Pith. sign in

REVIEW 3 major objections 4 minor 83 references

Randomness with constraints: constructing minimal models for high-dimensional biology

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read Constrained random models can reproduce high-dimensional biological observations without fitting every parameter.

desk verdict A clear, honest review that packages a long-standing paradigm under one banner; the central 'consistently captures' claim outruns the curated evidence, but the paper itself flags where the needed tests are. read the letter →

arxiv 2509.03765 v1 pith:LCE33BJL submitted 2025-09-03 physics.bio-ph q-bio.QM

Ilya Nemenman , Pankaj Mehta This is my paper · ORCID
classification physics.bio-phq-bio.QM
keywords constrainedrandomensemblesminimalmodelstypicalityhigh-dimensionalbiologyneuralnetworksconsumer-resourceecologicalphasetransitionsepistasis
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

The paper argues that many observed behaviors of complex living systems—neural population activity, microbial community composition, evolutionary epistasis, tissue mechanics—are typical outcomes of random interactions, not products of finely tuned wiring. It defends a "random-with-constraints" modeling strategy: draw interaction matrices or couplings at random from ensembles that respect only broad biological constraints, then compare the ensemble's emergent dynamics to experiments. Across neuroscience, ecology, evolution, and other fields, the paper assembles cases where such models match quantitative experimental data without fitting every microscopic parameter. If this holds, it offers a minimal-model philosophy for high-dimensional biology, standing alongside small-circuit models and full simulations.

What carries the argument

The central object is a constrained random ensemble: a probability distribution over interaction matrices or coupling parameters in which only broad structural constraints are fixed—sign structure of interactions, balance between positive and negative couplings, sparsity, conservation laws, or metabolic limits. The method is to draw many random instances from such an ensemble, analyze the ensemble's typical dynamics (attractors, covariance spectra, stability boundaries, phase transitions), and compare these to experimental observables. The load-bearing analogy is to nuclear physics, where random matrices constrained by symmetry give universal level-spacing statistics; here the constraints ar

What would settle it

For a specific dataset—say neural population recordings or a defined microbial community—fix the constraint set before looking at the data, generate the constrained random ensemble's predictions, and compare them with predictions from the same ensemble with constraints changed or removed; if unconstrained or mis-constrained randomness fits the data equally well or better, the constraints are not doing the explanatory work.

Watch

Extended reading notes

Core claim

The central claim is that the random-with-constraints paradigm consistently captures experimentally observed dynamical and statistical features of living systems across many domains. The paper argues that rather than asking what happens in one specific wiring diagram, one should ask what happens in a "typical" high-dimensional system whose interactions are random but respect biologically motivated constraints—for example, excitatory-inhibitory balance and sparsity in neural circuits, metabolic flux balance in microbial communities, or random structure in fitness landscapes. These constrained ensembles produce attractors, spectra, phase transitions, and other observables that match experiment

Load-bearing premise

The load-bearing premise is that the reported agreements are genuine predictions rather than post-hoc fits—the constraint sets must be chosen without first seeing the data they are used to explain; if the constraints were tuned after the fact, the claim would be circular.

Editorial extensions

If this is right

  • If the paradigm is right, quantitative biological models may not need to fit every rate, weight, or interaction; specifying the right structural constraints could be enough for whole classes of predictions.
  • Deviations between a constrained random ensemble and real data become interpretable signals of special biological organization, rather than model failures.
  • Systematically comparing different constraint sets against the same data would reveal which constraints are essential for which observables, guiding model selection.
  • The approach gives high-throughput, high-dimensional datasets a direct theoretical target: ensemble statistics rather than a single fitted simulation.

