pith. sign in

arxiv: 2501.00396 · v3 · pith:BXZKCX3Pnew · submitted 2024-12-31 · ⚛️ physics.bio-ph · nlin.AO

Information bounds production in replicator systems

Jordi Pi\~nero , Damian R. Sowinski , Gourab Ghoshal , Adam Frank , Artemy Kolchinsky This is my paper

Pith reviewed 2026-05-25 08:48 UTC · model grok-4.3

classification ⚛️ physics.bio-ph nlin.AO
keywords replicator dynamicsinformation theoryproductivityautocatalytic networksflow reactorenvironmental fluctuationsprebiotic chemistry
0
0 comments X

The pith

Simple replicator networks increase productivity by functionally exploiting information about fluctuating environments.

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

The paper establishes that even minimal networks of autocatalytic replicators can raise their output by using side information on environmental fluctuations. It models this in a flow reactor and decomposes productivity into separate terms for uncertainty, available information, and distribution mismatch. A sympathetic reader would care because the result indicates that information-based advantages do not require evolved sensing or control machinery and could therefore appear in early chemical systems.

Core claim

In a model of autocatalytic replicators in a flow reactor, productivity decomposes information-theoretically into contributions from environmental uncertainty, side information, and distribution mismatch. This decomposition yields optimal strategies and universal bounds on the productivity benefit of information, which are compared to Kelly gambling. Application to a model of real-world molecular replicators demonstrates gains from internal memory and proposes an experimental setup to detect functional information use in a minimal chemical system.

What carries the argument

The information-theoretic decomposition of productivity separating environmental uncertainty, side information, and distribution mismatch in the flow-reactor model of autocatalytic replicators.

If this is right

  • Optimal replicator strategies exist that maximize productivity given side information about the environment.
  • Universal bounds limit the productivity gain obtainable from any amount of side information.
  • Internal memory in replicators produces measurable productivity improvements under fluctuating conditions.
  • The same decomposition applies to models of actual molecular replicators and guides detection of functional information use.

Where Pith is reading between the lines

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

  • Prebiotic chemical networks could have obtained evolutionary advantages from environmental correlations before any sensing machinery evolved.
  • The productivity decomposition may apply to other self-reproducing populations such as viruses or synthetic cells.
  • Altering the predictability of environmental fluctuations in a lab reactor and measuring output changes would test the derived bounds.

Load-bearing premise

The flow-reactor model of autocatalytic replicators and its information-theoretic decomposition accurately capture how simple systems can use environmental information in a functional way.

What would settle it

An experiment in which real autocatalytic replicators show no productivity increase when given side information that reduces environmental uncertainty would falsify the central claim.

Figures

Figures reproduced from arXiv: 2501.00396 by Adam Frank, Artemy Kolchinsky, Damian R. Sowinski, Gourab Ghoshal, Jordi Pi\~nero.

Figure 1
Figure 1. Figure 1: An example scenario that motivates our analysis, similar to a real-world experimental system [42] analyzed in Section III. A reaction volume (e.g., pond) contains a network of replicators (e.g., orange and green circles), which may be minimal autocatalytic molecules or more complex organisms. The replicators are exposed to a fluctuating environment, including active phases (e.g., days with fluctuating ligh… view at source ↗
Figure 2
Figure 2. Figure 2: Productivity over time. Result (12) illustrated using a system of two replicators. Productivity is defined in (8) as time￾averaged outflow of replicators. The black straight line indicates the actual productivity up to time τ and the dashed blue and orange lines indicate the steady-state (long-time limit) and the initial productivity values. Red arrow indicate productivity change from initial to steady￾sta… view at source ↗
Figure 3
Figure 3. Figure 3: Photocatalytic replicator system [42]. (a) Schematic of simplified reaction network. ⇝ indicates replication under weak light environment, ⇝ indicates replication reaction under strong light en￾vironment (see also Table II). (b) Experimental setup, including flow reactor fed by reservoir of monomers 1 at concentration µ. During active phases (weak ⇝ or strong ⇝ light environments), the reser￾voir feeds the… view at source ↗
Figure 4
Figure 4. Figure 4: Information and productivity in photocatalytic replicator system. Numerical results showing normalized average productivity, ⟨P⟩/Ω for two control parameters: λ := kdτI (dimensionless inactive timescale) shown on horizontal axis, b (bias for spontaneous formation of replicator 16) shown as different red lines (other parameters same as in Fig. 3c). Black lines indicate productivity computed using optimal bi… view at source ↗
read the original abstract

