Pith. sign in

REVIEW 2 major objections 4 minor 63 references

Continual Evolution in Nonreciprocal Ecological Models

T0 review · 2 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read Asymmetric ecological interactions can maintain a Red Queen eco-evolutionary steady state with continual strain turnover and roughly constant invasion probability.

desk verdict The exact Red Queen solution in the simplest limit is real and striking; the advertised robustness to large general-fitness differences is not yet supported, and the paper knows it. read the letter →

arxiv 2411.17148 v1 pith:NH7MQDTV submitted 2024-11-26 q-bio.PE cond-mat.dis-nncond-mat.stat-mech

Aditya Mahadevan , Daniel S. Fisher This is my paper · ORCID
classification q-bio.PEcond-mat.dis-nncond-mat.stat-mech
keywords RedQueenevolutioneco-evolutionarydynamicsconsumer-resourcemodelLotka-Volterradynamicalmean-fieldtheorynonreciprocalinteractionspermanentextinctionsoligarchphase
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 claims that a community of interacting microbial strains, evolving slowly with permanent extinctions, can settle into a "Red Queen" steady state: new variants keep invading at a roughly constant rate, biodiversity keeps turning over, and diversity is set by the number of niche dimensions rather than collapsing. Resource-mediated models reach this phase for any amount of asymmetry between consumption and growth, and a linearized resource model shows the same phase, while generalized Lotka-Volterra models show it for moderate interaction symmetry. A particular limit is solved exactly by dynamical mean-field theory, giving diversity $L \approx 0.58 Q^2$ and exponential decay of turnover correlations. The picture fails for perfectly symmetric interactions, where a Lyapunov function makes invasions ever rarer, and in the Lotka-Volterra model for strong symmetry an "oligarch" phase of slowing turnover appears. The result matters because it shows continual evolution can arise from ecology alone, without host-pathogen arms races.

What carries the argument

The dynamical cavity method, a dynamic mean-field theory applied to evolutionary epochs, carries the argument. It tracks a focal "cavity strain" that may invade, persist, and eventually hit an absorbing extinction boundary. For $\gamma=0$, $\Sigma=0$, the paper assumes the strain's drive is an Ornstein-Uhlenbeck process, computes its abundance statistics with an absorbing boundary via the method of images, and enforces self-consistency with the community's own autocorrelation $C(\tau)=\sum_j \nu_j(T)\nu_j(T+\tau)$. This yields the exponential $C(\tau)$, the diversity formula, and the lifetime distribution; general memory kernels are set up but not solved for $\gamma \neq 0$.

What would settle it

Run the $\gamma=0$, $\Sigma=0$ Lotka-Volterra model with independent invaders at large $Q$ and measure the evolutionary-time autocorrelation $C(\tau)$ and steady-state diversity. The paper predicts $C(\tau)=\frac{2\pi\lambda^2}{Q^2} e^{-2\lambda\tau/Q^2}$ with $\lambda=(1+2\log 2)/4$ and $L/Q^2 \to \frac{2\log 2}{1+2\log 2}\approx 0.58$; a persistent non-exponential tail in $C(\tau)$ or a limiting $L/Q^2$ different from $0.58$ as $Q$ grows would falsify the exact solution.

Watch

Extended reading notes

Core claim

The central discovery is the Red Queen eco-evolutionary steady state: after a transient, the community reaches a statistically stationary high-diversity state in which the invasion probability of new strains is roughly constant, diversity is $L \sim \kappa^2 D$ in the linearized resource model (or $L \approx 0.58 Q^2$ in the exactly solved $\gamma=0$, $\Sigma=0$ Lotka-Volterra limit), and strain lifetimes have mean $L$ epochs with a correlation decay time of order $L$. In this state the width of the extant general-fitness distribution narrows until intrinsic growth-rate differences are comparable to community-driven "drive" fluctuations, which is what allows the constant turnover.

Load-bearing premise

The load-bearing premise is the Ansatz that the fluctuating part of an invader's growth rate is an Ornstein-Uhlenbeck process with exponentially decaying autocorrelation; the paper notes this is assumed rather than derived, and the generalized analysis further assumes Gaussian statistics for rare large fluctuations, which Appendix K finds contradicted by numerics for large general-fitness widths.

Editorial extensions

If this is right

  • In resource-mediated models, the Red Queen phase exists for any nonzero asymmetry between consumption and growth, with diversity of order $\kappa^2 D$; at perfect symmetry the invasion probability instead decreases without bound.
  • In the exactly solved limit, steady-state diversity is $L = \frac{2\log 2}{1+2\log 2} Q^2 \approx 0.58 Q^2$, the average strain lifetime equals $L$, and the turnover correlation function decays exponentially on that timescale.
  • General fitness differences do not destroy the Red Queen phase provided their distribution decays fast enough: diversity becomes roughly independent of the fitness scale, while the invasion probability is strongly controlled by the tail of the fitness distribution.
  • For strongly symmetric Lotka-Volterra interactions above a sharp transition around $\gamma_c \approx 0.65$, the Red Queen phase gives way to an oligarch phase in which a few strains hold an order-one fraction of abundance while turnover continually slows.

