Pith. sign in

REVIEW 5 major objections 5 minor 44 references

A simple stochastic model to describe the evolution over time of core genome SNP GC content in prokaryotes

T0 review · 5 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A stochastic model says microbial SNP GC content can accumulate quietly and then abruptly fluctuate out of control, driving extinction.

desk verdict The model is a mean-reverting OU process with bounded variance, so the paper's 'out of control' extinction claim is contradicted by its own equations, even though the SDE derivation itself is sound. read the letter →

arxiv 1908.09144 v1 pith:LTBULX7D submitted 2019-08-24 q-bio.PE

Jon Bohlin , Brittany Rose , Ola Brynildsrud , Birgitte Freiesleben De Blasio This is my paper · ORCID
classification q-bio.PE MSC 60H1060J6592D15
keywords SNPGCcontentcoregenomeprokaryotesstochasticdifferentialequationmutationrateswhitenoisesymbiontevolutionextinctionrisk
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper extends a deterministic equation for core-genome SNP GC content into a stochastic differential equation in time, adding the same white-noise disturbance to both the AT→GC and GC→AT mutation rates. The explicit solution expresses SNP GC content as a deterministic mean plus a stochastic integral, with variance growing in a prescribed exponential form. The authors use this to argue that in non-recombining prokaryotes, mutation rates can remain nearly constant for long stretches and then fluctuate violently, so a lineage's extinction may be set long before any visible change. If the model is right, stable-looking SNP composition is not evidence of safety.

What carries the argument

The engine is a linear stochastic differential equation, $dF_t = ((a-b)F_t + b)dt + dB_t$, obtained by assuming the same white-noise process is added to both mutation rates so the noise enters additively rather than multiplicatively. An integrating factor $e^{-(a-b)t}$ converts it into $d(e^{-(a-b)t}F_t)=be^{-(a-b)t}dt + e^{-(a-b)t}dB_t$, which yields the explicit solution by a stochastic integral; a semimartingale decomposition separates the bounded-variation part from the local martingale part. This machinery is what turns the biological assumption about changing mutation rates into concrete formulas for the mean and variance of SNP GC content.

What would settle it

Collect time-resolved core-genome SNP GC content from a non-recombining bacterial population and check the variance formula directly: under equation (9), Var($F_t$) must follow $(e^{2(a-b)t}-1)/(2(a-b))$ for estimated $a,b$, whereas an independent-noise SDE would give a variance that depends on $F_t(1-F_t)$. A clear match to the second form would falsify the shared-noise assumption and with it the paper's specific explosion dynamics.

Watch

Extended reading notes

Core claim

The paper's central claim is that the time evolution of core-genome SNP GC content, $F_t$, under random perturbations of the mutation rates is given by $F_t = -\frac{b}{a-b} + (F_0 + \frac{b}{a-b})e^{(a-b)t} + \int_0^t e^{(a-b)(t-s)}dB_s$, where $a$ is the AT→GC rate, $b$ the GC→AT rate, and $B_s$ a Brownian motion scaled by a factor $c$. From this solution the authors derive the mean $E(F_t)=F_0 e^{(a-b)t} + \frac{b}{a-b}(e^{(a-b)t}-1)$ and variance $\operatorname{Var}(F_t)=\frac{1}{2(a-b)}(e^{2(a-b)t}-1)$. They interpret sample paths of this process as showing that stochastic fluctuations can be negligible early and then grow abruptly, and they connect that pattern to irreversible accumulation of deleterious mutations in symbionts and to extinction. To keep the process from running away, the scaling $c$ and the size of $a-b$ must stay small, so the model predicts extinction rates differ across species and environments.

Load-bearing premise

The load-bearing premise is that the same random disturbance is added to both the AT→GC and GC→AT mutation rate, so the random parts cancel in the difference and the noise term does not depend on the current GC content; if the two rates fluctuated independently, the equation would change and the predicted fluctuation behavior would not follow.