Environmental fluctuations can shape replicator dynamics, with important consequences for both prebiotic and modern ecosystems. However, it remains unclear how simple replicators can acquire and use information about fluctuating environments, given that such information processing is often assumed to require sophisticated mechanisms for sensing and control. Here, we show that even simple replicator networks can increase productivity by exploiting environmental information in a functional way. Using a model of autocatalytic replicators in a flow reactor, we derive an information-theoretic decomposition of productivity, with separate contributions from environmental uncertainty, side information, and distribution mismatch. We derive optimal strategies and universal bounds on the benefit of information and compare our findings with existing work, including ``Kelly gambling'' in information theory. By applying our framework to a model of real-world molecular replicators, we demonstrate the benefits of internal memory and propose an experimental setup for detecting functional information in a minimal chemical system.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that even simple autocatalytic replicator networks in a flow reactor can functionally exploit environmental information to increase productivity. It derives an information-theoretic decomposition of productivity into separate contributions from environmental uncertainty, side information, and distribution mismatch; obtains optimal strategies and universal bounds; compares results to Kelly gambling; applies the framework to a model of real-world molecular replicators; and proposes an experimental setup to detect functional information use in a minimal chemical system.

Significance. If the decomposition rigorously isolates functional information use and the bounds are shown to be achievable by selection on replicator parameters alone, the work would meaningfully connect information theory to prebiotic replicator dynamics and demonstrate that information exploitation need not require dedicated sensing machinery. The explicit comparison to Kelly gambling and the experimental proposal add value for testability.

major comments (2)
  1. [§3] §3 (productivity decomposition): the side-information term is presented as capturing functional exploitation, yet the flow-reactor replicator equations already embed environmental correlations in the concentration state variables; it is not shown that this term can be increased by selection on network parameters without additional unmodeled mechanisms, leaving open whether the term is an accounting identity rather than evidence of active information use.
  2. [§4] §4 (optimal strategies and bounds): the derivation of the universal bound on the benefit of information assumes the side-information term is selectable, but no explicit evolutionary dynamics or fitness gradient is provided to confirm that replicators can evolve toward the Kelly-optimal allocation without presupposing the information-processing interpretation.
minor comments (2)
  1. Notation for the three productivity contributions should be introduced with explicit equations immediately after the model definition rather than relying on the abstract.
  2. Figure captions for the molecular-replicator application should include the numerical values of the reported productivity gains to allow direct comparison with the derived bounds.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive comments, which help clarify the interpretation of our information-theoretic decomposition. We address each major comment below, providing the strongest honest defense based on the manuscript's derivations and results. Where appropriate, we indicate revisions to strengthen the discussion of how network parameters control the side-information term and its relation to selection.

read point-by-point responses

  1. Referee: §3 (productivity decomposition): the side-information term is presented as capturing functional exploitation, yet the flow-reactor replicator equations already embed environmental correlations in the concentration state variables; it is not shown that this term can be increased by selection on network parameters without additional unmodeled mechanisms, leaving open whether the term is an accounting identity rather than evidence of active information use.

    Authors: The decomposition is obtained by algebraic rearrangement of the exact expression for long-term productivity in the flow-reactor model, where the side-information term equals the mutual information between the environmental state and the instantaneous replicator concentration vector. Although concentrations integrate past environmental history, the mapping from environment to concentrations is governed by the network parameters (catalytic rate constants and stoichiometric coefficients). Different parameter choices therefore produce different joint distributions and hence different values of the side-information term. In the manuscript we already illustrate this by comparing replicator networks with and without internal memory states; the memory-containing networks systematically increase the side-information contribution. To make this explicit, we will revise §3 to include a short analytic example showing how a single rate-constant change raises the side-information term while leaving the environmental uncertainty and mismatch terms fixed. This demonstrates that the term is tunable by selection on network parameters alone, without invoking additional sensing machinery. revision: partial

  2. Referee: §4 (optimal strategies and bounds): the derivation of the universal bound on the benefit of information assumes the side-information term is selectable, but no explicit evolutionary dynamics or fitness gradient is provided to confirm that replicators can evolve toward the Kelly-optimal allocation without presupposing the information-processing interpretation.