Reading between the lines

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

  • One step the paper leaves open: nested comparisons of constraint sets (adding one constraint at a time and watching predictive gain) could test whether the constraints genuinely explain the data or merely add flexible fitting capacity.
  • If the environmental random-feature explanation holds, the same logic should generalize to other sensory or physiological datasets, where natural input statistics may themselves be described by random latent features.
  • A strong corollary, not developed here, is that much biological variation may be selectively neutral: phenotypes may occupy broad "allowed" volumes in interaction space, making constrained randomness the appropriate null model for measuring evolutionary or functional constraint.
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

3 major / 4 minor

Summary. This perspective argues that high-dimensional biological systems can be modeled with 'random-with-constraints' ensembles: interaction matrices are drawn randomly subject to biologically motivated constraints (e.g., Dale's principle, E-I balance, metabolic flux balance, sparsity), and ensemble-typical dynamics are compared with experiments. The paper traces the idea from Wigner's random-matrix approach in nuclear physics through Kauffman, May, Derrida, and Sompolinsky, then surveys successes in neuroscience, ecology/evolution, and other fields (soft matter, immunology, gene regulation). The stated central claim is that this paradigm 'consistently captures experimentally observed dynamical and statistical features of living systems across many domains of science' (Discussion, Section IV). The authors also identify open questions, especially why such models work and how to select constraints in advance.

Significance. If the central claim were established, the paper would make a useful case for constrained random ensembles as a minimal modeling philosophy for high-dimensional biology, complementing small-circuit models. The review is valuable as a curated entry point to a growing literature, and it correctly emphasizes falsifiable, quantitative comparisons with data as the relevant test. It is also honest in flagging open questions and in citing open-source simulation tools (e.g., [60], [61]). However, the paper is a perspective, not a systematic review: it presents a curated set of positive examples with no defined success criterion, no systematic comparison against alternative models, and no negative examples. The strength of the central claim is therefore substantially ahead of the evidence presented.

major comments (3)
  1. [Section IV, Discussion (first sentence)] The claim that the paradigm 'consistently captures experimentally observed dynamical and statistical features of living systems across many domains of science' is load-bearing but exceeds the evidence. The survey reports a curated set of successes, many from the authors' own prior work, with no systematic comparison, no pre-specified success metric, and no accounting for unpublished or negative cases. The Discussion itself concedes that systematic comparisons and error analyses are still needed. Please temper the claim to 'captures the features in the cases surveyed' and add an explicit paragraph on selection bias and how future systematic comparisons would test the generalization.
  2. [Section III.C (immunology) and Section IV (Discussion)] The manuscript includes immunology among the domains where the emerging picture is 'similar' (Section III.C), but immediately states that 'experimental confirmations of these models are still wanting.' The Discussion nevertheless groups immunology into the across-domains success claim. This is internally inconsistent. Please distinguish between experimentally confirmed cases and prospective or semi-quantitative ones, and ensure that the Discussion's summary counts only the confirmed cases as evidence for 'consistently captures experimental features.'
  3. [Section IV (Discussion, final paragraph)] The phrase 'predictive, quantitative descriptions without overfitting' presupposes that the constraints were not chosen after seeing the data being explained. The paper does not address this post-hoc-selection risk for most of the cited examples, and the Discussion lists 'developing predictive criteria for selecting the appropriate constraint set in advance' as an open question. Because the flexibility of the constraint set is the main potential source of circularity, please either (i) identify which surveyed examples used constraints fixed before comparison, or (ii) explicitly state that the predictive power claim applies only to those examples and that constraint selection remains an open methodological concern.
minor comments (4)
  1. [Abstract] The abstract says the paradigm 'represents a promising new modeling strategy' and 'provides a powerful minimal modeling philosophy.' Consider aligning this language with the more conditional conclusion of the Discussion, since the body already contains important caveats.
  2. [Acknowledgments] Typo: 'Chan-Zuckerburg Initiative' should be 'Chan-Zuckerberg Initiative.'
  3. [References / Equations] Several references contain LaTeX-encoding artifacts in the full text (e.g., 'Erd¨ os–R´ enyi' and 'perhaps. . . too coura- geously[ly]'). A final typesetting pass would improve readability.
  4. [Figure 2] The table-like figure is helpful, but it would benefit from a column stating whether each listed example involves quantitative agreement, qualitative agreement, or is still awaiting experimental confirmation. This would make the evidential status of each domain visible at a glance.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the review's claim rests on external benchmarks; self-citations are normal evidence.