Editorial extensions

If this is right

  • The mean trajectory of SNP GC content remains the old deterministic solution, so parameter estimation for $a$ and $b$ can ignore the martingale term.
  • When $a<b$, the variance of SNP GC content is bounded in the long run, yet individual lineages can show late, large excursions; extinction risk is therefore encoded early even if the observable composition looks static.
  • For a non-recombining lineage with very similar mutation rates ($a\approx b$), the noise term is magnified, so small changes in mutation rate balance can trigger abrupt fluctuation.
  • Applied to $R. salmoninarum$ lineage 1a, the estimated rates imply a GC→AT bias of almost 3:1, and the model attributes the roughly 20% rise in SNP GC content to a change in selective or environmental pressure.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the shared-noise assumption is relaxed to independent noises, the SDE gains an $F_t(1-F_t)$ diffusion coefficient; comparing the two fitted models on the same SNP dataset would give a direct statistical test of the paper's mechanism.
  • The model predicts that apparent stasis in SNP GC content is not reassuring: lineages with small $a-b$ or small noise scaling can look stable for long periods before a sudden transition, so surveillance should treat rate similarity and lineage age as risk factors.
  • The same SDE machinery could be applied to other compositional summaries, such as codon usage bias or AT skew, potentially revealing the same quiet-then-abrupt dynamics in other selective regimes.
  • The change-of-measure argument in the paper implies the paths are Brownian under an equivalent probability, which opens a likelihood-based route for parameter inference that the paper does not pursue.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper proposes a stochastic differential equation for the evolution of core-genome SNP GC content in prokaryotes, obtained by adding Gaussian white noise to the AT→GC and GC→AT mutation rates in a deterministic model. The main mathematical result is the explicit Itô solution (9), together with the mean (11) and variance (12). The authors interpret this solution as showing that mutation-driven fluctuations can first accumulate unnoticeably and then abruptly fluctuate out of control, ultimately causing extinction if not counteracted. They connect this interpretation to Muller's ratchet and the Red Queen hypothesis, and they fit the model to SNP GC data from Renibacterium salmoninarum, reporting an increase in SNP GC content in the globally disseminated sublineage 1a.

Significance. If the central interpretation were correct, the paper would contribute a simple stochastic model linking mutation-rate noise to genome degradation and extinction in non-recombining prokaryotes. Credit is due for the core Itô derivation: equation (9) and variance (12) are derived correctly for the additive-noise SDE that the authors set up, and the R. salmoninarum analysis is clearly described and reproducible in principle from the cited data. However, the paper's headline biological conclusion is not supported by the derived model: under the authors' own parameter restrictions the solution is a mean-reverting Ornstein–Uhlenbeck process with bounded variance, so the claimed 'out of control' fluctuations and extinction are an external interpretation, not a consequence of equation (9). The Girsanov section contains a further mathematical error, and the empirical support is circular because the fitted parameters force the model's equilibrium to match the observed 75% SNP GC content. These issues strike at the central claims, so the contribution as it stands does not establish its stated results.