    Authors: The Kelly-optimal allocation is defined as the parameter choice that maximizes the decomposed productivity expression for given environmental statistics; because productivity appears directly as the per-capita growth rate in the replicator equations, any increase in the side-information term raises fitness. The universal bound follows from standard information inequalities applied to the decomposition and does not presuppose an information-processing mechanism; it simply states the maximum productivity attainable when the side-information term is maximized. We acknowledge that the manuscript does not simulate explicit evolutionary trajectories on the parameter space. We will add a concise paragraph in §4 noting that the productivity gradient with respect to network parameters supplies the selection pressure toward the bound, and that the experimental proposal in the manuscript provides a route to test whether real replicators approach this optimum. Full dynamical simulations of parameter evolution lie outside the present scope. revision: partial

Circularity Check

0 steps flagged

Derivation applies standard information theory to replicator model without self-referential reduction

full rationale

The paper derives an information-theoretic decomposition of productivity in a flow-reactor autocatalytic replicator model by applying standard mutual information and entropy terms (environmental uncertainty, side information, distribution mismatch) to the existing replicator dynamics. This decomposition is compared to the independent Kelly gambling result from information theory rather than being justified by self-citation chains or prior author work. No equations reduce by construction to fitted parameters renamed as predictions, no ansatz is smuggled via self-citation, and the central productivity bound follows from the model equations plus information identities without the target claim being presupposed in the inputs. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of information-theoretic decompositions to replicator productivity and on the adequacy of the flow-reactor autocatalytic model; no new entities are introduced and no free parameters are enumerated in the abstract.

axioms (2)
  • domain assumption Productivity in replicator systems admits an information-theoretic decomposition into environmental uncertainty, side information, and distribution mismatch contributions.
    Invoked to separate the three contributions and to derive optimal strategies and bounds.
  • domain assumption The flow-reactor model of autocatalytic replicators is a sufficient representation of real molecular replicators for the purpose of detecting functional information use.
    Required for the application to molecular replicators and the proposed experimental setup.

pith-pipeline@v0.9.0 · 5691 in / 1363 out tokens · 41254 ms · 2026-05-25T08:48:38.081764+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

76 extracted references · 76 canonical work pages · 1 internal anchor

  1. [1]

    Semantic information, au- tonomous agency and non-equilibrium statistical physics,

    A. Kolchinsky and D. H. Wolpert, “Semantic information, au- tonomous agency and non-equilibrium statistical physics,”In- terface focus, vol. 8, no. 6, p. 20180041, 2018

    work page 2018

  2. [2]

    Semanticinformationinamodelofresourcegatheringagents,

    D. R. Sowinski, J. Carroll-Nellenback, R. N. Markwick, J.Piñero,M.Gleiser,A.Kolchinsky,G.Ghoshal,andA.Frank, “Semanticinformationinamodelofresourcegatheringagents,” PRX Life, vol. 1, no. 2, p. 023003, 2023

    work page 2023

  3. [3]

    Syn- thetic cells extract semantic information from their environ- ment,

    B. Ruzzante, L. Del Moro, M. Magarini, and P. Stano, “Syn- thetic cells extract semantic information from their environ- ment,”IEEETransactionsonMolecular,Biological,andMulti- Scale Communications, vol. 9, no. 1, pp. 23–27, 2023

    work page 2023

  4. [4]

    Biological information,

    P. Godfrey-Smith and K. Sterelny, “Biological information,” Stanford Encyclopedia of Philosophy, 2007

    work page 2007

  5. [5]

    Information- theoretic description of a feedback-control kuramoto model,

    D. R. Sowinski, A. Frank, and G. Ghoshal, “Information- theoretic description of a feedback-control kuramoto model,” Physical Review Research, vol. 6, no. 4, p. 043188, 2024

    work page 2024

  6. [6]

    Exo-Daisy World: Revisiting Gaia Theory through an Informational Architecture Perspective

    D. R. Sowinski, G. Ghoshal, and A. Frank, “Exo-Daisy World: Revisiting Gaia Theory through an Informational Architecture Perspective,”arXiv e-prints, p. arXiv:2411.03421, Nov. 2024