full rationale

The paper is a perspective review, not a derivation. It argues that random-with-constraints models capture experimental features by citing a body of prior work, including some by the authors. However, these citations are not definitional: they refer to separate studies with their own models, data, and comparisons (e.g., Sederberg & Nemenman 2020 vs. mouse cortex recordings; Cui, Marsland & Mehta 2021 vs. random ecosystem analysis). The central claim is an empirical generalization, not a tautology. No equation in the paper reduces a prediction to a fitted input; no parameter is renamed as a prediction; no uniqueness theorem from the authors' prior work is invoked to force a choice. The Discussion explicitly identifies open questions (why the models work, how to choose constraints in advance), acknowledging that predictive selection criteria are not yet established. This is a limitation of support, not circular reasoning. Self-citations are present but are not load-bearing in a circular sense because they are independent, externally checkable results. Score 1 reflects minor self-citation in a review, with no circular structure.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The paper itself fits no parameters and introduces no new entities. Its argument rests on the correctness of background statistical physics, the reliability of the cited experiments, and the unproven typicality premise.

assumptions (3)
  • standard math Random matrix theory, dynamical mean-field theory, and replica calculations cited in Sections II and III correctly describe the statistical behavior of the constrained random ensembles.
    The review's argument relies on these methods being correct, but they are not re-derived; they are background from cited papers such as [22], [51], [52].
  • domain assumption The experimental datasets and comparisons reported in the cited papers are accurate, and the models' predictions were not obtained by fitting the observational data.
    The central claim that random-with-constraints models 'consistently capture' experimental features depends on the veracity and non-tuned nature of the cited agreements (Section III and Discussion).
  • domain assumption Biological systems are sufficiently high-dimensional and heterogeneous that the 'typical' behavior of a constrained random ensemble is a good approximation to the observed system.
    This is the core premise of the paradigm, stated in the Introduction as 'embrace the idea that many biological behaviors we observe are typical.' It is argued by example but not proven.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Randomness with constraints: constructing minimal models for high-dimensional biology." pith.science (2026). https://pith.science/paper/LCE33BJL

@misc{pith2026250903765,
  author       = {Pith},
  title        = {Pith review of: Randomness with constraints: constructing minimal models for high-dimensional biology},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LCE33BJL}},
  note         = {Machine review of arXiv:2509.03765}
}
read the original abstract

Biologists and physicists have a rich tradition of modeling living systems with simple models composed of a few interacting components. Despite the remarkable success of this approach, it remains unclear how to use such finely tuned models to study complex biological systems composed of numerous heterogeneous, interacting components. One possible strategy for taming this biological complexity is to embrace the idea that many biological behaviors we observe are ``typical'' and can be modeled using random systems that respect biologically-motivated constraints. Here, we review recent works showing how this approach can be used to make close connection with experiments in biological systems ranging from neuroscience to ecology and evolution and beyond. Collectively, these works suggest that the ``random-with-constraints'' paradigm represents a promising new modeling strategy for capturing experimentally observed dynamical and statistical features in high-dimensional biological data and provides a powerful minimal modeling philosophy for biology.

Figures

Figures reproduced from arXiv: 2509.03765 by the authors.