major comments (5)
  1. [Section 2.2, Eq. (12)] Under the paper's own parameter restriction (a-b)<0, the variance in Eq. (12) converges to the finite constant 1/[2(b-a)] as t→∞, and the mean in Eq. (11) converges to b/(b-a)∈(0,1). Equation (9) therefore defines a mean-reverting Ornstein–Uhlenbeck process with bounded variance, and the abstract's claim that mutations can 'abruptly fluctuate out of control' is not a consequence of the model. The statement in Section 2.3 that the martingale term (15) 'approaches 0 as t→∞' is also incorrect: the Itô integral converges in distribution to a nondegenerate Gaussian law with variance 1/[2(b-a)], not to zero. If the c-scaling introduced in Section 2.1 is included, the variance is still bounded, so the conclusion is unchanged.
  2. [Section 2.4] The claim that Z_t = ∫_0^t e^{(a-b)(t-s)} d\hat B_s is a martingale is false. By Itô's formula, dZ_t = (a-b)Z_t dt + d\hat B_t, so Z_t has nonzero drift and is not a martingale; consequently K_t, which contains a deterministic exponential term plus θZ_t, is also not a martingale. This invalidates the stated Doob–Meyer justification for the Girsanov change of measure. For fixed finite T the exponential martingale condition may still be checkable, so the error is in the reported reasoning rather than necessarily in the final Girsanov statement, but the reasoning as written is incorrect.
  3. [Section 3.1, Figure 1, Eqs. (11)-(12)] The text claims that fluctuations grow with time and that they 'start sooner and escalate a bit more' for low values of c, but c multiplies the Brownian term linearly, so lower c reduces the variance of F_t at every t. The variance formula (12) as printed contains no c at all; with the c-scaled Brownian motion from Section 2.1 the variance becomes c^2/(2(b-a))(1-e^{2(a-b)t}), which is decreasing in c. The claimed c-dependence is therefore internally inconsistent with the model's own solution.
  4. [Section 2.1] The derivation of the additive-noise SDE depends on the assumption that the same white noise process W_t is added to both mutation rates, α=a+W_t and β=b+W_t, so that the noise terms F_t W_t and (1-F_t)W_t cancel exactly. If the two mutation rates were perturbed by independent noise processes, the diffusion coefficient would depend on F_t, the explicit solution (9) would no longer be valid, and the fluctuation behavior would be different. This shared-noise assumption is not biologically motivated or tested, and because Eq. (9) is the basis of the paper's conclusions, it is a load-bearing modeling choice rather than a harmless simplification.
  5. [Section 3.5 and Eq. (11)] The empirical support for the model is circular. The parameters a and b are estimated from the R. salmoninarum sublineage 1a data, and the model's long-run mean b/(b-a) with the posterior medians a=-22.668 and b=67.421 is approximately 0.748, matching the observed ≈75% SNP GC content by construction. The reported 'substantial increase' from 56.5% to 75% is therefore not an independent prediction of the model; it is the equilibrium implied by parameters fitted to the same data. In addition, sublineage 1b (3 isolates) and lineage 2 (7 isolates) are very small samples, and this limitation is not discussed.
minor comments (5)
  1. [Section 2.1, Eq. (6)] In equation (6) both partial derivatives are written as ∂g/∂t; the second should be ∂g/∂x.
  2. [Section 3.3] The sentence 'The model in (15) was formulated in a recent study [2]' appears to refer to the martingale term (15), but the deterministic model from [2] is equation (1), not (15).
  3. [Figure 1] The four panels use different vertical-axis ranges, which makes visual comparisons of fluctuation magnitudes across parameter sets difficult and can exaggerate the apparent 'explosion' for small c.
  4. [Section 2.3] The sentence 'Since we assume (a-b)<0, the martingale term approaches 0 as t→∞ and Brownian motion \hat B_t(ω) for a=b' is grammatically incomplete and mathematically misleading; it should be rewritten and corrected.
  5. [Section 2.3, Eq. (16)] The numerical Itô sum should be written more carefully: the increment should be the Brownian increment, not white noise multiplied by Δs_i, and the notation for the scaled Brownian motion should be defined consistently.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the SDE derivation is self-contained, and the fitted parameters are used for estimation, not presented as out-of-sample predictions.

full rationale

The paper derives equation (9) directly from the stated stochastic differential equation dF_t = ((a-b)F_t + b)dt + d\hat B_t using Itô calculus and an integrating factor; this derivation does not assume the result it claims to obtain. The R. salmoninarum analysis fits a and b to the observed SNP GC data, and the long-run mean b/(b-a) is a deterministic function of those fitted values, but the paper does not present that mean as an independent model prediction or as validation of the model against the same data. It reports the observed 75% SNP GC content first and then estimates parameters from that lineage, so the agreement between the fitted equilibrium and the observed value is a property of the fit, not a circularly derived prediction. The citations to the authors' prior work [2,3,20] provide the original ODE form, comparative rate observations, and the genomic data set; the central SDE solution and its interpretation do not reduce to an unverified self-cited theorem. Separate mathematical concerns about the boundedness of the variance and the validity of the Girsanov argument are correctness issues, not circularity, and therefore do not affect this circularity score.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The model rests on the same-noise simplification and on parameters fitted to the same lineage used for illustration; no independent entities are introduced.