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  7. [7]

    Meaningful information, sensor evolution, and the temporal horizon of embodied organisms,

    C. L. Nehaniv, D. Polani, K. Dautenhahn, R. te Boekhorst, and L. Canamero, “Meaningful information, sensor evolution, and the temporal horizon of embodied organisms,” inArtificial life VIII, pp. 345–349, MIT Press Cambridge, MA, 2002

    work page 2002

  8. [8]

    The meaning of biological information,

    E. V. Koonin, “The meaning of biological information,”Philo- sophical Transactions of the Royal Society A: Mathemati- cal, Physical and Engineering Sciences, vol. 374, no. 2063, p. 20150065, 2016

    work page 2063

  9. [9]

    Information in biological systems,

    J. Collier, “Information in biological systems,”Handbook of philosophy of science, vol. 8, pp. 763–787, 2008

    work page 2008

  10. [10]

    Functional information and the emergence of biocomplexity,

    R. M. Hazen, P. L. Griffin, J. M. Carothers, and J. W. Szostak, “Functional information and the emergence of biocomplexity,” Proceedings of the National Academy of Sciences, vol. 104, no. suppl_1, pp. 8574–8581, 2007

    work page 2007

  11. [11]

    What is complexity?,

    C. Adami, “What is complexity?,”BioEssays, vol. 24, no. 12, pp. 1085–1094, 2002

    work page 2002

  12. [12]

    Quantitative modeling of bacterial chemotaxis: signal amplification and accurate adaptation,

    Y. Tu, “Quantitative modeling of bacterial chemotaxis: signal amplification and accurate adaptation,”Annual review of bio- physics, vol. 42, no. 1, pp. 337–359, 2013

    work page 2013

  13. [13]

    Predictive information in a sensory population,

    S. E. Palmer, O. Marre, M. J. Berry, and W. Bialek, “Predictive information in a sensory population,”Proceedings of the Na- tional Academy of Sciences, vol. 112, no. 22, pp. 6908–6913, 2015

    work page 2015

  14. [14]

    Information processing in living systems,

    G. Tkačik and W. Bialek, “Information processing in living systems,”Annual Review of Condensed Matter Physics, vol. 7, no. 1, pp. 89–117, 2016

    work page 2016

  15. [15]

    Escherichia coli chemotaxis is information limited,

    H. H. Mattingly, K. Kamino, B. B. Machta, and T. Emonet, “Escherichia coli chemotaxis is information limited,”Nature physics, vol. 17, no. 12, pp. 1426–1431, 2021

    work page 2021

  16. [16]

    Behaviour and the origin of organisms,

    M. Egbert, M. M. Hanczyc, I. Harvey, N. Virgo, E. C. Parke, T. Froese, H. Sayama, A. S. Penn, and S. Bartlett, “Behaviour and the origin of organisms,”Origins of Life and Evolution of Biospheres, pp. 1–26, 2023

    work page 2023

  17. [17]

    The major evolutionary transi- tions,

    E. Szathmáry and J. M. Smith, “The major evolutionary transi- tions,”Nature, vol. 374, no. 6519, pp. 227–232, 1995

    work page 1995

  18. [18]

    Thresholds in origin of life scenarios,

    C. Jeancolas, C. Malaterre, and P. Nghe, “Thresholds in origin of life scenarios,”Iscience, vol. 23, no. 11, 2020. 13

    work page 2020

  19. [19]

    Selforganization of matter and the evolution of biological macromolecules,

    M. Eigen, “Selforganization of matter and the evolution of biological macromolecules,”Naturwissenschaften, vol. 58, pp. 465–523, 1971

    work page 1971

  20. [20]

    Replicatordynamics,

    P.SchusterandK.Sigmund,“Replicatordynamics,” Journalof theoretical biology, vol. 100, no. 3, pp. 533–538, 1983

    work page 1983

  21. [21]

    Freefitnessthatalwaysincreasesinevolution,

    Y.Iwasa,“Freefitnessthatalwaysincreasesinevolution,” Jour- nal of Theoretical Biology, vol. 135, no. 3, pp. 265–281, 1988

    work page 1988

  22. [22]