Figure 1
Figure 1. FIG. 1. Traditional approaches to modeling in biology start with a precisely specified small system, which is then made more [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. III. CHALLENGING RANDOM NETWORK MODELS BY EXPERIMENTS A. Neuroscience As the number of neurons one can record from simulta￾neously has steadily increased over the last decades, and the connectomics data exploded, large-scale fine-tuned circuit models have not kept up with assimilating these data. Instead, random network models have increasingly moved from purely theoretical constructs to tools that quantitatively ac… view at source ↗
Figure 2
Figure 2. FIG. 2. “Random-with-constraints” approach started in nuclear physics. Applications in neuroscience and ecology, discussed [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

83 extracted references · 78 canonical work pages

  1. [60]

    P.-Y. Ho, B. H. Good, and K. C. Huang, Competition for fluctuating resources reproduces statistics of species abundance over time across wide-ranging microbiotas, eLife 11, e75168 (2022)

    2022

  2. [61]

    Grilli, Macroecological laws describe variation and di- versity in microbial communities, Nature Commun

    J. Grilli, Macroecological laws describe variation and di- versity in microbial communities, Nature Commun. 11, 4743 (2020)

    work page 2020

  3. [1]

    A. L. Hodgkin and A. F. Huxley, A quantitative descrip- tion of membrane current and its application to conduc- tion and excitation in nerve, J. Physiol. 117, 500 (1952)

    1952

  4. [2]

    A. J. Lotka, Elements of physical biology (Williams & Wilkins, 1925)

    work page 1925

  5. [3]

    random- with-constraints

    to study large ecosystems [45, 50–53]. Since it is impossible to measure all ecological interactions experi- mentally, physicists have naturally adopted the random- with-constraints paradigm to ask if one can explain the patterns seen in large-scale ecological datasets. This program has been remarkably successful. One in- sight has been that, just like ph...

    2019

  6. [4]

    R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon, Network motifs: simple building blocks of complex networks, Science 298, 824 (2002)

    work page 2002

  7. [5]

    Karin, A

    O. Karin, A. Swisa, B. Glaser, Y. Dor, and U. Alon, Dy- namical compensation in physiological circuits, Molecu- lar Systems Biol. 12, 886 (2016)

    work page 2016

  8. [6]

    Leonardo da Vinci

    V. Volterra, Variazioni e fluttuazioni del numero d’individui in specie animali conviventi (Societ` a anonima tipografica “Leonardo da Vinci”, 1926)

    work page 1926

Show all 83 references
  1. [7]

    random-with-constraints

    or other model networks that preserve degree distri- butions [8], to ask whether observed features (e.g., clus- tering, motifs) exceed chance expectations. For example, one can compare the frequency of a feedforward loop in a real gene network to its frequency in a randomized ...

    2025 arXiv

  2. [8]

    Barab´ asi and R

    A.-L. Barab´ asi and R. Albert, Emergence of scaling in random networks, Science 286, 509 (1999)

    1999

  3. [9]

    Newman, Networks (Oxford University Press, 2018)

    M. Newman, Networks (Oxford University Press, 2018)

    2018

  4. [10]

    Erdos and A

    P. Erdos and A. Renyi, On random graphs. i, Publica- tiones Mathematicae 6, 290–297 (1959)

    1959

  5. [11]

    Wigner, Conference on neutron physics by time-of- flight, Oak Ridge National Lab

    E. Wigner, Conference on neutron physics by time-of- flight, Oak Ridge National Lab. Report ORNL-2309 (1957)

    1957

  6. [12]

    E. P. Wigner, On the statistical distribution of the widths and spacings of nuclear resonance levels, in Mathemati- cal Proceedings of the Cambridge Philosophical Society , Vol. 47 (Cambridge University Press, 1951) pp. 790–798

    1951

  7. [13]

    F. J. Dyson, Statistical theory of the energy levels of complex systems. I, J. Math. Phys. 3, 140 (1962)

    1962

  8. [14]

    A. S. Perelson and G. F. Oster, Theoretical studies of clonal selection: minimal antibody repertoire size and reliability of self-non-self discrimination, J. Theor. Biol. 81, 645 (1979)

    1979

  9. [15]

    S. A. Kauffman, Metabolic stability and epigenesis in randomly constructed genetic nets, J. Theor. Biol. 22, 437 (1969)

    1969

  10. [16]

