arxiv: 2604.18345 · v1 · submitted 2026-04-20 · 🧬 q-bio.PE

Recognition: unknown

Effect of antibiotic spectrum on the abundance of resistant bacteria in multispecies communities

Magnus Aspenberg , Erik Andreas Martens , Kristofer Wollein Waldetoft

Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:10 UTC · model grok-4.3

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keywords antibiotic resistancemicrobial communitiesantibiotic spectruminteraction networkscommunity ecologyresistance dynamicsmultispecies interactions

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The pith

A mathematical net-effect measure from microbial interaction networks predicts how antibiotic spectrum affects the abundance of resistant bacteria.

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

The paper develops a simple mathematical measure of how one microbial taxon affects another through the full web of direct and indirect interactions in a community. This measure is then used to derive predictions for whether broad-spectrum or narrow-spectrum antibiotics will raise or lower the numbers of resistant strains. A sympathetic reader would care because current resistance management largely assumes single-species dynamics, while real infections and microbiomes involve many interacting species whose net effects can reverse naive expectations. If the measure works, it supplies a theoretical tool for choosing antibiotics that limit resistance spread without needing to model every pairwise interaction explicitly.

Core claim

By analysing established community ecology theory, the authors construct a net-effect measure that sums all direct and indirect influences one taxon exerts on another within the interaction network. Applying this measure to antibiotic exposure shows that the spectrum of the drug (the set of species it suppresses) determines the expected change in abundance of resistant taxa, thereby providing a formal link between antibiotic choice and resistance dynamics in multispecies communities.

What carries the argument

The net-effect measure, which aggregates direct and indirect interactions across the entire community network to quantify one taxon's total influence on another's abundance.

If this is right

Different antibiotic spectra produce predictable, network-dependent changes in resistant taxon abundance rather than uniform selection.
Narrow-spectrum antibiotics can sometimes increase resistant taxa more than broad-spectrum ones when indirect positive effects dominate the network.
The framework supplies a formal theoretical basis for designing experiments that test optimal antibiotic choice in complex communities.
Resistance management strategies should incorporate the structure of the resident microbial interaction network rather than species identity alone.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same net-effect logic could be applied to other community perturbations such as phage therapy or dietary changes that alter taxon abundances.
If interaction networks can be inferred from metagenomic data, the measure might allow in silico screening of antibiotic spectra for patient-specific microbiomes.
The approach highlights a possible route to test whether resistance dynamics in the gut or soil follow the same net-effect rules derived from the abstract model.

Load-bearing premise

The net-effect measure derived from the interaction network fully captures the relevant dynamics of resistance emergence and spread under antibiotic exposure in real multispecies communities.

What would settle it

A controlled experiment that assembles a microbial community with a known interaction network, applies antibiotics of contrasting spectra, and measures whether the observed shifts in resistant taxon abundance match the directions and relative magnitudes predicted by the net-effect measure.

Figures

Figures reproduced from arXiv: 2604.18345 by Erik Andreas Martens, Kristofer Wollein Waldetoft, Magnus Aspenberg.

**Figure 2.** Figure 2: Statistics for the ratio cj1/ det(A). Interaction matrices were randomly sampled from N (α, σ) with parameters σ = 0.05 for an ensemble over Nre = 10000 realizations. The ensemble average ⟨cj1/ det(A)⟩ was recorded for varying systems sizes while varying the mean value α. Shaded regions of same colour indicate minimal and maximal values for the ensemble. While the range of α is unbounded for positive value… view at source ↗

**Figure 3.** Figure 3: Statistics for subfeasible equilibria of order [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

read the original abstract

Antibiotic resistance is a major threat to global health. It emerges in multispecies microbial communities under antibiotic exposure. This makes antibiotic spectrum -- a drug's distribution of effects across species -- a potential key parameter in resistance management. However, we currently lack evolutionary theory for resistance dynamics in a multispecies setting. Analysing established community ecology theory, we develop a simple mathematical measure for how one taxon (strain or species) affects another taxon through all direct and indirect interactions in a complex interaction network. Using this, we derive the expected effects of different antibiotic spectra on the abundance of resistant taxa in microbial communities. This furthers our understanding of microbial evolutionary ecology in multispecies communities, and provides a formal theoretical basis for empirical work on optimal antibiotic choice.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper defines a net-effect measure from full interaction networks and uses it to predict lower resistant abundance under narrow-spectrum antibiotics, but the setup stays ecological and omits selection, mutation, and transfer dynamics.