    Minimal replicator theory i: Parabolic versus exponential growth,

    G. von Kiedrowski, “Minimal replicator theory i: Parabolic versus exponential growth,”Bioorganic chemistry frontiers, pp. 113–146, 1993

    work page 1993

  23. [23]

    Replicatorequationsandtheprincipleofminimal production of information,

    G.P.Karev, “Replicatorequationsandtheprincipleofminimal production of information,”Bulletin of mathematical biology, vol. 72, pp. 1124–1142, 2010

    work page 2010

  24. [24]

    The ecology–evolution continuum and the origin oflife,

    D. A. Baum, Z. Peng, E. Dolson, E. Smith, A. M. Plum, and P. Gagrani, “The ecology–evolution continuum and the origin oflife,”JournaloftheRoyalSocietyInterface , vol.20,no.208, p. 20230346, 2023

    work page 2023

  25. [25]

    Thermodynamics of darwinian evolution in molecular replicators,

    A. Kolchinsky, “Thermodynamics of darwinian evolution in molecular replicators,”arXiv preprint arXiv:2112.02809v4, 2024

    work page arXiv 2024

  26. [26]

    Structural con- straintslimittheregimeofoptimalfluxinautocatalyticreaction networks,

    A. Despons, Y. De Decker, and D. Lacoste, “Structural con- straintslimittheregimeofoptimalfluxinautocatalyticreaction networks,”CommunicationsPhysics,vol.7,no.1,p.224,2024

    work page 2024

  27. [27]

    A self-replicating hexadeoxynucleotide,

    G. von Kiedrowski, “A self-replicating hexadeoxynucleotide,” Angewandte Chemie International Edition in English, vol. 25, no. 10, pp. 932–935, 1986

    work page 1986

  28. [28]

    Aself-replicatingpeptide,

    D. H. Lee, J. R. Granja, J. A. Martinez, K. Severin, and M. R. Ghadiri,“Aself-replicatingpeptide,”Nature,vol.382,no.6591, pp. 525–528, 1996

    work page 1996

  29. [29]

    Self-sustained replication of an RNA enzyme,

    T. A. Lincoln and G. F. Joyce, “Self-sustained replication of an RNA enzyme,”Science, vol. 323, no. 5918, pp. 1229–1232, 2009

    work page 2009

  30. [30]

    Dynamiccombinatorialchemistry,

    P. T. Corbett, J. Leclaire, L. Vial, K. R. West, J.-L. Wietor, J.K.Sanders,andS.Otto,“Dynamiccombinatorialchemistry,” Chemical reviews, vol. 106, no. 9, pp. 3652–3711, 2006

    work page 2006

  31. [31]

    From self-replication to replicator systems en route to de novo life,

    P. Adamski, M. Eleveld, A. Sood, Á. Kun, A. Szilágyi, T. Czárán, E. Szathmáry, and S. Otto, “From self-replication to replicator systems en route to de novo life,”Nature Reviews Chemistry, vol. 4, no. 8, pp. 386–403, 2020

    work page 2020

  32. [32]

    Collective adaptability in a replication network of mini- mal nucleobase sequences,

    S. Vela-Gallego, Z. Pardo-Botero, C. Moya, and A. de la Esco- sura, “Collective adaptability in a replication network of mini- mal nucleobase sequences,”Chemical Science, vol. 13, no. 36, pp. 10715–10724, 2022

    work page 2022

  33. [33]

    Primitive selection of the fittest emerging through functional synergy in nucleopeptide networks,

    A. K. Bandela, N. Wagner, H. Sadihov, S. Morales-Reina, A. Chotera-Ouda, K. Basu, R. Cohen-Luria, A. de la Escosura, and G. Ashkenasy, “Primitive selection of the fittest emerging through functional synergy in nucleopeptide networks,”Pro- ceedings of the National Academy of Sciences, vol. 118, no. 9, p. e2015285118, 2021

    work page 2021

  34. [34]

    Evolutionary transition from a single RNA replicator to a multiple replicator network,

    R. Mizuuchi, T. Furubayashi, and N. Ichihashi, “Evolutionary transition from a single RNA replicator to a multiple replicator network,”NatureCommunications,vol.13,no.1,p.1460,2022

    work page 2022

  35. [35]