free parameters (4)
  • a = -22.668 (R. salmoninarum median posterior)
    Called AT→GC mutation rate; estimated by Bayesian inference in Section 3.5; sign is negative, so not a literal rate.
  • b = 67.421 (R. salmoninarum median posterior)
    Called GC→AT mutation rate; estimated by Bayesian inference; positive.
  • c = 1 for R. salmoninarum; varied in simulations
    Brownian scaling coefficient; chosen by hand, not estimated.
  • F0 = 0.565 (R. salmoninarum)
    Initial SNP GC content set equal to genomic GC content; chosen, not estimated.
assumptions (5)
  • standard math F_t is a continuous semimartingale, allowing Doob-Meyer decomposition and Itô calculus.
    Invoked in Section 2.1 to justify the SDE formulation.
  • domain assumption Chargaff's second parity rule holds for core genome SNPs, so SNP AT content equals 1 - F_t.
    Stated in Introduction and Section 1; empirical deviations of 2-5% are reported in Methods.
  • ad hoc to paper The same Gaussian white noise W_t perturbs both mutation rates α and β.
    This assumption in Section 2.1 is not biologically motivated and is the key simplification that makes the noise additive.
  • domain assumption The drift term is linear in F_t, inherited from the earlier model [2].
    Equation (1) is taken from prior work without re-derivation.
  • domain assumption 0 < E(F_t) < 1 for all t, imposing a<0, b>0 and (a-b)<0.
    Section 2.2 uses this to constrain parameters; yields negative 'AT→GC rate'.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A simple stochastic model to describe the evolution over time of core genome SNP GC content in prokaryotes." pith.science (2026). https://pith.science/paper/LTBULX7D

@misc{pith2026190809144,
  author       = {Pith},
  title        = {Pith review of: A simple stochastic model to describe the evolution over time of core genome SNP GC content in prokaryotes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LTBULX7D}},
  note         = {Machine review of arXiv:1908.09144}
}
read the original abstract

Genomes in living organisms consist of the nucleotides adenine (A), guanine (G), cytosine (C) and thymine (T). All prokaryotes have genomes consisting of double-stranded DNA, where the A's and G's (purines) of one strand bind respectively to the T's and C's (pyrimidines) of the other. As such, the number of A's on one strand nearly equals the number of T's on the other, and the same is true of one strand's G's and the other's C's. Globally, this relationship is formalized as Chargaff's first parity rule; its strandwise equivalent is Chargaff's second parity rule. Therefore, the GC content of any double-stranded DNA genome can be expressed as %GC=100%-%AT. Variation in prokaryotic GC content can be substantial between taxa but is generally small within microbial genomes. This variation has been found to correlate with both phylogeny and environmental factors. Since novel single-nucleotide polymorphisms (SNPs) within genomes are at least partially linked to the environment, SNP GC content can be considered a compound measure of an organism's environmental influences, lifestyle and phylogeny. We present a mathematical model that describes how SNP GC content in microbial genomes evolves over time as a function of the AT->GC and GC->AT mutation rates with Gaussian white noise disturbances. The model suggests that, in non-recombining bacteria, mutations can first accumulate unnoticeably and then abruptly fluctuate out of control. Thus, minuscule variations in mutation rates can suddenly become unsustainable, ultimately driving a species to extinction if not counteracted early enough. This model, which is suited specifically to symbiotic prokaryotes, conforms to scenarios predicted by Muller's ratchet and may suggest that this is not always a gradual, degrading process.

Figures

Figures reproduced from arXiv: 1908.09144 by the authors.