Reading between the lines

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

  • Beyond the paper: if the Red Queen phase is generic in well-mixed models, fine-scale microbial diversity in nature need not be stabilized by niche differences; it can be a nonequilibrium feature of ecology.
  • The paper leaves the small-effect mutation limit $\rho \to 1$ open; a natural extension is to ask whether the Red Queen phase survives when mutants are nearly identical to parents, and whether the resulting phylogenies resemble known coalescent trees.
  • The oligarch phase suggests a condensation phenomenon: few strains absorb an order-one abundance while total diversity stays roughly constant, and quench experiments through the transition create apparently stable hybrid states. Testing whether this transition sharpens as $Q$ grows is a concrete next step the paper does not close.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper studies slow sequential introduction of new strains into consumer-resource and Lotka-Volterra models with permanent extinctions, and identifies a 'Red Queen' phase of continual evolution and biodiversity turnover with a roughly constant invasion probability. The main claimed result is that this phase is robust across models and parameters, including arbitrary asymmetry in resource-mediated interactions and general-fitness differences with sufficiently fast-decaying tails. The paper provides an exact solution of the evolutionary steady state in the special limit γ=0, Σ=0 via a dynamical cavity method with an Ornstein-Uhlenbeck ansatz, together with scaling arguments and simulations for general parameters. It also reports an 'oligarch' phase in generalized Lotka-Volterra models with strongly asymmetric interactions, where evolution continually slows down.

Significance. If the central claim holds, the paper establishes a conceptually important mechanism for continual evolution without host-pathogen arms races, with a concrete analytically solvable example: the exact solution in Section IV C yields parameter-free predictions, including L ≈ 0.58 Q², the correlation function C(τ), and the lifetime distribution pT(T), all checked against simulations in Figure 10. The distinction between top-down assembled and evolved communities, the depletion of low-abundance strains, and the identification of the oligarch phase are valuable contributions that should stimulate further work. The main weakness is that the broadest robustness claims, especially those involving arbitrarily large general-fitness differences, rest on unresolved rare-event statistics that the paper itself acknowledges as incomplete.

major comments (2)
  1. [Section IV E and Appendix K] The claim that the Red Queen phase is robust to 'arbitrarily large general fitness differences' is not established for large Σ. Section IV E states that the subtle effects of the tails of p(s) are unresolved, and Appendix K (Figure 21A, QΣ=8) reports a lifetime-distribution exponent β ≈ 1.7 where the Gaussian-cavity analysis predicts β ≈ 0.06, with Figure 20 showing that ⟨T|s⟩ grows much more slowly than the Gaussian barrier-crossing prediction. Because extinction of high-fitness strains is controlled by exactly these rare fluctuations of the drive, the numerical evidence in the large-Σ regime does not currently support the phase-robustness claim. The authors should either provide a controlled argument that these non-Gaussian deviations do not affect the existence of the Red Queen phase in the L→∞ limit, or explicitly restrict the claim to Σ below the crossover scale and state the resulting limitations in the abstract and discussion.
  2. [Section IV A and Figures 5C, 6C] The quantitative characterization of the Red Queen phase for Σ>0 rests on a conjecture that the assembled-community scalings Υ∼Σ² and −log pinv∼Σ² hold in the evolved steady state 'with unknown coefficients' (Section IV A), and the comparisons in Figures 5C and 6C are rough fits rather than parameter-free predictions. The exact solution of Section IV C applies only to the line γ=0, Σ=0; for general asymmetry and general-fitness parameters, no analogous closed-form solution is provided. The paper should state more explicitly that these scaling relations are conjectural, and the fitted dotted/dashed lines should not be presented as confirmations of the theory.
minor comments (4)
  1. [Appendix D] In step 3 of the fixed-point algorithm, 'invsade' is a typo and should read 'invade.'
  2. [Section IV C] The phrase 'thalf-gaussian measure' appears to be missing an article and should read 'the half-gaussian measure.'
  3. [Section IV D] 'Weiner-Hopf factorization' should be spelled 'Wiener-Hopf factorization.'
  4. [Figures 5 and 6] The captions and text use both 'log pinv' and 'log pinv' for the time-averaged logarithm of the invasion probability; the notational distinction between the average of the logarithm and the logarithm of the average should be clarified and applied consistently.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity: the exact Red Queen solution is a self-consistent DMFT ansatz checked against independent numerics; only minor non-load-bearing self-citations appear.

