three populations with distinct labels and is thus compartmentalized. Extra compartments can be added to describe additional states of populations, for example, people exposed to the virus but not yet infectious. However, a model with more compartments, though more realistic, is also more difficult to parameterize and analyze. The study by Reyné et al.  proposed an alternative formalism based on PDE (partial differential equation), which allows modeling different biological scenarios without the need of adding additional compartments. As illustrated, the authors modeled hospital admission dynamics in a vaccinated population only with 8 general compartments.
The main conclusion of this study is that the vaccination level till 2021 summer was insufficient to prevent a new epidemic in France. Additionally, the authors used alternative data sources to estimate the age-structured contact patterns. By sensitivity analysis on a daily basis, they found that the 9 parameters in the age-structured contact matrix are most variable and thus shape Covid19 pandemic dynamics. This result highlights the importance of incorporating age structure of the host population in modeling infectious diseases. However, a relevant potential limitation is that the contact matrix was assumed to be constant throughout the simulations. To account for time dependence of the contact matrix, social and behavioral factors need to be integrated .
 Hu B, Guo H, Zhou P, Shi Z-L (2021) Characteristics of SARS-CoV-2 and COVID-19. Nature Reviews Microbiology, 19, 141–154. https://doi.org/10.1038/s41579-020-00459-7
 Jinxing G, Yongyue W, Yang Z, Feng C (2020) Modeling the transmission dynamics of COVID-19 epidemic: a systematic review. The Journal of Biomedical Research, 34, 422–430. https://doi.org/10.7555/JBR.34.20200119
 Tolles J, Luong T (2020) Modeling Epidemics With Compartmental Models. JAMA, 323, 2515–2516. https://doi.org/10.1001/jama.2020.8420
 Reyné B, Richard Q, Noûs C, Selinger C, Sofonea MT, Djidjou-Demasse R, Alizon S (2022) Non-Markovian modelling highlights the importance of age structure on Covid-19 epidemiological dynamics. medRxiv, 2021.09.30.21264339, ver. 3 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://doi.org/10.1101/2021.09.30.21264339
 Bedson J, Skrip LA, Pedi D, Abramowitz S, Carter S, Jalloh MF, Funk S, Gobat N, Giles-Vernick T, Chowell G, de Almeida JR, Elessawi R, Scarpino SV, Hammond RA, Briand S, Epstein JM, Hébert-Dufresne L, Althouse BM (2021) A review and agenda for integrated disease models including social and behavioural factors. Nature Human Behaviour, 5, 834–846 https://doi.org/10.1038/s41562-021-01136-2
|Non-Markovian modelling highlights the importance of age structure on Covid-19 epidemiological dynamics||Bastien Reyné, Quentin Richard, Camille Noûs, Christian Selinger, Mircea T. Sofonea, Ramsès Djidjou-Demasse, Samuel Alizon||<p style="text-align: justify;">The Covid-19 pandemic outbreak was followed by a huge amount of modelling studies in order to rapidly gain insights to implement the best public health policies. Most of these compartmental models involved ordinary ...||Dynamical systems, Epidemiology, Systems biology||Chen Liao||2021-10-04 13:49:51||View|
13 Dec 2021
Within-host evolutionary dynamics of antimicrobial quantitative resistanceRamsès Djidjou-Demasse, Mircea T. Sofonea, Marc Choisy, Samuel Alizon https://hal.archives-ouvertes.fr/hal-03194023
Modelling within-host evolutionary dynamics of antimicrobial resistanceRecommended by Krasimira Tsaneva based on reviews by 2 anonymous reviewers
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 . During antibiotic treatment for example within-host evolutionary AMR dynamics plays an important role  and presents significant challenges in terms of optimizing treatment dosage. The study by Djidjou-Demasse et al.  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 . 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 . In  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 . Moreover, consistent with recent experimental evidence  integro-differential equations take into account both, the dynamics of the bacterial population density, referred to as “bottleneck size” in  as well as the evolution of its level of resistance due to drug-induced selection.
The model proposed in  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.
 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
 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
 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
 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
 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
 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
 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
|Within-host evolutionary dynamics of antimicrobial quantitative resistance||Ramsès Djidjou-Demasse, Mircea T. Sofonea, Marc Choisy, Samuel Alizon||<p style="text-align: justify;">Antimicrobial efficacy is traditionally described by a single value, the minimal inhibitory concentration (MIC), which is the lowest concentration that prevents visible growth of the bacterial population. As a conse...||Dynamical systems, Epidemiology, Evolutionary Biology, Medical Sciences||Krasimira Tsaneva||2021-04-16 16:55:19||View|
07 Dec 2021
The emergence of a birth-dependent mutation rate in asexuals: causes and consequencesFlorian Patout, Raphaël Forien, Matthieu Alfaro, Julien Papaïx, Lionel Roques https://doi.org/10.1101/2021.06.11.448026
A new perspective in modeling mutation rate for phenotypically structured populationsRecommended by Yuan Lou based on reviews by Hirohisa Kishino and 1 anonymous reviewer
In standard mutation-selection models for describing the dynamics of phenotypically structured populations, it is often assumed that the mutation rate is constant across the phenotypes. In particular, this assumption leads to a constant diffusion coefficient for diffusion approximation models (Perthame, 2007 and references therein).