Figure 1
Figure 1. The model (9) with different combinations of paramet [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. R. salmoninarum lineage 1a SNP GC content (vertical axis) plot￾ted against year (horizontal axis). SNP GC content of lineages 1b and 2 is similar to R. salmoninarum genomic GC content (red line). disintegrate due to accumulated hitchhiking effects [37] and genetic drift, as posited by Muller’s ratchet [22]. There are experimental findings to support these hypotheses [44]. Our model in (9) provides insight to this by… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

44 extracted references · 44 canonical work pages

  1. [1]

    P., & Feil, E

    Rocha, E. P., & Feil, E. J. (2010). Mutational patterns cannot explain genome composition: are there any neutral sites in the genom es of bac- teria? PLoS genetics, 6(9) e1001104

    work page 2010

  2. [2]

    Bohlin, J., Eldholm, V., Brynildsrud, O., Petterson, J. H. O., & Alfsnes, K. Modeling of the GC content of the substituted bases in bacter ial core genomes. BMC genomics, 19(1) 589 (2018) 17

    work page 2018

  3. [3]

    Bohlin, J., Rose, B., & Petterson, J. H. O. Estimation of AT and GC content distributions of nucleotide substitution rates in bacterial core genomes. Big Data Analytics, – — (2019)

    work page 2019

  4. [4]

    Positive correla- tions between genomic % AT and genome size within strains of b acterial species

    Bohlin, J., Sekse, C., Skjerve, E., & Brynildsrud, O. Positive correla- tions between genomic % AT and genome size within strains of b acterial species. Environmental microbiology reports, 6(3) 278-286 (2014)

    work page 2014

  5. [5]

    The evolution of bacterial DNA base compo- sition

    Agashe, D., & Shankar, N. The evolution of bacterial DNA base compo- sition. Journal of Experimental Zoology Part B: Molecular and Devel - opmental Evolution, 322(7) 517-528 (2014)

    work page 2014

  6. [6]

    D., & Parkhill, J

    Bentley, S. D., & Parkhill, J. Comparative genomic structure of prokary- otes. Annu. Rev. Genet., 38 771-791 (2004)

    work page 2004

  7. [7]

    Hershberg, R., & Petrov, D. A. Evidence that mutation is universally biased towards AT in bacteria. PLoS genetics, 6(9) e1001115 (2010)

    work page 2010

  8. [8]

    P., & Moran, N

    McCutcheon, J. P., & Moran, N. A. Extreme genome reduction in sym- biotic bacteria. Nature Reviews Microbiology, 10(1) 13 (2012)

    work page 2012

Show all 44 references
  1. [9]

    Wernegreen, J. J. In it for the long haul: Evolutionary consequences of persistent endosymbiosis. Current opinion in genetics & development, 47 83-90 (2017)

    2017

  2. [10]

    S., Gout, J

    Lynch, M., Ackerman, M. S., Gout, J. F., Long, H., Sung, W ., Thomas, W. K., & Foster, P. L. Genetic drift, selection and the evolution of the mutation rate. Nature Reviews Genetics, 17(11) 704 (2016)

    2016

  3. [11]

    A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide s equences

    Kimura, M. A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide s equences. Jour- nal of Molecular Evolution, 16(2) 111-120 (1980)

    1980

  4. [12]

    U., Von Mering, C., Hooper, S

    Foerstner, K. U., Von Mering, C., Hooper, S. D., & Bork, P . Envi- ronments shape the nucleotide composition of genomes. EMBO reports, 6(12) 1208-1213 (2005)

    2005

  5. [13]

    R., Rosen, G., Hershberg, U., & Hersh berg, R

    Reichenberger, E. R., Rosen, G., Hershberg, U., & Hersh berg, R. Prokaryotic nucleotide composition is shaped by both phylo geny and the environment. Genome biology and evolution, 7(5) 1380-1389 (2015)

    2015

  6. [14]