full rationale

The paper's central derivation is self-contained rather than circular. The exact solution in Section IV C explicitly introduces an exponential-correlation Ornstein-Uhlenbeck ansatz for the cavity drive ('Hoping for some luck, we then make the simplest possible Ansatz for the statistics of ζ0(T): namely that it has an exponentially decaying correlation function'), then fixes the parameters b and J through the DMFT self-consistency condition (Equation 10) and the normalization condition, and validates the resulting correlation function, diversity L/Q^2, and lifetime distribution against independent simulations with no fit parameters. The exponential form is an acknowledged ansatz, not a fitted parameter renamed as a prediction, and the numerical agreement supplies the evidence. Scaling relations for Σ>0 are introduced explicitly as conjectures ('We conjecture that the forms of the scalings of Υ and log S with Σ in the assembled community also describe the time-averaged quantities in the Red Queen steady state...'), and the dotted lines in Figures 5C and 6C are labeled 'rough fit to predicted form,' so they are not presented as derived predictions. Self-citations such as [5], [17], [23], and [43] are contextual or motivational; none is load-bearing for the main claim, and the central result does not reduce to those papers. The admitted breakdown of the Gaussian-tail assumption for large QΣ (Appendix K: observed exponent β≈1.7 versus predicted β≈0.06) is a correctness/robustness limitation, not circularity, because the analysis's assumption is contradicted by numerics rather than confirmed by construction. Overall, the derivation chain has no significant circularity; the score reflects only the presence of minor non-load-bearing self-citations.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The ledger records the modeling assumptions and fitted constants on which the Red Queen claims rest. Most entries are standard random-ensemble and ecological assumptions; the OU and tail-Gaussian ansatze are specific to this paper, though they are checked against numerics.

free parameters (2)
  • OU ansatz parameters b and J = b = 2 lambda / Q^2, J = 4 pi lambda^3 / Q^4 with lambda = (1 + 2 log 2)/4
    Phenomenological parameters in the exponential-correlation ansatz for the cavity drive. They are fixed by self-consistency equations rather than fitted to data, so they are not free after the ansatz is imposed.
  • Scaling coefficients in Upsilon approximately Sigma^2 and log p_inv approximately -Sigma^2 relations = Unknown coefficients; dotted line fits in Figures 5C and 6C use approximate factors of 9 and -40
    The predicted functional forms are tested by fitting proportionality constants to simulation data, rather than derived parameter-free. These fits appear in the scaling arguments but are not the core exact solution.
assumptions (7)
  • domain assumption Ecological dynamics reach a stable fixed point between successive invasions and evolution is slow enough for a clean timescale separation.
    Invoked throughout Section II B and assumed for the epoch-based evolutionary dynamics. If ecology were chaotic or not fast enough, the serial invasion steady state could change.
  • domain assumption Extinctions are permanent and extinct strains cannot reinvade.
    Defined in Section II B and used in the absorbing boundary condition of the cavity calculation. This distinguishes the work from migration-based models such as de Pirey and Bunin.
  • domain assumption Strain phenotypes and interactions are drawn from Gaussian random ensembles with specified means, variances, and correlations.
    Used in Sections II A and III to define the CR, linearized, and Lotka-Volterra ensembles, and to generate invaders conditioned on invasion success.
  • standard math Cavity and dynamical mean field self-averaging assumptions hold at large D.
    Invoked in Sections IV A and IV C and Appendices F and H. The analysis assumes the statistics of a cavity strain match the community statistics, a standard but nontrivial mean-field assumption.
  • ad hoc to paper The cavity drive has exponentially decaying autocorrelation and Ornstein-Uhlenbeck dynamics in the gamma equal to 0, Sigma equal to 0 solution.
    Introduced in Section IV C as an Ansatz, with the comment 'Hoping for some luck'. It is checked self-consistently and against numerics, but not derived from the microscopic dynamics.
  • ad hoc to paper Gaussian stationary statistics for the drive extend into rare-event tails that control extinctions of high-fitness strains.
    Used in the Section IV E analysis of large general fitnesses. The paper later reports that numerics contradict the predicted rare-event lifetimes, and leaves the resolution unresolved.
  • ad hoc to paper Assembled-community scalings conjecture: Upsilon and log invasion probability in the Red Queen steady state scale as in the saturated assembled community.
    Stated as a conjecture in Section IV A and applied in Sections IV E and Appendix J. The proportionality constants are fit to numerics rather than derived.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Continual Evolution in Nonreciprocal Ecological Models." pith.science (2026). https://pith.science/paper/NH7MQDTV

@misc{pith2026241117148,
  author       = {Pith},
  title        = {Pith review of: Continual Evolution in Nonreciprocal Ecological Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NH7MQDTV}},
  note         = {Machine review of arXiv:2411.17148}
}
read the original abstract