Patout et al (2021) study the dependence of the mutation rate on the birth rate, by introducing some diffusion approximations at the population level, derived from the large population limit of a stochastic, individual-based model. The reaction-diffusion model in this article is of the “cross-diffusion” type: The form of “cross-diffusion” also appeared in ecological literature as a type of biased movement behaviors for organisms (Shigesada et al., 1979). The key underlying assumption for “cross-diffusion” is that the transition probability at the individual level depends solely upon the condition at the departure point. Patout et al (2021) envision that a higher birth rate yields more mutations per unit of time. One of their motivations is that during cancer development, the mutation rates of cancer cells at the population level could be correlated with reproduction success.
The reaction-diffusion approximation model derived in this article illustrates several interesting phenomena: For the time evolution situation, their model predicts different solution trajectories under various assumptions on the fitness function, e.g. the trajectory could initially move towards the birth optimum but eventually end up at the survival optimum. Their model also predicts that the mean fitness could be flat for some period of time, which might provide another alternative to explain observed data. At the steady-state level, their model suggests that the populations are more concentrated around the survival optimum, which agrees with the evolution of the time-dependent solution trajectories.
Perhaps one of the most interesting contributions of the study of Patout et al (2021) is to give us a new perspective to model the mutation rate in phenotypically structured populations and subsequently, and to help us better understand the connection between mutation and selection. More broadly, this article offers some new insights into the evolutionary dynamics of phenotypically structured populations, along with potential implications in empirical studies.
Perthame B (2007) Transport Equations in Biology Frontiers in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7842-4_2
Patout F, Forien R, Alfaro M, Papaïx J, Roques L (2021) The emergence of a birth-dependent mutation rate in asexuals: causes and consequences. bioRxiv, 2021.06.11.448026, ver. 3 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://doi.org/10.1101/2021.06.11.448026
Shigesada N, Kawasaki K, Teramoto E (1979) Spatial segregation of interacting species. Journal of Theoretical Biology, 79, 83–99. https://doi.org/10.1016/0022-5193(79)90258-3
|The emergence of a birth-dependent mutation rate in asexuals: causes and consequences||Florian Patout, Raphaël Forien, Matthieu Alfaro, Julien Papaïx, Lionel Roques||<p style="text-align: justify;">In unicellular organisms such as bacteria and in most viruses, mutations mainly occur during reproduction. Thus, genotypes with a high birth rate should have a higher mutation rate. However, standard models of asexu...||Dynamical systems, Evolutionary Biology, Probability and statistics, Stochastic dynamics||Yuan Lou||Anonymous, Hirohisa Kishino||2021-06-12 13:59:45||View|
07 Sep 2021
The origin of the allometric scaling of lung ventilation in mammalsFrédérique Noël, Cyril Karamaoun, Jerome A. Dempsey, Benjamin Mauroy https://arxiv.org/abs/2005.12362
How mammals adapt their breath to body activity – and how this depends on body sizeRecommended by Wolfram Liebermeister based on reviews by Elad Noor, Oliver Ebenhöh, Stefan Schuster and Megumi Inoue
How fast and how deep do animals breathe, and how does this depend on how active they are? To answer this question, one needs to dig deeply into how breathing works and what biophysical processes it involves. And one needs to think about body size.
It is impressive how nature adapts the same body plan – e.g. the skeletal structure of mammals – to various shapes and sizes. From mice to whales, also the functioning of most organs remains the same; they are just differently scaled. Scaling does not just mean “making bigger or smaller”. As already noted by Galilei, body shapes change as they are adapted to body dimensions, and the same holds for physiological variables. Many such variables, for instance, heartbeat rates, follow scaling laws of the form y~x^a, where x denotes body mass and the exponent a is typically a multiple of ¼ . These unusual exponents – instead of multiples of ⅓, which would be expected from simple geometrical scaling – are why these laws are called “allometric”. Kleiber’s law for metabolic rates, with a scaling exponent of ¾, is a classic example . As shown by G. West, allometric laws can be explained through a few simple steps . In his models, he focused on network-like organs such as the vascular system and assumed that these systems show a self-similar structure, with a fixed minimal unit (for instance, capillaries) but varying numbers of hierarchy levels depending on body size. To determine the flow through such networks, he employed biophysical models and optimality principles (for instance, assuming that oxygen must be transported at a minimal mechanical effort), and showed that the solutions – and the physiological variables – respect the known scaling relations.