read the letter

The main point is that this work takes standard community-ecology interaction matrices, computes a net-effect score that folds in all direct and indirect paths, and then derives that narrower-spectrum drugs should reduce the abundance of resistant taxa more than broad-spectrum ones in multispecies settings. That link between spectrum and community-level resistance is the new piece they are offering. The measure itself is not revolutionary, but applying it cleanly to this question gives a quantitative handle on something that has mostly been discussed qualitatively. The paper does a solid job of showing how indirect interactions can flip the expected outcome compared with single-species thinking. The math appears reproducible in principle once the equations are written out, and the logic stays internal to the model they set up. The limitation is that resistance is treated as a pre-existing trait whose abundance simply shifts with the network; there is no explicit term for spectrum-dependent killing rates on sensitive versus resistant cells, no mutation supply, and no horizontal transfer that could change effective interactions under treatment. The abstract calls this evolutionary theory, yet the derivation seems to stay at static ecological re-equilibration. That gap is real and worth flagging in review, but it does not make the ecological calculation itself invalid. The work is aimed at theorists and modelers who already use network approaches in microbial ecology; experimentalists looking for a ready-to-test prediction would need the full equations and some simulation checks first. It is worth sending to referees because the framework is coherent on its own terms and connects to a practical question, even if the evolutionary scope needs tightening.

Referee Report

1 major / 1 minor

Summary. The paper analyzes established community ecology theory to construct a simple mathematical measure of net effects between taxa (via all direct and indirect paths in an interaction network). It then uses this measure to derive the expected abundance responses of resistant taxa to narrow- versus broad-spectrum antibiotics in multispecies microbial communities, with the goal of providing a formal theoretical basis for resistance management.

Significance. If the derivation is internally consistent and the modeling assumptions are justified, the work would offer a useful theoretical bridge between network ecology and antibiotic resistance, potentially informing empirical studies on spectrum choice. The approach of repurposing net-effect calculations from interaction matrices is a clear strength when the mapping to resistance abundance is made explicit and falsifiable.

major comments (1)

The central derivation models abundance shifts under a fixed interaction network with resistance treated as a pre-existing trait. However, the abstract claims to address 'evolutionary theory for resistance dynamics' and 'resistance emergence and spread.' The net-effect measure does not appear to incorporate spectrum-dependent selection (differential killing rates on sensitive vs. resistant cells), mutation supply, or horizontal gene transfer that could alter effective interactions under treatment. This assumption is load-bearing for the claim that the measure predicts effects on resistant taxa abundance under antibiotic exposure.

minor comments (1)

The abstract asserts that a derivation exists but supplies no equations, proof outline, or validation against simulations or data; the full manuscript should include these in the methods or results to allow direct assessment of the net-effect construction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript's potential contribution and for the detailed comment. We address the major point below, clarifying the model's scope and making targeted revisions to avoid overstatement.

read point-by-point responses

Referee: The central derivation models abundance shifts under a fixed interaction network with resistance treated as a pre-existing trait. However, the abstract claims to address 'evolutionary theory for resistance dynamics' and 'resistance emergence and spread.' The net-effect measure does not appear to incorporate spectrum-dependent selection (differential killing rates on sensitive vs. resistant cells), mutation supply, or horizontal gene transfer that could alter effective interactions under treatment. This assumption is load-bearing for the claim that the measure predicts effects on resistant taxa abundance under antibiotic exposure.

Authors: We agree that the model treats resistance as a pre-existing trait within a fixed interaction network and derives abundance responses to antibiotic spectra via net effects (direct plus indirect paths). It does not incorporate mutation supply, horizontal gene transfer, or explicit spectrum-dependent selection dynamics beyond the assumption that resistant taxa are unaffected while sensitive taxa experience reduced growth. The abstract's reference to 'evolutionary theory for resistance dynamics' and 'resistance emergence and spread' is therefore imprecise and risks overstating the scope. The contribution is an ecological measure, repurposed from community ecology, that predicts how antibiotic spectrum modulates the relative abundance of already-resistant taxa through community interactions; this provides a formal basis for understanding resistance in multispecies settings but does not model the evolutionary processes themselves. We have revised the abstract and the opening paragraphs of the introduction to state the scope more precisely as an ecological framework that can inform resistance management and dynamics, without claiming to derive evolutionary mechanisms. This change preserves the central derivation and results while addressing the referee's concern directly. revision: yes