Feedbacks between evolution and ecology are ubiquitous, with ecological interactions determining which mutants are successful, and these mutants in turn modifying community structure. We study the evolutionary dynamics of several ecological models with overlapping niches, including consumer resource and Lotka-Volterra models. Evolution is assumed slow and extinctions are permanent, with ecological dynamics reaching a stable fixed point between introductions of invaders or mutants. When new strains are slowly added to the community, the ecosystem converges, after an initial evolutionary transient, to a diverse eco-evolutionary steady state. In this "Red Queen" phase of continual evolution, the biodiversity continues to turn over without the invasion probability of new variants getting any smaller. For resource-mediated interactions, the Red Queen phase obtains for any amount of asymmetry in the interactions between strains, and is robust to "general fitness" differences in the intrinsic growth rates of strains. Via a dynamical mean field theory framework valid for high-dimensional phenotype space, we analytically characterize the Red Queen eco-evolutionary steady state in a particular limit of model parameters. Scaling arguments enable a more general understanding of the steady state and evolutionary transients toward it. This work therefore establishes simple models of continual evolution in an ecological context without host-pathogen arms races, and points to the generality of Red Queen evolution. However, we also find other eco-evolutionary phases in simple models: For generalized Lotka-Volterra models with weakly asymmetric interactions an "oligarch" phase emerges in which the evolutionary dynamics continually slow down and a substantial fraction of the community's abundance condenses into a handful of slowly turning-over strains.

Figures

Figures reproduced from arXiv: 2411.17148 by the authors.

Figure 2
Figure 2. The CR model reaches a steady state for symme [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. (A)–(B) Mean and standard deviation (weighted by [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 5
Figure 5. Dynamics and steady state of Lagrange multiplier [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figures from the paper (15 more)
Figure 6
Figure 6. Figure 6: Dynamics of invasion probability, and mean logarithm [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Same steady state is reached in LV model for a range [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Maximum diversity and stability to evolutionary per [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Number density Π(z) of the scaled abundance z = Q 2 ν in the γ = 0, Σ = 0 LV model with Q = 20: for saturated assem￾bled community (yellow) and evolved Red Queen steady state (blue), with normalization R dzΠ(z) = L/Q2 . Histograms are numerical data and solid lines pre…
Figure 10
Figure 10. Figure 10: Predictions of evolutionary cavity calculation and [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: Strain trajectories (subset of strains shown) for LV [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]
Figure 12
Figure 12. Figure 12: Evolution in LV model (Q = 20, Σ = 0) undergoes a transition from Red Queen for γ < γc ∼= 0.65 to oligarch phase for γ > γc. (A) L is roughly constant in both phases. (B) Υ fluctuates around steady state in Red Queen phase but increases without bound in oligarch phase…
Figure 13
Figure 13. Figure 13: Effects of parent-mutant correlation, ρ, on evolution in CR model with D = 50, κ = 0.4. (A) Steady state L is a decreasing function of ρ. (B) log pinv is a nonmonotonic function of ρ, largest for intermediate ρ. (C) After initial transient, community-mean general fitn…
Figure 15
Figure 15. Figure 15: Evolutionary dynamics of LV model (with Σ = 0) [PITH_FULL_IMAGE:figures/full_fig_p026_15.png]
Figure 16
Figure 16. Figure 16: Transition between Red Queen and oligarch phases is first order, and exhibits hysteresis and phase coexistence when [PITH_FULL_IMAGE:figures/full_fig_p027_16.png]
Figure 17
Figure 17. Figure 17: Fluctuations of L and Υ in the Red Queen phase of the linearized model with κ = 0.8, ρ = 0 and Σ = 0. (A)–(B) Both the mean and variance of L scale roughly linearly with D √ , so that fluctuations are smaller than the mean by a factor of D. (C)–(D) The mean Υ in stead…
Figure 18
Figure 18. Figure 18: Transient behavior of Υ during the evolutionary [PITH_FULL_IMAGE:figures/full_fig_p031_18.png]
Figure 19
Figure 19. Figure 19: In the LV model with Q = 20 and Σ = 0, C(τ /L) decays more slowly with increasing γ (normalization of τ by L eliminates the trivial scaling of the decay timescale with L). Dashed black line is the simple-exponential prediction for γ = 0, with deviations from this resu…
Figure 20
Figure 20. Figure 20: Joint distribution of strain lifetimes Ti and general fitnesses si in γ = 0 LV model (Q = 10, yielding L ≈ 70). (A) Data for ΣQ = 1. Red line shows the mean lifetime ⟨T |s⟩ conditioned on s within a given range. Black line shows naive theoretical expectation ⟨T |s⟩ ∼ …
Figure 22
Figure 22. Figure 22: Fluctuations in γ = 0.LV model as function of Σ. (A) Distributions of L showing that L and the fluctuations of L depend only weakly on Σ. (B) Distributions of fluctuations in Υ (whose mean scales as QΣ 2 ) increase with Σ. The scale of these fluctuations is Q 2 at Σ =…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