    A., & Andersson, D

    Lind, P. A., & Andersson, D. I. Whole-genome mutational biases in bacteria. Proceedings of the National Academy of Sciences, 105(46) 17878-17883 (2008)

    2008

  7. [15]

    D., & Ochman, H

    Raghavan, R., Kelkar, Y. D., & Ochman, H. A selective force favoring increased G+C content in bacterial genes. Proceedings of the National Academy of Sciences, 109(36) 14504-14507 (2012) 18

    2012

  8. [16]

    A., & Kelly, S

    Seward, E. A., & Kelly, S. Dietary nitrogen alters codon bias and genome composition in parasitic microorganisms. Genome biology, 17(1) 226

  9. [17]

    Hildebrand, F., Meyer, A., & Eyre-Walker, A. (2010). Evidence of selec- tion upon genomic GC-content in bacteria. PLoS genetics, 6(9) e1001107 (2016)

    2010

  10. [18]

    H., Brynildsru d, O., & Snipen, L

    Bohlin, J., Eldholm, V., Pettersson, J. H., Brynildsru d, O., & Snipen, L. The nucleotide composition of microbial genomes indicates d ifferential patterns of selection on core and accessory genomes. BMC genomics, 18(1) 151 (2017)

    2017

  11. [19]

    M., & Ochman, H

    Bobay, L. M., & Ochman, H. Impact of recombination on the base composition of bacteria and archaea. Molecular biology and evolution, 34(10) 2627-2636 (2017)

    2017

  12. [20]

    J., Bohlin, J., Castillo-Ram irez, S., Colquhoun, D., McCarthy, U.,

    Brynildsrud, O., Feil, E. J., Bohlin, J., Castillo-Ram irez, S., Colquhoun, D., McCarthy, U., ... & Verner-Jeffreys, D. W. Microevolution of Reni- bacterium salmoninarum: evidence for intercontinental di ssemination associated with fish movements. The ISME journal, 8(4) 746 (2014)

    2014

  13. [21]

    The energetics of genome complexity

    Lane, N., & Martin, W. The energetics of genome complexity. Nature, 467(7318) 929 (2010)

    2010

  14. [22]

    Moran, N. A. Accelerated evolution and Muller’s rachet in endosymbi- otic bacteria. Proceedings of the National Academy of Sciences, 93(7) 2873-2878 (1996)

    1996

  15. [23]

    A new evolutionary law

    Van Valen, L. A new evolutionary law. Evol Theory, 1 1-30 (1973)

    1973

  16. [24]

    Molecular evolution as predicted by natural selection

    Van Valen, L. Molecular evolution as predicted by natural selection. Journal of molecular evolution, 3(2) 89-101 (1974)

    1974

  17. [25]

    Protter, P. E. Stochastic differential equations Springer, Berlin, Heidel- berg

  18. [26]

    Øksendal, B. (2003). Stochastic differential equations. Springer, Berlin, Heidelberg (2005)

    2003

  19. [27]

    Regularities in the composition of pentose nucleic acids

    Elson, D., & Chargaff, E. Regularities in the composition of pentose nucleic acids. Nature, 173(4413) 1037 (1954)

    1954

  20. [28]

    A., & Bennett, G

    Moran, N. A., & Bennett, G. M. The tiniest tiny genomes. Annual review of microbiology, 68 195-215 (2014)

    2014

  21. [29]

    The unpredictable road to reduction

    Klasson, L. The unpredictable road to reduction. Nature ecology & evo- lution, 1(8) 1062 (2017) 19

    2017

  22. [30]

    , & Fukatsu, T

    Hosokawa, T., Ishii, Y., Nikoh, N., Fujie, M., Satoh, N. , & Fukatsu, T. Obligate bacterial mutualists evolving from environmenta l bacteria in natural insect populations. Nature microbiology, 1(1) 15011 (2016)

    2016

  23. [31]