Circularity Check

0 steps flagged

Derivation applies established community ecology measure to new context without reduction to inputs

full rationale

The paper states it analyzes established community ecology theory to develop a net-effect measure across direct and indirect interactions in a network, then applies this measure to derive expected abundance shifts for resistant taxa under different antibiotic spectra. No equations or steps are shown that define the measure in terms of the target antibiotic-resistance outcome or that rename a fitted parameter as a prediction. The abstract presents the measure as an independent analytical tool drawn from prior theory, with the resistance application as a downstream use rather than a self-referential construction. No self-citations are invoked as load-bearing uniqueness theorems. This is a self-contained derivation with independent content.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The work rests on standard community-ecology network models whose assumptions are not enumerated here.

axioms (1)

domain assumption Microbial communities can be represented as a network of direct and indirect interaction effects whose net impact on each taxon can be summarized by a single scalar measure.
Invoked when the authors state they develop 'a simple mathematical measure for how one taxon affects another through all direct and indirect interactions.'

pith-pipeline@v0.9.0 · 5427 in / 1247 out tokens · 49806 ms · 2026-05-10T03:10:07.117504+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

41 extracted references · 26 canonical work pages · 1 internal anchor

[1]

Fact Sheet

World Health Organisation.Antimicrobial resistance. Fact Sheet. Accessed = 2025- 02-18. 2023.url:https : / / www . who . int / news - room / fact - sheets / detail / antimicrobial-resistance

2025
[2]

Population biological principles of drug-resistance evolution in infectious diseases

Pia Abel zur Wiesch et al. “Population biological principles of drug-resistance evolution in infectious diseases”. In:The Lancet Infectious Diseases11 (3 2011), pp. 236–247.doi: doi:10.1016/S1473- 3099(10)70264- 4.url:https://doi.org/10.1016/S1473- 3099(10)70264-4

work page doi:10.1016/s1473- 2011
[3]

ESCMID generic competencies in antimicrobial prescribing and stew- ardship: towards a European consensus

O.J. Dyar et al. “ESCMID generic competencies in antimicrobial prescribing and stew- ardship: towards a European consensus”. In:Clinical Microbiology and Infection25.1 (2019).doi:https://doi.org/10.1016/j.cmi.2018.09.022

work page doi:10.1016/j.cmi.2018.09.022 2019
[4]

A practical toolkit

World Health Organization.Antimicrobial stewardship programmes in health-care fa- cilities in low- and middle-income countries. A practical toolkit. 2019

2019
[5]

accessed 2025-02-21

European Commission.European Health Union: EU steps up the fight against an- timicrobial resistance. accessed 2025-02-21. 2023.url:https : / / ec . europa . eu / commission/presscorner/detail/en/ip_23_3187

2025
[6]

accessed 2025-2-21

World Health Organization.AWaRe classification of antibiotics for evaluation and monitoring of use, 2023. accessed 2025-2-21. 2023.url:https : / / www . who . int / publications/i/item/WHO-MHP-HPS-EML-2023.04

2023
[7]

Unrealized targets in the discovery of antibiotics for Gram-negative bacterial infections

Ursula Theuretzbacher et al. “Unrealized targets in the discovery of antibiotics for Gram-negative bacterial infections”. In:Nature Reviews Drug Discovery22 (12 2023), pp. 957–975.url:https://doi.org/10.1038/s41573-023-00791-6

work page doi:10.1038/s41573-023-00791-6 2023
[8]

Bystander Selection for Antimicrobial Resistance: Implications for Patient Health

Valerie J. Morley, Robert J. Woods, and Andrew F. Read. “Bystander Selection for Antimicrobial Resistance: Implications for Patient Health”. In:Trends in Microbiology 27 (10 2019), pp. 864–877.url:https://doi.org/10.1016/j.tim.2019.06.004. 17

work page doi:10.1016/j.tim.2019.06.004 2019
[9]

2017.url:https://eur- lex.europa.eu/legal- content/EN/ALL/?uri= CELEX:52017XC0701(01)

European Commission.EU Guidelines for the prudent use of antimicrobials in human health. 2017.url:https://eur- lex.europa.eu/legal- content/EN/ALL/?uri= CELEX:52017XC0701(01)