63 extracted references · 63 canonical work pages

  1. [1]

    V ∗ is the submatrix of inter- actions for the extant strains, and therefore contains the rows and columns corresponding to strains in C

    Initialize C as the set of all strains in the community (including the new invader) and initialize the extinct set E as an empty set. V ∗ is the submatrix of inter- actions for the extant strains, and therefore contains the rows and columns corresponding to strains in C

    work page

  2. [2]

    In general some of the ν∗ i will be negative

    Invert V ∗ to find a fixed point of the dynamics via ν∗ i = Υ∗ P j V ∗−1 ij and P i ν∗ i = 1 which fixes Υ ∗. In general some of the ν∗ i will be negative. Remove the set {i|ν∗ i < 0} from C and add it to E

    work page

  3. [3]

    Transfer the set of strains that could invsade, {j|ξj > 0}, from E to C

    Calculate the invasion fitnesses ξj of each strain in E as ξj = P k∈C Vjk ν∗ k − Υ∗. Transfer the set of strains that could invsade, {j|ξj > 0}, from E to C

    work page

  4. [4]

    quenched

    Iterate steps 2 and 3 until convergence to sets C and E such that ν∗ i > 0 for all i ∈ Cand ξj < 0 for all 26 0 100000 200000 300000 400000 500000 epoch 101 102 (A) E [∑ j Fjαn∗ j ] α Std [∑ j Fjαn∗ j ] α 0 100000 200000 300000 400000 500000 epoch 0 20 40 60 80N (B) κ 0.4 Figure 14. In Red Queen phase of the CR model ( D = 50, κ = 0.4), linearization of r...

    work page

  5. [5]

    Structure and function of the global ocean microbiome

    Shinichi Sunagawa, Luis Pedro Coelho, Samuel Chaffron, Jens Roat Kultima, Karine Labadie, Guillem Salazar, Bardya Djahanschiri, Georg Zeller, Daniel R Mende, Adri- ana Alberti, et al. Structure and function of the global ocean microbiome. Science, 348(6237):1261359, 2015

    work page 2015

  6. [6]

    Nature, 486 (7402):215–221, 2012

    A framework for human microbiome research. Nature, 486 (7402):215–221, 2012

    work page 2012

  7. [7]

    Embracing the unknown: disentangling the complexities of the soil microbiome

    Noah Fierer. Embracing the unknown: disentangling the complexities of the soil microbiome. Nature Reviews Mi- crobiology, 15(10):579–590, 2017

    work page 2017

  8. [8]

    Single-cell genomics reveals hundreds of co- existing subpopulations in wild prochlorococcus

    Nadav Kashtan, Sara E Roggensack, S´ ebastien Rodrigue, Jessie W Thompson, Steven J Biller, Allison Coe, Huim- ing Ding, Pekka Marttinen, Rex R Malmstrom, Roman Stocker, et al. Single-cell genomics reveals hundreds of co- existing subpopulations in wild prochlorococcus. Science, 344(6182):416–420, 2014

    work page 2014

Show all 63 references
  1. [9]

    Fine-scale diversity and extensive recom- bination in a quasisexual bacterial population occupying a broad niche

    Michael J Rosen, Michelle Davison, Devaki Bhaya, and Daniel S Fisher. Fine-scale diversity and extensive recom- bination in a quasisexual bacterial population occupying a broad niche. Science, 348(6238):1019–1023, 2015

    2015

  2. [10]

    Microbial evolution in a simple unstructured environment: genetic differentiation in escherichia coli

    R Frank Rosenzweig, RR Sharp, David S Treves, and Ju- lian Adams. Microbial evolution in a simple unstructured environment: genetic differentiation in escherichia coli. Ge- netics, 137(4):903–917, 1994

    1994

  3. [11]

    Experimental evidence for sympatric eco- logical diversification due to frequency-dependent competi- tion in escherichia coli

    Maren L Friesen, Gerda Saxer, Michael Travisano, and Michael Doebeli. Experimental evidence for sympatric eco- logical diversification due to frequency-dependent competi- tion in escherichia coli. Evolution, 58(2):245–260, 2004

    2004

  4. [12]

    Clonal adaptive radiation in a constant environment

    Ram Maharjan, Shona Seeto, Lucinda Notley-McRobb, and Thomas Ferenci. Clonal adaptive radiation in a constant environment. Science, 313(5786):514–517, 2006

    2006

  5. [13]

    The dynamics of molecular evolution over 60,000 generations

    Benjamin H Good, Michael J McDonald, Jeffrey E Barrick, Richard E Lenski, and Michael M Desai. The dynamics of molecular evolution over 60,000 generations. Nature, 551 (7678):45–50, 2017

    2017

  6. [14]

    Experimental evolution and the dynam- ics of adaptation and genome evolution in microbial popu- lations