    N. K. Jerne, Towards a network theory of the immune system, Ann. Immunol. (Inst. Pasteur), C 125, 373 (1974)

    1974

  11. [17]

    Parisi, A simple model for the immune network, Proc

    G. Parisi, A simple model for the immune network, Proc. Natl. Acad. Sci. (USA) 87, 429 (1990)

    1990

  12. [18]

    A. S. Perelson, Immune network theory, Immunol. Rev 110, 36 (1989)

    1989

  13. [19]

    R. J. De Boer and A. S. Perelson, Size and connectivity as emergent properties of a developing immune network, J. Theor. Biol. 149, 381 (1991)

    1991

  14. [20]

    J. D. Bryngelson and P. G. Wolynes, Spin glasses and the statistical mechanics of protein folding., Proc. Natl. Acad. Sci. (USA) 84, 7524 (1987)

    1987

  15. [21]

    R. M. May, Will a large complex system be stable?, Na- ture 238, 413 (1972)

    1972

  16. [22]

    importance

    introduced a continuous-time neural network of many rate-based neurons coupled by Gaussian random synaptic weights and solved its dynamics via dynamical mean-field theory (DMFT), demonstrating emergence of high-dimensional chaos. Subsequent extensions by van Vreeswijk and Somp...

  17. [23]

    Derrida, Random-energy model: Limit of a family of disordered models, Phys

    B. Derrida, Random-energy model: Limit of a family of disordered models, Phys. Rev. Lett. 45, 79 (1980)

    1980

  18. [24]

    D. J. Amit, Modeling brain function: The world of attrac- tor neural networks (Cambridge university press, 1989)

    1989

  19. [25]

    Sompolinsky, A

    H. Sompolinsky, A. Crisanti, and H.-J. Sommers, Chaos in random neural networks, Phys. Rev. Lett. 61, 259 (1988)

    1988

  20. [26]

    Van Vreeswijk and H

    C. Van Vreeswijk and H. Sompolinsky, Chaos in neuronal networks with balanced excitatory and inhibitory activ- ity, Science 274, 1724 (1996)

    1996

  21. [27]

    echo state

    H. Jaeger, The “echo state” approach to analysing and training recurrent neural networks-with an erratum note, Bonn, Germany: German national research center for in- formation technology GMD Techn. Rep. 148, 13 (2001)

    2001

  22. [28]

    Maass, T

    W. Maass, T. Natschl¨ ager, and H. Markram, Real-time computing without stable states: A new framework for neural computation based on perturbations, Neural Com- putation 14, 2531 (2002)

    2002

  23. [29]

    Hu and H

    Y. Hu and H. Sompolinsky, The spectrum of covariance matrices of randomly connected recurrent neuronal net- works with linear dynamics, PLOS Comput. Biol. 18, e1010327 (2022)

    2022

  24. [30]

    Ahmadian and K

    Y. Ahmadian and K. D. Miller, What is the dynamical regime of cerebral cortex?, Neuron 109, 3373 (2021)

    2021

  25. [31]

    Sederberg and I

    A. Sederberg and I. Nemenman, Randomly connected networks generate emergent selectivity and predict de- coding properties of large populations of neurons, PLOS Comput. Biol. 16, e1007875 (2020)

    2020

  26. [32]

    Huang, D

    C. Huang, D. A. Ruff, R. Pyle, R. Rosenbaum, M. R. Cohen, and B. Doiron, Circuit models of low-dimensional shared variability in cortical networks, Neuron 101, 337 (2019)

    2019

  27. [33]

    Singer, Cortical dynamics revisited, Trends Cogn

    W. Singer, Cortical dynamics revisited, Trends Cogn. Sci. 17, 616 (2013)

    2013

  28. [34]

    P. Enel, E. Procyk, R. Quilodran, and P. F. Dominey, Reservoir computing properties of neural dynamics in prefrontal cortex, PLOS Comput. Biol. 12, e1004967 (2016)