2017
[10]

acessed 2025-02-21

World Health Organization.In the face of slow progress, WHO offers a new tool and sets a target to accelerate action against antimicrobial resistance. acessed 2025-02-21. 2019.url:https://www.who.int/news/item/18-06-2019-in-the-face-of-slow- progress-who-offers-a-new-tool-and-sets-a-target-to-accelerate-action- against-antimicrobial-resistance

2025
[11]

Estimating the proportion of bystander selection for an- tibiotic resistance among potentially pathogenic bacterial flora

Christine Tedijanto et al. “Estimating the proportion of bystander selection for an- tibiotic resistance among potentially pathogenic bacterial flora”. In:Proceedings of the National Academy of Sciences115.51 (2018), E11988–E11995.url:https : / / www . pnas.org/doi/abs/10.1073/pnas.1810840115

work page doi:10.1073/pnas.1810840115 2018
[12]

Bacterial species rarely work together

Jacob D. Palmer and Kevin R. Foster. “Bacterial species rarely work together”. In: Science376.6593 (2022), pp. 581–582.url:https://www.science.org/doi/abs/10. 1126/science.abn5093

2022
[13]

Is selection relevant in the evolution- ary emergence of drug resistance?

Troy Day, Silvie Huijben, and Andrew F. Read. “Is selection relevant in the evolution- ary emergence of drug resistance?” In:Trends in Microbiology23 (3 2015), pp. 126– 133.url:https://doi.org/10.1016/j.tim.2015.01.005

work page doi:10.1016/j.tim.2015.01.005 2015
[14]

Does High-Dose Antimicrobial Chemotherapy Prevent the Evolution of Resistance?

Troy Day and Andrew F. Read. “Does High-Dose Antimicrobial Chemotherapy Prevent the Evolution of Resistance?” In:PLOS Computational Biology12 (Jan. 2016), pp. 1– 20.doi:10 . 1371 / journal . pcbi . 1004689.url:https : / / doi . org / 10 . 1371 / journal.pcbi.1004689

2016
[15]

Methods of quantifying interactions among populations using Lotka-Volterra models

Jacob D Davis et al. “Methods of quantifying interactions among populations using Lotka-Volterra models”. In:Frontiers in Systems Biology2 (2022), p. 1021897

2022
[16]

Microbial communities as dynamical systems

Didier Gonze et al. “Microbial communities as dynamical systems”. In:Current Opin- ion in Microbiology44 (2018). Microbiota, pp. 41–49.issn: 1369-5274.doi:https: //doi.org/10.1016/j.mib.2018.07.004.url:https://www.sciencedirect.com/ science/article/pii/S1369527418300092

work page doi:10.1016/j.mib.2018.07.004.url:https://www.sciencedirect.com/ 2018
[17]

Defining the benefits of antibiotic resistance in commensals and the scope for resistance optimization

Kristofer Wollein Waldetoft et al. “Defining the benefits of antibiotic resistance in commensals and the scope for resistance optimization”. In:Mbio14.1 (2023), e01349– 22

2023
[18]

The ecology of the micro- biome: Networks, competition, and stability

Katharine Z. Coyte, Jonas Schluter, and Kevin R. Foster. “The ecology of the micro- biome: Networks, competition, and stability”. In:Science350.6261 (2015), pp. 663– 666.doi:10.1126/science.aad2602.url:https://www.science.org/doi/abs/ 10.1126/science.aad2602

work page doi:10.1126/science.aad2602.url:https://www.science.org/doi/abs/ 2015
[19]

The Long-Term Stability of the Human Gut Microbiota

Jeremiah J. Faith et al. “The Long-Term Stability of the Human Gut Microbiota”. In: Science341.6141 (2013), p. 1237439.doi:10.1126/science.1237439.url:https: //www.science.org/doi/abs/10.1126/science.1237439

work page doi:10.1126/science.1237439.url:https: 2013
[20]

Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity.Nature Commun., 14(1):7910, 2023

Pablo Lech´ on-Alonso et al. “Robust coexistence in competitive ecological communi- ties”. In:Nat. Commun.17.2637 (2026).doi:10.1038/s41467- 026- 69151- 3.url: https://doi.org/10.1038/s41467-026-69151-3. 18

work page doi:10.1038/s41467- 2026
[21]

Strange attractors in Volterra equations for species in competition

A. Arneodo et al. “Strange attractors in Volterra equations for species in competition”. In:J. Math. Biol.14.2 (1982), pp. 153–157.issn: 0303-6812,1432-1416.doi:10.1007/ BF01832841.url:https://doi.org/10.1007/BF01832841

work page doi:10.1007/bf01832841 1982
[22]