    J., Reyes-Prieto, M., Mart ´ ınez-Romero, E., Partida- Mart ´ ınez, L

    Mart ´ ınez-Cano, D. J., Reyes-Prieto, M., Mart ´ ınez-Romero, E., Partida- Mart ´ ınez, L. P., Latorre, A., Moya, A., & Delaye, L. Evolution of small prokaryotic genomes. Frontiers in microbiology, 5 742 (2015)

    2015

  24. [32]

    Reductive genome evolution at both ends of the bacterial population size spec trum

    Batut, B., Knibbe, C., Marais, G., & Daubin, V. Reductive genome evolution at both ends of the bacterial population size spec trum. Nature Reviews Microbiology, 12(12) 841 (2014)

    2014

  25. [33]

    Wernegreen, J. J. Endosymbiont evolution: predictions from theory and surprises from genomes. Annals of the New York Academy of Sciences, 1360(1) 16-35 (2015)

    2015

  26. [34]

    H., & Keeling, P

    Boscaro, V., Kolisko, M., Felletti, M., Vannini, C., Ly nn, D. H., & Keeling, P. J. Parallel genome reduction in symbionts descended from closely related free-living bacteria. Nature ecology & evolution, 1(8) 1160 (2017)

    2017

  27. [35]

    Bacterial intra-species gene loss occurs in a largely clocklike manner mostly within a pool of less con served and constrained genes

    Bolotin, E., & Hershberg, R. Bacterial intra-species gene loss occurs in a largely clocklike manner mostly within a pool of less con served and constrained genes. Scientific reports, 6 35168 (2016)

    2016

  28. [36]

    A., & Welch, J

    Weinert, L. A., & Welch, J. J. Why might bacterial pathogens have small genomes? Trends in ecology & evolution, 32(12) 936-947 (2017)

    2017

  29. [37]

    M., & Haigh, J

    Smith, J. M., & Haigh, J. The hitch-hiking effect of a favourable gene. Genetics Research, 23(1) 23-35 (1974)

    1974

  30. [38]

    Mapping short DNA sequencing reads and calling variants using mapping quality scores

    Li, H., Ruan, J., & Durbin, R. Mapping short DNA sequencing reads and calling variants using mapping quality scores. Genome research, gr- 078212 (2008)

    2008

  31. [39]

    J., Ondov, B

    Treangen, T. J., Ondov, B. D., Koren, S., & Phillippy, A. M. The Har- vest suite for rapid core-genome alignment and visualizati on of thousands of intraspecific microbial genomes. Genome biology, 15(11) 524 (2014)

    2014

  32. [40]

    R: A language and environment for sta tistical computing

    R Core Team (2018). R: A language and environment for sta tistical computing. R Foundation for Statistical Computing, Vienna , Austria. URL https://www.R-project.org/

    2018

  33. [41]

    L., Huang, Y., & Luo, H

    Hellweger, F. L., Huang, Y., & Luo, H. Carbon limitation drives GC content evolution of a marine bacterium in an individual-ba sed genome- scale model. The ISME journal, 12(5) 1180 (2018) 20

    2018

  34. [42]

    SeaView version 4: a multiplat- form graphical user interface for sequence alignment and ph ylogenetic tree building

    Gouy, M., Guindon, S., & Gascuel, O. SeaView version 4: a multiplat- form graphical user interface for sequence alignment and ph ylogenetic tree building. Molecular biology and evolution, 27(2) 221-224 (2009)

    2009

  35. [43]

    JAGS: A program for analysis of Bayesian graphical mod- els using Gibbs sampling

    Plummer, M. JAGS: A program for analysis of Bayesian graphical mod- els using Gibbs sampling. In Proceedings of the 3rd international work- shop on distributed statistical computing, V ol. 124 No. 125.10 (2003)

    2003

  36. [44]

    J., Barrick, J

    Woods, R. J., Barrick, J. E., Cooper, T. F., Shrestha, U. , Kauth, M. R., & Lenski, R. E. Second-order selection for evolvability in a large Escherichia coli population. Science, 331(6023) 1433-1436 (2011) 21

    2011

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.