    2016

  29. [35]

    D. G. Clark and M. Beiran, Structure of activity in mul- tiregion recurrent neural networks, Proc. Natl. Acad. Sci. (USA) 122, e2404039122 (2025)

    2025

  30. [36]

    G. J. Tian, O. Zhu, V. Shirhatti, C. M. Greenspon, J. E. Downey, D. J. Freedman, and B. Doiron, Firing rate di- versity lowers the dimension of population covariability in neuronal networks, bioRxiv 2024.08.30.610535 (2024)

    2024

  31. [37]

    M. C. Morrell, A. J. Sederberg, and I. Nemenman, Latent dynamical variables produce signatures of spatiotempo- ral criticality in large biological systems, Phys. Rev. Lett. 126, 118302 (2021)

    2021

  32. [38]

    Meshulam, J

    L. Meshulam, J. L. Gauthier, C. D. Brody, D. W. Tank, and W. Bialek, Coarse graining, fixed points, and scaling 8 in a large population of neurons, Phys. Rev. Lett. 123, 178103 (2019)

    2019

  33. [39]

    M. C. Morrell, I. Nemenman, and A. Sederberg, Neu- ral criticality from effective latent variables, eLife 12, RP89337 (2024)

    2024

  34. [40]

    M´ ezard, G

    M. M´ ezard, G. Parisi, and A. Zee, Spectra of euclidean random matrices, Nuclear Phys. B 559, 689 (1999)

    1999

  35. [41]

    Z. Wang, W. Mai, Y. Chai, K. Qi, H. Ren, C. Shen, S. Zhang, G. Tan, Y. Hu, and Q. Wen, The geometry and dimensionality of brain-wide activity, eLife14, RP100666 (2025)

    2025

  36. [42]

    J. J. Pattadkal, G. Mato, C. van Vreeswijk, N. J. Priebe, and D. Hansel, Emergent orientation selectivity from ran- dom networks in mouse visual cortex, Cell Rep. 24, 2042 (2018)

  37. [43]

    Breffle, H

    J. Breffle, H. Germaine, J. D. Shin, S. P. Jadhav, and P. Miller, Intrinsic dynamics of randomly clustered net- works generate place fields and preplay of novel environ- ments, eLife 13, RP93981 (2024)

    2024

  38. [44]

    J. L. Natale, H. G. E. Hentschel, and I. Nemenman, Pre- cise spatial memory in local random networks, Phys. Rev. E 102, 022405 (2020)

    2020

  39. [45]

    Rosenbaum, M

    R. Rosenbaum, M. A. Smith, A. Kohn, J. E. Rubin, and B. Doiron, The spatial structure of correlated neuronal variability, Nature Neurosci. 20, 107 (2017)

    2017

  40. [46]

    O. Maoz, G. Tkaˇ cik, M. S. Esteki, R. Kiani, and E. Schneidman, Learning probabilistic neural representa- tions with randomly connected circuits, Proc. Natl. Acad. Sci. (USA) 117, 25066 (2020)

    2020

  41. [47]

    Litwin-Kumar, K

    A. Litwin-Kumar, K. D. Harris, R. Axel, H. Sompolinsky, and L. Abbott, Optimal degrees of synaptic connectivity, Neuron 93, 1153 (2017)

    2017

  42. [48]

    W. Cui, R. Marsland III, and P. Mehta, Les houches lectures on community ecology: From niche theory to statistical mechanics, arXiv 2403.05497 (2024)

    2024 arXiv

  43. [49]

    P. J. Turnbaugh, R. E. Ley, M. Hamady, C. M. Fraser- Liggett, R. Knight, and J. I. Gordon, The human micro- biome project, Nature 449, 804 (2007)

    2007

  44. [50]

    Lloyd-Price, A

    J. Lloyd-Price, A. Mahurkar, G. Rahnavard, J. Crabtree, J. Orvis, A. B. Hall, A. Brady, H. H. Creasy, C. Mc- Cracken, M. G. Giglio, et al. , Strains, functions and dy- namics in the expanded human microbiome project, Na- ture 550, 61 (2017)