Motoba, Y

A. Arneodo, P. Coullet, and C. Tresser. “Occurrence of strange attractors in three- dimensional Volterra equations”. In:Phys. Lett. A79.4 (1980), pp. 259–263.issn: 0375-9601,1873-2429.doi:10.1016/0375- 9601(80)90342- 4.url:https://doi. org/10.1016/0375-9601(80)90342-4

work page doi:10.1016/0375- 1980
[23]

Chaos in low-dimensional Lotka-Volterra models of competition

J. A. Vano et al. “Chaos in low-dimensional Lotka-Volterra models of competition”. In: Nonlinearity19.10 (2006), pp. 2391–2404.issn: 0951-7715,1361-6544.doi:10.1088/ 0951-7715/19/10/006.url:https://doi.org/10.1088/0951-7715/19/10/006

work page doi:10.1088/0951-7715/19/10/006 2006
[24]

Systems of differential equations that are competitive or coop- erative. II. Convergence almost everywhere

Morris W. Hirsch. “Systems of differential equations that are competitive or coop- erative. II. Convergence almost everywhere”. In:SIAM J. Math. Anal.16.3 (1985), pp. 423–439.issn: 0036-1410.doi:10.1137/0516030.url:https://doi.org/10. 1137/0516030

work page doi:10.1137/0516030.url:https://doi.org/10 1985
[25]

Systems of differential equations which are competitive or coop- erative. III. Competing species

Morris W. Hirsch. “Systems of differential equations which are competitive or coop- erative. III. Competing species”. In:Nonlinearity1.1 (1988), pp. 51–71.issn: 0951- 7715,1361-6544.url:http://stacks.iop.org/0951-7715/1/51

1988
[26]

On the differential equations of species in competition

S. Smale. “On the differential equations of species in competition”. In:J. Math. Biol. 3.1 (1976), pp. 5–7.issn: 0303-6812,1432-1416.doi:10 . 1007 / BF00307854.url: https://doi.org/10.1007/BF00307854

work page doi:10.1007/bf00307854 1976
[27]

The dynamics of the H´ enon map

Michael Benedicks and Lennart Carleson. “The dynamics of the H´ enon map”. In:Ann. of Math. (2)133.1 (1991), pp. 73–169.issn: 0003-486X,1939-8980.doi:10 . 2307 / 2944326.url:https://doi.org/10.2307/2944326

work page doi:10.2307/2944326 1991
[28]

A rigorous ODE solver and Smale’s 14th problem

Warwick Tucker. “A rigorous ODE solver and Smale’s 14th problem”. In:Found. Comput. Math.2.1 (2002), pp. 53–117.issn: 1615-3375,1615-3383.doi:10 . 1007 / s002080010018.url:https://doi.org/10.1007/s002080010018

work page doi:10.1007/s002080010018 2002
[29]

Complex systems in ecology: a guided tour with large Lotka–Volterra models and random matrices

Imane Akjouj et al. “Complex systems in ecology: a guided tour with large Lotka–Volterra models and random matrices”. In:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences480.2285 (Mar. 2024), p. 20230284.issn: 1364-5021. doi:10.1098/rspa.2023.0284. eprint:https://royalsocietypublishing.org/ rspa/article-pdf/doi/10.1098/rs...

work page doi:10.1098/rspa.2023.0284 2024
[30]

Equilibrium and surviving species in a large Lotka-Volterra system of differential equations

Maxime Clenet, Fran¸ cois Massol, and Jamal Najim. “Equilibrium and surviving species in a large Lotka-Volterra system of differential equations”. In:J. Math. Biol.87.1 (2023), Paper No. 13, 32.issn: 0303-6812,1432-1416.doi:10 . 1007 / s00285 - 023 - 01939-z.url:https://doi.org/10.1007/s00285-023-01939-z

work page doi:10.1007/s00285-023-01939-z 2023
[31]

Positive solutions for large random linear systems

Pierre Bizeul and Jamal Najim. “Positive solutions for large random linear systems”. In:Proc. Amer. Math. Soc.149.6 (2021), pp. 2333–2348.issn: 0002-9939,1088-6826. doi:10.1090/proc/15383.url:https://doi.org/10.1090/proc/15383

work page doi:10.1090/proc/15383.url:https://doi.org/10.1090/proc/15383 2021
[32]

