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 [2] 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 [2] 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 [2]  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 [2] 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 [1].

Mazet  and  Noûs  [2]  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?

REFERENCES

[1] 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

[2] 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.

[3] 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.

The paper [1] 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 [2].

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.

REFERENCES

[1] 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. 
https://doi.org/10.1101/2020.05.06.058180

[2] 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

​​​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

Unlike a species tree, a gene tree results not only from speciation events, but also from events acting at the gene level, such as duplications and losses of gene copies, and gene transfer events [1]. The reconciliation of phylogenetic trees consists in embedding a given gene tree into a known species tree and, doing so, determining the location of these gene-level events on the gene tree [2]. Reconciled gene trees can be seen as phylogenetic trees where internal node labels are used to discriminate between different gene-level events. Comparing them is of foremost importance in order to assess the performance of various reconciliation methods (e.g. [3]).
A paper describing an extension of the widely used Robinson-Foulds (RF) distance [4] to trees with labeled internal nodes was presented earlier this year [5]. This distance, called ELRF, is based on edge edits and coincides with the RF distance when all internal labels are identical; unfortunately, the ELRF distance is very costly to compute. In the present paper [6], the authors introduce a distance called LRF, which is inspired by the TED (Tree Edit Distance [7]) and is based on node edits. As the ELRF, the new distance coincides with the RF distance for identically-labeled internal nodes, but has the additional desirable features of being computable in linear time. Also, in the ELRF distance, an edge can be deleted if only it connects nodes with the same label. The new formulation does not have this restriction, and this is, in my opinion, an improvement since the restriction makes little sense in the comparison of reconciled gene trees.
The authors show the pertinence of this new distance by studying the impact of taxon sampling on reconciled gene trees when internal labels are computed via a method based on species overlap. The linear algorithm to compute the LRF distance presented in the paper has been implemented and the software —written in Python— is freely available for the community to use it. I bet that the LRF distance will be widely used in the coming years!

References

[1] Maddison, W. P. (1997). Gene trees in species trees. Systematic biology, 46(3), 523-536. doi: https://doi.org/10.1093/sysbio/46.3.523
[2] Boussau, B., and Scornavacca, C. (2020). Reconciling gene trees with species trees. Phylogenetics in the Genomic Era, p. 3.2:1–3.2:23. [3] Doyon, J. P., Chauve, C., and Hamel, S. (2009). Space of gene/species trees reconciliations and parsimonious models. Journal of Computational Biology, 16(10), 1399-1418. doi: https://doi.org/10.1089/cmb.2009.0095
[4] Robinson, D. F., and Foulds, L. R. (1981). Comparison of phylogenetic trees. Mathematical biosciences, 53(1-2), 131-147. doi: https://doi.org/10.1016/0025-5564(81)90043-2
[5] Briand, B., Dessimoz, C., El-Mabrouk, N., Lafond, M. and Lobinska, G. (2020). A generalized Robinson-Foulds distance for labeled trees. BMC Genomics 21, 779. doi: https://doi.org/10.1186/s12864-020-07011-0
[6] Briand, S., Dessimoz, C., El-Mabrouk, N. and Nevers, Y. (2020) A linear time solution to the labeled Robinson-Foulds distance problem. bioRxiv, 2020.09.14.293522, ver. 4 peer-reviewed and recommended by PCI Mathematical and Computational Biology. doi: https://doi.org/10.1101/2020.09.14.293522
[7] Zhang, K., and Shasha, D. (1989). Simple fast algorithms for the editing distance between trees and related problems. SIAM journal on computing, 18(6), 1245-1262. doi: https://doi.org/10.1137/0218082

Significant progress has been made in developing computational methods to tackle the analysis of the numerous (genome-wide scale) metabolic networks that have been documented for a wide range of species. Understanding the behaviours of these complex reaction networks is crucial in various domains such as biotechnology and medicine.

Metabolic rewiring is essential as it enables cells to adapt their metabolism to changing environmental conditions. Identifying the metabolites around which metabolic rewiring occurs is certainly useful in the case of metabolic engineering, which relies on metabolic rewiring to transform micro-organisms into cellular factories [1], as well as in other contexts.

This paper by F. Mairet [2] introduces a method to disclose these metabolites, named switch nodes, relying on the analysis of the flux distributions for different input conditions. Basically, considering fluxes for different inputs, which can be computed using e.g. Parsimonious Flux Balance Analysis (pFBA), the proposed method consists in identifying metabolites involved in reactions whose different flux vectors are not collinear. The approach is supported by four case studies, considering core and genome-scale metabolic networks of Escherichia coli, Saccharomyces cerevisiae and the diatom Phaeodactylum tricornutum.

Whilst identified switch nodes may be biased because computed flux vectors satisfying given objectives are not necessarily unique, the proposed method has still a relevant predictive potential, complementing the current array of computational methods to study metabolism.

References

[1] Tao Yu, Yasaman Dabirian, Quanli Liu, Verena Siewers, Jens Nielsen (2019) Strategies and challenges for metabolic rewiring. Current Opinion in Systems Biology, Vol 15, pp 30-38. https://doi.org/10.1016/j.coisb.2019.03.004.

[2] Francis Mairet (2024) In silico identification of switching nodes in metabolic networks. bioRxiv, ver.3 peer-reviewed and recommended by PCI Math Comp Biol https://doi.org/10.1101/2023.05.17.541195