    2017

  45. [51]

    A. G. Cheng, P.-Y. Ho, A. Aranda-D ´ ıaz, S. Jain, F. B. Yu, X. Meng, M. Wang, M. Iakiviak, K. Nagashima, A. Zhao, et al. , Design, construction, and in vivo aug- mentation of a complex gut microbiome, Cell 185, 3617 (2022)

    2022

  46. [52]

    Marsland III, W

    R. Marsland III, W. Cui, and P. Mehta, A minimal model for microbial biodiversity can reproduce experimentally observed ecological patterns, Scientific Rep. 10, 3308 (2020)

    2020

  47. [53]

    C. K. Fisher and P. Mehta, The transition between the niche and neutral regimes in ecology, Proc. Natl. Acad. Sci. (USA) 111, 13111 (2014)

    2014

  48. [54]

    Bunin, Ecological communities with lotka-volterra dy- namics, Phys

    G. Bunin, Ecological communities with lotka-volterra dy- namics, Phys. Rev. E 95, 042414 (2017)

    2017

  49. [55]

    Tikhonov and R

    M. Tikhonov and R. Monasson, Collective phase in re- source competition in a highly diverse ecosystem, Phys. Rev. Lett. 118, 048103 (2017)

    2017

  50. [56]

    M. T. Pearce, A. Agarwala, and D. S. Fisher, Stabiliza- tion of extensive fine-scale diversity by ecologically driven spatiotemporal chaos, Proc. Natl. Acad. Sci. (USA) 117, 14572 (2020)

    2020

  51. [57]

    J. Hu, D. R. Amor, M. Barbier, G. Bunin, and J. Gore, Emergent phases of ecological diversity and dynamics mapped in microcosms, Science 378, 85 (2022)

    2022

  52. [58]

    J. E. Goldford, N. Lu, D. Baji´ c, S. Estrela, M. Tikhonov, A. Sanchez-Gorostiaga, D. Segr` e, P. Mehta, and A. Sanchez, Emergent simplicity in microbial community assembly, Science 361, 469 (2018)

    2018

  53. [59]

    Dal Bello, H

    M. Dal Bello, H. Lee, A. Goyal, and J. Gore, Resource– diversity relationships in bacterial communities reflect the network structure of microbial metabolism, Nature Ecology Evol. 5, 1424 (2021)

    2021

  54. [62]

    W. R. Shoemaker, ´A. S´ anchez, and J. Grilli, Macroeco- logical patterns in experimental microbial communities, PLOS Comput. Biol. 21, e1013044 (2025)

    2025

  55. [63]

    Marsland, W

    R. Marsland, W. Cui, J. Goldford, and P. Mehta, The community simulator: A Python package for microbial ecology, Plos one 15, e0230430 (2020)

    2020

  56. [64]

    Y. Gao, Y. S ¸im¸ sek, E. Gheysen, T. Borman, Y. Li, L. Lahti, K. Faust, and D. R. Garza, miaSim: an R/Bioconductor package to easily simulate microbial community dynamics, Meth. Ecol. Evol. 14, 1967 (2023)

    1967

  57. [65]

    Reddy and M

    G. Reddy and M. M. Desai, Global epistasis emerges from a generic model of a complex trait, eLife 10, e64740 (2021)

    2021

  58. [66]

    B. H. Good and L. B. Rosenfeld, Eco-evolutionary feed- backs in the human gut microbiome, Nature Commun. 14, 7146 (2023)

    2023

  59. [67]

    B. H. Good, S. Martis, and O. Hallatschek, Adapta- tion limits ecological diversification and promotes eco- logical tinkering during the competition for substitutable resources, Proc. Natl. Acad. Sci. (USA) 115, E10407 (2018)

    2018

  60. [68]