    Richard E Lenski. Experimental evolution and the dynam- ics of adaptation and genome evolution in microbial popu- lations. The ISME journal , 11(10):2181–2194, 2017

    2017

  7. [15]

    Evolution of microbial diversity during prolonged starvation

    Steven E Finkel and Roberto Kolter. Evolution of microbial diversity during prolonged starvation. Proceedings of the National Academy of Sciences , 96(7):4023–4027, 1999

    1999

  8. [16]

    Long-term stability and red queen-like strain dynamics in marine viruses

    J Cesar Ignacio-Espinoza, Nathan A Ahlgren, and Jed A Fuhrman. Long-term stability and red queen-like strain dynamics in marine viruses. Nature Microbiology, 5(2):265– 271, 2020

    2020

  9. [17]

    Rapid diver- sification of coevolving marine synechococcus and a virus

    Marcia F Marston, Francis J Pierciey Jr, Alicia Shepard, Gary Gearin, Ji Qi, Chandri Yandava, Stephan C Schuster, Matthew R Henn, and Jennifer BH Martiny. Rapid diver- sification of coevolving marine synechococcus and a virus. Proceedings of the National Academy of Sciences , ...

    2012

  10. [18]

    Antagonistic coevolu- tion between a bacterium and a bacteriophage

    Angus Buckling and Paul B Rainey. Antagonistic coevolu- tion between a bacterium and a bacteriophage. Proceedings of the Royal Society of London. Series B: Biological Sci- ences, 269(1494):931–936, 2002

    2002

  11. [19]

    A new evolutionary law

    Leigh Van Valen. A new evolutionary law. Evolutionary Theory, 1:1, 1973

    1973

  12. [20]

    Empirical fit- ness landscapes and the predictability of evolution

    J Arjan GM De Visser and Joachim Krug. Empirical fit- ness landscapes and the predictability of evolution. Nature Reviews Genetics, 15(7):480–490, 2014

    2014

  13. [21]

    Inevitability of red queen evolution driven by organismic complexity and simple feedback via environ- mental modification

    Daniel S Fisher. Inevitability of red queen evolution driven by organismic complexity and simple feedback via environ- mental modification. bioRxiv, pages 2021–09, 2021

    2021

  14. [22]

    Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics

    Atish Agarwala and Daniel S Fisher. Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics. Theoretical Population Biol- ogy, 130:13–49, 2019

    2019

  15. [23]

    Ecological communities with lotka-volterra dy- namics

    Guy Bunin. Ecological communities with lotka-volterra dy- namics. Physical Review E , 95(4):042414, 2017

    2017

  16. [24]

    Phase transition and 1/f noise in a game dynamical model

    Manfred Opper and Sigurd Diederich. Phase transition and 1/f noise in a game dynamical model. Physical Review Let- ters, 69(10):1616, 1992

    1992

  17. [25]

    Phase transition to chaos in complex ecosystems with non- reciprocal species-resource interactions

    Emmy Blumenthal, Jason W Rocks, and Pankaj Mehta. Phase transition to chaos in complex ecosystems with non- reciprocal species-resource interactions. Physical Review Letters, 132(12):127401, 2024

    2024

  18. [26]

    Generalized lotka-volterra equations with random, nonreciprocal interactions: The typical number of equilibria

    Valentina Ros, Felix Roy, Giulio Biroli, Guy Bunin, and Ari M Turner. Generalized lotka-volterra equations with random, nonreciprocal interactions: The typical number of equilibria. Physical Review Letters, 130(25):257401, 2023

    2023

  19. [27]

    Stabilization of extensive fine-scale diversity by ecologically driven spatiotemporal chaos

    Michael T Pearce, Atish Agarwala, and Daniel S Fisher. Stabilization of extensive fine-scale diversity by ecologically driven spatiotemporal chaos. Proceedings of the National Academy of Sciences, 117(25):14572–14583, 2020

    2020

  20. [28]

    kill the winner

    Chi Xue and Nigel Goldenfeld. Coevolution maintains di- versity in the stochastic “kill the winner” model. Physical Review Letters, 119(26):268101, 2017

    2017

  21. [29]

    Towards a solution of the plankton para- dox: the importance of physiology and life history

    Jef Huisman, Anna M Johansson, Eelke O Folmer, and Franz J Weissing. Towards a solution of the plankton para- dox: the importance of physiology and life history. Ecology Letters, 4(5):408–411, 2001

    2001

  22. [30]

    Phylo- dynamic theory of persistence, extinction and speciation of rapidly adapting pathogens

    Le Yan, Richard A Neher, and Boris I Shraiman. Phylo- dynamic theory of persistence, extinction and speciation of rapidly adapting pathogens. Elife, 8:e44205, 2019

    2019

  23. [31]

    Competitive exclusion

    Robert A Armstrong and Richard McGehee. Competitive exclusion. The American Naturalist, 115(2):151–170, 1980

    1980

  24. [32]