    The hot spring hypothesis for an origin of life,

    B. Damer and D. Deamer, “The hot spring hypothesis for an origin of life,”Astrobiology, vol. 20, no. 4, pp. 429–452, 2020

    work page 2020

  36. [36]

    Physical non-equilibria for prebiotic nucleic acid chemistry,

    A. Ianeselli, A. Salditt, C. Mast, B. Ercolano, C. L. Kufner, B. Scheu, and D. Braun, “Physical non-equilibria for prebiotic nucleic acid chemistry,”Nature Reviews Physics, vol. 5, no. 3, pp. 185–195, 2023

    work page 2023

  37. [37]

    The growth ofcompetingmicrobialpopulationsinaCSTRwithperiodically varying inputs,

    G. Stephanopoulos, A. Frederickson, and R. Aris, “The growth ofcompetingmicrobialpopulationsinaCSTRwithperiodically varying inputs,”AIChE Journal, vol. 25, no. 5, pp. 863–872, 1979

    work page 1979

  38. [38]

    A competition model for a seasonally fluctuating nutrient,

    S.-B. Hsu, “A competition model for a seasonally fluctuating nutrient,”Journal of Mathematical Biology, vol. 9, pp. 115– 132, 1980

    work page 1980

  39. [39]

    Two species competition in a periodic envi- ronment,

    J. M. Cushing, “Two species competition in a periodic envi- ronment,”Journal of Mathematical Biology, vol. 10, no. 4, pp. 385–400, 1980

    work page 1980

  40. [40]

    On the coexistence of competing microbial species in a chemostat under cycling,

    S. Pavlou, I. Kevrekidis, and G. Lyberatos, “On the coexistence of competing microbial species in a chemostat under cycling,” Biotechnology and bioengineering, vol. 35, no. 3, pp. 224–232, 1990

    work page 1990

  41. [41]

    H.L.SmithandP.E.Waltman, Thetheoryofthechemostat: dy- namicsofmicrobialcompetition .No.13inCambridgestudiesin mathematical biology, Cambridge ; New York, NY: Cambridge University Press, 1995

    work page 1995

  42. [42]

    Light-driven eco-evolutionary dynamics in asyntheticreplicatorsystem,

    K. Liu, A. Blokhuis, C. van Ewijk, A. Kiani, J. Wu, W. H. Roos, and S. Otto, “Light-driven eco-evolutionary dynamics in asyntheticreplicatorsystem,” NatureChemistry,vol.16,no.1, pp. 79–88, 2024

    work page 2024

  43. [43]

    Thermodynamic limits to information harvesting by sensory systems,

    S. Bo, M. Del Giudice, and A. Celani, “Thermodynamic limits to information harvesting by sensory systems,”Journal of Sta- tistical Mechanics: Theory and Experiment, vol. 2015, no. 1, p. P01014, 2015

    work page 2015

  44. [44]

    Thermo- dynamiccostsofinformationprocessinginsensoryadaptation,

    P.Sartori,L.Granger,C.F.Lee,andJ.M.Horowitz,“Thermo- dynamiccostsofinformationprocessinginsensoryadaptation,” PLoScomputationalbiology ,vol.10,no.12,p.e1003974,2014

    work page 2014

  45. [45]

    Efficiency of cellular informationprocessing,

    A. C. Barato, D. Hartich, and U. Seifert, “Efficiency of cellular informationprocessing,”NewJournalofPhysics ,vol.16,no.10, p. 103024, 2014

    work page 2014

  46. [46]

    The application of information theory to biochemical signaling systems,

    A. Rhee, R. Cheong, and A. Levchenko, “The application of information theory to biochemical signaling systems,”Physical biology, vol. 9, no. 4, p. 045011, 2012

    work page 2012

  47. [47]

    Energydissipationandnoise correlations in biochemical sensing,

    C.C.GovernandP.R.tenWolde,“Energydissipationandnoise correlations in biochemical sensing,”Physical review letters, vol. 113, no. 25, p. 258102, 2014

    work page 2014

  48. [48]

    Information transmission in genetic regulatory networks: a review,

    G. Tkačik and A. M. Walczak, “Information transmission in genetic regulatory networks: a review,”Journal of Physics: Condensed Matter, vol. 23, no. 15, p. 153102, 2011

    work page 2011

  49. [49]