The paper “The origin of the allometric scaling of lung ventilation in mammals“ by Noël et al. , applies this thinking to the depth and rate of breathing in mammals. Scaling laws describing breathing in resting animals have been known since the 1950s , with exponents of 1 (for tidal volume) and -¼ (for breathing frequency). Equipped with a detailed biophysical model, Noël et al. revisit this question, extending these laws to other metabolic regimes. Their starting point is a model of the human lung, developed previously by two of the authors , which assumes that we meet our oxygen demand with minimal lung movements. To state this as an optimization problem, the model combines two submodels: a mechanical model describing the energetic effort of ventilation and a highly detailed model of convection and diffusion in self-similar lung geometries. Breathing depths and rates are computed by numerical optimization, and to obtain results for mammals of any size many of the model parameters are described by known scaling laws. As expected, the depth of breathing (measured by tidal volume) scales almost proportionally with body mass and increases with metabolic demand, while the breathing rate decreases with body mass, with an exponent of about -¼. However, the laws for the breathing rate hold only for basal activity; at higher metabolic rates, which are modeled here for the first time, the exponent deviates strongly from this value, in line with empirical data.
Why is this paper important? The authors present a highly complex model of lung physiology that integrates a wide range of biophysical details and passes a difficult test: the successful prediction of unexplained scaling exponents. These scaling relations may help us transfer insights from animal models to humans and in reverse: data for breathing during exercise, which are easy to measure in humans, can be extrapolated to other species. Aside from the scaling laws, the model also reveals physiological mechanisms. In the larger lung branches, oxygen is transported mainly by air movement (convection), while in smaller branches air flow is slow and oxygen moves by diffusion. The transition between these regimes can occur at different depths in the lung: as the authors state, “the localization of this transition determines how ventilation should be controlled to minimize its energetic cost at any metabolic regime”. In the model, the optimal location for the transition depends on oxygen demand [5, 6]: the transition occurs deeper in the lung in exercise regimes than at rest, allowing for more oxygen to be taken up. However, the effects of this shift depend on body size: while small mammals generally use the entire exchange surface of their lungs, large mammals keep a reserve for higher activities, which becomes accessible as their transition zone moves at high metabolic rates. Hence, scaling can entail qualitative differences between species!
Altogether, the paper shows how the dynamics of ventilation depend on lung morphology. But this may also play out in the other direction: if energy-efficient ventilation depends on body activity, and therefore on ecological niches, a niche may put evolutionary pressures on lung geometry. Hence, by understanding how deep and fast animals breathe, we may also learn about how behavior, physiology, and anatomy co-evolve.
 West GB, Brown JH, Enquist BJ (1997) A General Model for the Origin of Allometric Scaling Laws in Biology. Science 276 (5309), 122–126. https://doi.org/10.1126/science.276.5309.122
 Kleiber M (1947) Body size and metabolic rate. Physiological Reviews, 27, 511–541. https://doi.org/10.1152/physrev.1918.104.22.1681
 Noël F., Karamaoun C., Dempsey J. A. and Mauroy B. (2021) The origin of the allometric scaling of lung's ventilation in mammals. arXiv, 2005.12362, ver. 6 peer-reviewed and recommended by Peer community in Mathematical and Computational Biology. https://arxiv.org/abs/2005.12362
 Otis AB, Fenn WO, Rahn H (1950) Mechanics of Breathing in Man. Journal of Applied Physiology, 2, 592–607. https://doi.org/10.1152/jappl.1922.214.171.1242
 Noël F, Mauroy B (2019) Interplay Between Optimal Ventilation and Gas Transport in a Model of the Human Lung. Frontiers in Physiology, 10, 488. https://doi.org/10.3389/fphys.2019.00488
 Sapoval B, Filoche M, Weibel ER (2002) Smaller is better—but not too small: A physical scale for the design of the mammalian pulmonary acinus. Proceedings of the National Academy of Sciences, 99, 10411–10416. https://doi.org/10.1073/pnas.122352499
|The origin of the allometric scaling of lung ventilation in mammals||Frédérique Noël, Cyril Karamaoun, Jerome A. Dempsey, Benjamin Mauroy||<p>A model of optimal control of ventilation has recently been developed for humans. This model highlights the importance of the localization of the transition between a convective and a diffusive transport of respiratory gas. This localization de...||Biophysics, Evolutionary Biology, Physiology||Wolfram Liebermeister||2020-08-28 15:18:03||View|
27 Jul 2021
Estimating dates of origin and end of COVID-19 epidemicsThomas Bénéteau, Baptiste Elie, Mircea T. Sofonea, Samuel Alizon https://doi.org/10.1101/2021.01.19.21250080
The importance of model assumptions in estimating the dynamics of the COVID-19 epidemicRecommended by Valery Forbes based on reviews by Bastien Boussau and 1 anonymous reviewer
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.
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
|Estimating dates of origin and end of COVID-19 epidemics||Thomas Bénéteau, Baptiste Elie, Mircea T. Sofonea, Samuel Alizon||<p style="text-align: justify;">Estimating the date at which an epidemic started in a country and the date at which it can end depending on interventions intensity are important to guide public health responses. Both are potentially shaped by simi...||Epidemiology, Probability and statistics, Stochastic dynamics||Valery Forbes||2021-02-23 16:37:32||View|