    Evo- lution exacerbates the paradox of the plankton

    Noam Shoresh, Matthew Hegreness, and Roy Kishony. Evo- lution exacerbates the paradox of the plankton. Proceedings of the National Academy of Sciences , 105(34):12365–12369, 2008

    2008

  25. [33]

    supersaturated coexistence

    Peter Schippers, Antonie M Verschoor, Matthijs Vos, and Wolf M Mooij. Does “supersaturated coexistence” resolve the “paradox of the plankton”? Ecology letters, 4(5):404– 407, 2001

    2001

  26. [34]

    Complexity and diversity

    Michael Doebeli and Iaroslav Ispolatov. Complexity and diversity. Science, 328(5977):494–497, 2010

    2010

  27. [35]

    Innovation rather than improvement: A solvable high-dimensional model highlights the limitations of scalar fitness

    Mikhail Tikhonov and Remi Monasson. Innovation rather than improvement: A solvable high-dimensional model highlights the limitations of scalar fitness. Journal of Sta- tistical Physics, 172:74–104, 2018

    2018

  28. [36]

    Tractable models of ecological assembly

    Carlos A Serv´ an and Stefano Allesina. Tractable models of ecological assembly. Ecology Letters, 24(5):1029–1037, 2021

    2021

  29. [37]

    Sta- tistical mechanics of ecosystem assembly

    Jos´ e A Capit´ an, Jos´ e A Cuesta, and Jordi Bascompte. Sta- tistical mechanics of ecosystem assembly. Physical Review Letters, 103(16):168101, 2009

    2009

  30. [38]

    Properties of equilibria and glassy phases of the ran- dom lotka-volterra model with demographic noise

    Ada Altieri, Felix Roy, Chiara Cammarota, and Giulio Biroli. Properties of equilibria and glassy phases of the ran- dom lotka-volterra model with demographic noise. Physical Review Letters, 126(25):258301, 2021

    2021

  31. [39]

    Collective phase in resource competition in a highly diverse ecosystem.Physical Review Letters, 118(4):048103, 2017

    Mikhail Tikhonov and Remi Monasson. Collective phase in resource competition in a highly diverse ecosystem.Physical Review Letters, 118(4):048103, 2017

    2017

  32. [40]

    36 Effect of resource dynamics on species packing in diverse ecosystems

    Wenping Cui, Robert Marsland III, and Pankaj Mehta. 36 Effect of resource dynamics on species packing in diverse ecosystems. Physical Review Letters, 125(4):048101, 2020

    2020

  33. [41]

    Marginally stable equilibria in critical ecosystems

    Giulio Biroli, Guy Bunin, and Chiara Cammarota. Marginally stable equilibria in critical ecosystems. New Journal of Physics , 20(8):083051, 2018

    2018

  34. [42]

    The minimum environmental perturbation principle: A new perspective on niche theory

    Robert Marsland III, Wenping Cui, and Pankaj Mehta. The minimum environmental perturbation principle: A new perspective on niche theory. The American Naturalist, 196 (3):291–305, 2020

    2020

  35. [43]

    Eco-evolutionary red queen dynamics regulate biodiversity in a metabolite-driven microbial system

    Juan A Bonachela, Meike T Wortel, and Nils Chr Stenseth. Eco-evolutionary red queen dynamics regulate biodiversity in a metabolite-driven microbial system. Scientific Reports, 7(1):17655, 2017

    2017

  36. [44]

    On evolu- tion under asymmetric competition

    Richard Law, Paul Marrow, and Ulf Dieckmann. On evolu- tion under asymmetric competition. Evolutionary Ecology, 11:485–501, 1997

    1997

  37. [45]

    Asymmetric ecological conditions favor red-queen type of continued evo- lution over stasis

    Jan Martin Nordbotten and Nils C Stenseth. Asymmetric ecological conditions favor red-queen type of continued evo- lution over stasis. Proceedings of the National Academy of Sciences, 113(7):1847–1852, 2016

    2016

  38. [46]

    Will a large complex system be stable? Nature, 238(5364):413–414, 1972

    Robert M May. Will a large complex system be stable? Nature, 238(5364):413–414, 1972

    1972

  39. [47]

    Spatiotemporal ecological chaos enables gradual evolution- ary diversification without niches or tradeoffs

    Aditya Mahadevan, Michael T Pearce, and Daniel S Fisher. Spatiotemporal ecological chaos enables gradual evolution- ary diversification without niches or tradeoffs. Elife, 12: e82734, 2023

    2023

  40. [48]

    Metabolic trade-offs promote diversity in a model ecosys- tem

    Anna Posfai, Thibaud Taillefumier, and Ned S Wingreen. Metabolic trade-offs promote diversity in a model ecosys- tem. Physical Review Letters, 118(2):028103, 2017

    2017

  41. [49]