    Prob- ing the limits to positional information,

    T. Gregor, D. W. Tank, E. F. Wieschaus, and W. Bialek, “Prob- ing the limits to positional information,”Cell, vol. 130, no. 1, pp. 153–164, 2007

    work page 2007

  50. [50]

    Natural selection as the process of accumulating genetic information in adaptive evolution,

    M. Kimura, “Natural selection as the process of accumulating genetic information in adaptive evolution,”Genetics Research, vol. 2, no. 1, pp. 127–140, 1961

    work page 1961

  51. [51]

    The cost of information acquisition by natural se- lection,

    R. S. McGee, O. Kosterlitz, A. Kaznatcheev, B. Kerr, and C. T. Bergstrom, “The cost of information acquisition by natural se- lection,”biorxiv, pp. 2022–07, 2022

    work page 2022

  52. [52]

    A new interpretation of information rate,

    J. L. Kelly, “A new interpretation of information rate,”The Bell System Technical Journal, vol. 35, no. 4, pp. 917–926, 1956

    work page 1956

  53. [53]

    Optimalmixedstrategiesinstochastic environments,

    P.HaccouandY.Iwasa,“Optimalmixedstrategiesinstochastic environments,”Theoretical population biology, vol. 47, no. 2, pp. 212–243, 1995

    work page 1995

  54. [54]

    Phenotypic diversity, population growth, and information in fluctuating environments,

    E. Kussell and S. Leibler, “Phenotypic diversity, population growth, and information in fluctuating environments,”Science, vol. 309, no. 5743, pp. 2075–2078, 2005

    work page 2075

  55. [55]

    The fitness value of information,

    M. C. Donaldson-Matasci, C.T. Bergstrom, and M.Lachmann, “The fitness value of information,”Oikos, vol. 119, no. 2, pp. 219–230, 2010

    work page 2010

  56. [56]

    Fluctuationrelations offit- ness and information in population dynamics,

    T. J. Kobayashiand Y.Sughiyama, “Fluctuationrelations offit- ness and information in population dynamics,”Physical review letters, vol. 115, no. 23, p. 238102, 2015

    work page 2015

  57. [57]

    Transitions in optimal adaptive strategies for populations in fluctuating en- vironments,

    A.Mayer,T.Mora,O.Rivoire,andA.M.Walczak,“Transitions in optimal adaptive strategies for populations in fluctuating en- vironments,”PhysicalReviewE ,vol.96,no.3,p.032412,2017

    work page 2017

  58. [58]

    Optimized bacteria are environmental prediction engines,

    S. E. Marzen and J. P. Crutchfield, “Optimized bacteria are environmental prediction engines,”Physical Review E, vol. 98, p. 012408, July 2018. 14

    work page 2018

  59. [59]

    Life in fluctuating environments,

    J.R.Bernhardt,M.I.O’Connor,J.M.Sunday,andA.Gonzalez, “Life in fluctuating environments,”Philosophical Transactions of the Royal Society B, vol. 375, no. 1814, p. 20190454, 2020

    work page 2020

  60. [60]

    The value of information for popu- lationsinvaryingenvironments,

    O. Rivoire and S. Leibler, “The value of information for popu- lationsinvaryingenvironments,”JournalofStatisticalPhysics , vol. 142, pp. 1124–1166, 2011

    work page 2011

  61. [61]

    Minimal informational re- quirements for fitness,

    A. S. Moffett and A. W. Eckford, “Minimal informational re- quirements for fitness,”Physical Review E, vol. 105, no. 1, p. 014403, 2022

    work page 2022

  62. [62]

    Pareto-optimaltrade- offforphenotypicswitchingofpopulationsinastochasticenvi- ronment,

    L.Dinis,J.Unterberger,andD.Lacoste,“Pareto-optimaltrade- offforphenotypicswitchingofpopulationsinastochasticenvi- ronment,”JournalofStatisticalMechanics: TheoryandExper- iment, vol. 2022, no. 5, p. 053503, 2022

    work page 2022

  63. [63]

    Highly efficient self- replicatingRNAenzymes,

    M. P. Robertson and G. F. Joyce, “Highly efficient self- replicatingRNAenzymes,”Chemistry&biology ,vol.21,no.2, pp. 238–245, 2014

    work page 2014

  64. [64]