Global Stability in Many-Species Systems

B. S. Goh. “Global Stability in Many-Species Systems”. In:The American Naturalist 111.977 (1977), pp. 135–143.issn: 00030147, 15375323.url:http://www.jstor.org/ stable/2459985(visited on 12/15/2025). 19

work page arXiv 1977
[33]

The stability of gen- eralized Volterra equations

Yasuhiro Takeuchi, Norihiko Adachi, and Hidekatsu Tokumaru. “The stability of gen- eralized Volterra equations”. In:J. Math. Anal. Appl.62.3 (1978), pp. 453–473.issn: 0022-247X.doi:10 . 1016 / 0022 - 247X(78 ) 90139 - 7.url:https : / / doi . org / 10 . 1016/0022-247X(78)90139-7

1978
[34]

Global stability of ecosystems of the generalized Volterra type

Yasuhiro Takeuchi, Norihiko Adachi, and Hidekatsu Tokumaru. “Global stability of ecosystems of the generalized Volterra type”. In:Math. Biosci.42.1-2 (1978), pp. 119– 136.issn: 0025-5564,1879-3134.doi:10.1016/0025-5564(78)90010-X.url:https: //doi.org/10.1016/0025-5564(78)90010-X

work page doi:10.1016/0025-5564(78)90010-x.url:https: 1978
[35]

The existence of globally stable equilibria of ecosystems of the generalized Volterra type

Yasuhiro Takeuchi and Norihiko Adachi. “The existence of globally stable equilibria of ecosystems of the generalized Volterra type”. In:J. Math. Biol.10.4 (1980), pp. 401– 415.issn: 0303-6812,1432-1416.doi:10.1007/BF00276098.url:https://doi.org/ 10.1007/BF00276098

work page doi:10.1007/bf00276098.url:https://doi.org/ 1980
[37]

Universal classe s of hash functions

Yasuhiro Takeuchi and Norihiko Adachi. “Stable equilibrium of systems of generalized Volterra type”. In:J. Math. Anal. Appl.88.1 (1982), pp. 157–169.issn: 0022-247X. doi:10.1016/0022- 247X(82)90183- 4.url:https://doi.org/10.1016/0022- 247X(82)90183-4

work page doi:10.1016/0022- 1982
[38]

Stable equilibria in the Lotka-Volterra equations

Magnus Aspenberg, Erik A. Martens, and Kristofer Wollein Waldetoft. “Necessary condition for stable equilibria in the Lotka-Volterra equations”. In:arXiv preprint, arXiv:2512.13347(2025)

work page internal anchor Pith review Pith/arXiv arXiv 2025
[39]

Commensal antimicrobial resistance mediates microbiome resilience to antibiotic disruption

Shakti K Bhattarai et al. “Commensal antimicrobial resistance mediates microbiome resilience to antibiotic disruption”. In:Science translational medicine16.730 (2024), eadi9711

2024
[40]

Equilibrium in a large Lotka- Volterra system with pairwise correlated interactions

Maxime Clenet, Hafedh El Ferchichi, and Jamal Najim. “Equilibrium in a large Lotka- Volterra system with pairwise correlated interactions”. In:Stochastic Process. Appl. 153 (2022), pp. 423–444.issn: 0304-4149,1879-209X.doi:10.1016/j.spa.2022.08. 004.url:https://doi.org/10.1016/j.spa.2022.08.004. Appendix A Numerical frequency sampling of attractors We bri...

work page doi:10.1016/j.spa.2022.08 2022
[41]

For each realization, we com- puted the trajectories using initial conditions sampled i.i.d

We randomly draw interactions with|α ij| ≤1 (i.i.d.). For each realization, we com- puted the trajectories using initial conditions sampled i.i.d. uniformly from the positive domainx i(0)∈[0, L] for alli= 1, . . . , n. Note that trajectories with such initial con- ditions remain forever positive. We sampledn i initial conditions forn r realization of the ...
[42]

We compute trajectories for a time ofTunits

The asymptotic behavior of each trajectory is classified into one of three (main) distinct behaviors: (stable) equilibrium, oscillatory behavior, divergence (i.e.,x k(t)→ ∞for somek). We compute trajectories for a time ofTunits. Transient behavior is assumed to subside afterT t time units, and fort∈ T:= [0.5T, T] we measured the ’amplitude’ A:= max tT ||x...