    Evolution of diversity in metabolic strategies

    Rodrigo Caetano, Yaroslav Ispolatov, and Michael Doebeli. Evolution of diversity in metabolic strategies. Elife, 10: e67764, 2021

    2021

  42. [50]

    Ecological diversity: measuring the unmeasurable

    Aisling J Daly, Jan M Baetens, and Bernard De Baets. Ecological diversity: measuring the unmeasurable. Mathe- matics, 6(7):119, 2018

    2018

  43. [51]

    Sampling the multivariate standard normal distribution under a weighted sum constraint

    Fr´ ed´ eric Vrins. Sampling the multivariate standard normal distribution under a weighted sum constraint. Risks, 6(3): 64, 2018

    2018

  44. [52]

    Replicators with ran- dom interactions: A solvable model

    Sigurd Diederich and Manfred Opper. Replicators with ran- dom interactions: A solvable model. Physical Review A, 39 (8):4333, 1989

    1989

  45. [53]

    Numerical implementation of dynamical mean field theory for disordered systems: Application to the lotka– volterra model of ecosystems

    Felix Roy, Giulio Biroli, Guy Bunin, and Chiara Cam- marota. Numerical implementation of dynamical mean field theory for disordered systems: Application to the lotka– volterra model of ecosystems. Journal of Physics A: Math- ematical and Theoretical, 52(48):484001, 2019

    2019

  46. [54]

    Glassy behaviour in disordered systems with nonrelaxational dynamics

    Leticia F Cugliandolo, Jorge Kurchan, Pierre Le Doussal, and Luca Peliti. Glassy behaviour in disordered systems with nonrelaxational dynamics. Physical Review Letters , 78(2):350, 1997

    1997

  47. [55]

    Many-species ecological fluctuations as a jump process from the brink of extinction

    Thibaut Arnoulx de Pirey and Guy Bunin. Many-species ecological fluctuations as a jump process from the brink of extinction. Physical Review X , 14(1):011037, 2024

    2024

  48. [56]

    Dynamics of immune memory and learning in bacterial communities

    Madeleine Bonsma-Fisher and Sidhartha Goyal. Dynamics of immune memory and learning in bacterial communities. Elife, 12:e81692, 2023

    2023

  49. [57]

    Antigenic waves of virus-immune co- evolution

    Jacopo Marchi, Michael L¨ assig, Aleksandra M Walczak, and Thierry Mora. Antigenic waves of virus-immune co- evolution. Proceedings of the National Academy of Sciences, 118(27):e2103398118, 2021

    2021

  50. [58]

    Interactions between strains govern the eco-evolutionary dynamics of microbial commu- nities

    Akshit Goyal, Leonora S Bittleston, Gabriel E Leventhal, Lu Lu, and Otto X Cordero. Interactions between strains govern the eco-evolutionary dynamics of microbial commu- nities. Elife, 11:e74987, 2022

    2022

  51. [59]

    Cryptic population dynamics: rapid evolu- tion masks trophic interactions

    Takehito Yoshida, Stephen P Ellner, Laura E Jones, Bren- dan J M Bohannan, Richard E Lenski, and Nelson G Hairston Jr. Cryptic population dynamics: rapid evolu- tion masks trophic interactions. PLoS Biology, 5(9):e235, 2007

    2007

  52. [60]

    The person-to-person transmission landscape of the gut and oral microbiomes

    Mireia Valles-Colomer, Aitor Blanco-M ´ ıguez, Paolo Manghi, Francesco Asnicar, Leonard Dubois, Davide Golzato, Federica Armanini, Fabio Cumbo, Kun D Huang, Serena Manara, et al. The person-to-person transmission landscape of the gut and oral microbiomes. Nature, 614 (7946):12...

    2023

  53. [61]

    Host-specific evolutionary and transmission dy- namics shape the functional diversification of staphylococ- cus epidermidis in human skin

    Wei Zhou, Michelle Spoto, Rachel Hardy, Changhui Guan, Elizabeth Fleming, Peter J Larson, Joseph S Brown, and Julia Oh. Host-specific evolutionary and transmission dy- namics shape the functional diversification of staphylococ- cus epidermidis in human skin. Cell, 180(3):454–470, 2020

    2020

  54. [62]

    High resolution time series reveals co- hesive but short-lived communities in coastal plankton

    Antonio M Martin-Platero, Brian Cleary, Kathryn Kauff- man, Sarah P Preheim, Dennis J McGillicuddy, Eric J Alm, and Martin F Polz. High resolution time series reveals co- hesive but short-lived communities in coastal plankton. Na- ture Communications, 9(1):266, 2018

    2018

  55. [63]

    First-passage-time density and moments of the ornstein-uhlenbeck process

    Luigi M Ricciardi and Shunsuke Sato. First-passage-time density and moments of the ornstein-uhlenbeck process. Journal of Applied Probability , 25(1):43–57, 1988

    1988

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.