    D. S. Fisher, Inevitability of red queen evolution driven by organismic complexity and simple feedback via en- vironmental modification, bioRxiv 2021.09.26.461893 (2021)

    2021

  61. [69]

    Z. Feng, E. Blumenthal, P. Mehta, and A. Goyal, A the- ory of ecological invasions and its implications for eco- evolutionary dynamics, arXiv 2503.10865 (2025)

    2025 arXiv

  62. [70]

    Goyal, L

    A. Goyal, L. S. Bittleston, G. E. Leventhal, L. Lu, and O. X. Cordero, Interactions between strains govern the eco-evolutionary dynamics of microbial communities, eLife 11, e74987 (2022)

    2022

  63. [71]

    Y. Chen, Y. Shen, P. Lin, D. Tong, Y. Zhao, S. Allesina, X. Shen, and C.-I. Wu, Gene regulatory network sta- bilized by pervasive weak repressions: microrna func- tions revealed by the may–wigner theory, National Sci- ence Rev. 6, 1176 (2019)

    2019

  64. [72]

    G. Bel, B. Munsky, and I. Nemenman, The simplicity of completion time distributions for common complex bio- chemical processes, Physical Biol. 7, 016003 (2009)

    2009

  65. [73]

    Beroz, L

    F. Beroz, L. M. Jawerth, S. M¨ unster, D. A. Weitz, C. P. Broedersz, and N. S. Wingreen, Physical limits to biome- chanical sensing in disordered fibre networks, Nature Commun. 8, 16096 (2017)

    2017

  66. [74]

    K. A. Jansen, A. J. Licup, A. Sharma, R. Rens, F. C. 9 MacKintosh, and G. H. Koenderink, The role of network architecture in collagen mechanics, Biophys. J.114, 2665 (2018)

    2018

  67. [75]

    D. T. Casey, S. Bou Jawde, J. Herrmann, V. Mori, J. M. Mahoney, B. Suki, and J. H. Bates, Percolation of col- lagen stress in a random network model of the alveolar wall, Scientific Rep. 11, 16654 (2021)

    2021

  68. [76]

    Stanifer, P

    E. Stanifer, P. Morse, A. Middleton, and M. L. Man- ning, Simple random matrix model for the vibrational spectrum of structural glasses, Phys. Rev. E 98, 042908 (2018)

    2018

  69. [77]

    Mayer, V

    A. Mayer, V. Balasubramanian, T. Mora, and A. M. Wal- czak, How a well-adapted immune system is organized, Proc. Natl. Acad. Sci. (USA) 112, 5950 (2015)

    2015

  70. [78]

    Marsland III, O

    R. Marsland III, O. Howell, A. Mayer, and P. Mehta, Tregs self-organize into a computing ecosystem and im- plement a sophisticated optimization algorithm for me- diating immune response, Proc. Natl. Acad. Sci. (USA) 118, e2011709118 (2021)

    2021

  71. [79]

    Fleig and I

    P. Fleig and I. Nemenman, Hidden data structures and statistics of natural images, PRX Life 3, 023014 (2025)

    2025

  72. [80]

    Goaillard and E

    J.-M. Goaillard and E. Marder, Ion channel degener- acy, variability, and covariation in neuron and circuit re- silience, Annual Rev. Neurosci. 44, 335 (2021)

    2021

  73. [81]

    Marder and A

    E. Marder and A. L. Taylor, Multiple models to capture the variability in biological neurons and networks, Nature Neurosci. 14, 133 (2011)

    2011

  74. [82]

    Frankle and M

    J. Frankle and M. Carbin, The lottery ticket hypothesis: Finding sparse, trainable neural networks, arXiv preprint arXiv:1803.03635 (2018)

    2018 arXiv

  75. [83]

    W. Cui, R. Marsland III, and P. Mehta, Diverse commu- nities behave like typical random ecosystems, Phys. Rev. E 104, 034416 (2021)

    2021

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.