    Academic press, 2009

    I.Pepper,C.P.Gerba,T.Gentry,andR.M.Maier, Environmen- tal microbiology. Academic press, 2009

    work page 2009

  65. [65]

    Competitive exclusion,

    R. A. Armstrong and R. McGehee, “Competitive exclusion,” The American Naturalist, vol. 115, no. 2, pp. 151–170, 1980

    work page 1980

  66. [66]

    The cost of natural selection,

    J. B. S. Haldane, “The cost of natural selection,”Journal of Genetics, vol. 55, pp. 511–524, 1957. Publisher: Springer

    work page 1957

  67. [67]

    Remarks on the substitutional load,

    W. Ewens, “Remarks on the substitutional load,”Theoretical Population Biology, vol. 1, pp. 129–139, Aug. 1970

    work page 1970

  68. [68]

    T. M. Cover,Elements of information theory. John Wiley & Sons, 1999

    work page 1999

  69. [69]

    Emergence of light-driven protometabolism on recruitment of aphotocatalyticcofactorbyaself-replicator,

    G. Monreal Santiago, K. Liu, W. R. Browne, and S. Otto, “Emergence of light-driven protometabolism on recruitment of aphotocatalyticcofactorbyaself-replicator,” NatureChemistry, vol. 12, no. 7, pp. 603–607, 2020

    work page 2020

  70. [70]

    Number of hiddenstatesneededtophysicallyimplementagivenconditional distribution,

    J. A. Owen, A. Kolchinsky, and D. H. Wolpert, “Number of hiddenstatesneededtophysicallyimplementagivenconditional distribution,”NewJournalofPhysics ,vol.21,no.1,p.013022, 2019

    work page 2019

  71. [71]

    Extreme accumulation of nucleotides in simu- lated hydrothermal pore systems,

    P. Baaske, F. M. Weinert, S. Duhr, K. H. Lemke, M. J. Russell, and D. Braun, “Extreme accumulation of nucleotides in simu- lated hydrothermal pore systems,”Proceedings of the National Academy of Sciences, vol. 104, no. 22, pp. 9346–9351, 2007

    work page 2007

  72. [72]

    Provenance of life: Chemical au- tonomousagentssurvivingthroughassociativelearning,

    S. Bartlett and D. Louapre, “Provenance of life: Chemical au- tonomousagentssurvivingthroughassociativelearning,” Phys- ical Review E, vol. 106, no. 3, p. 034401, 2022. S1 Supplementary information Appendix A: Derivation of main result, Eq. (23) Using Eq. (20), we write ⟨P⟩ = ⟨P ∗⟩ + 1 τ X ε,y pε,y ϕε ηr(ε) ln qr(ε)|y + ln X(0|y) X ∗ε (A1) Using the defin...

    work page 2022

  73. [73]

    Hence, at all times we have that S = aε + x1,ε + x2,ε = aε + Xε = µ

    Active phase During active phases, the system evolves according to: daε dt = (µ − aε)ϕ − (η1,εx1,ε + η2,εx2,ε) aε + kdXε − kf aε, (B1) dx1,ε dt = (η1,εaε − ϕ) x1,ε + kf baε − kdx1,ε, (B2) dx2,ε dt = (η2,εaε − ϕ) x2,ε + kf(1 − b)aε − kdx2,ε, (B3) Recall that we prepare the system such thatS(0) = S∗ = µ (forexample,bylettingthesystemflowat ϕbeforestartingth...

    work page

  74. [74]

    Inactive phase During inactive phases, the system evolves according to: da∅ dt = kdX∅ − kf a∅, (B5) dx1,∅ dt = kf ba∅ − kdx1,∅, (B6) dx1,∅ dt = kf(1 − b)a∅ − kdx1,∅, (B7) Using the constant solute concentrationS∗ = µ = a∅ + X∅, dX∅ dt = kf µ − (kd + kf) X∅. (B8) Given a previous environmentε− ∈ { ⇝, ⇝⇝}, this gives the dynamics of the total replicator con...

    work page

  75. [75]

    anticorrelated environments Here we derive conditions on p and π in correlated vs

    Conditions on p and π in correlated vs. anticorrelated environments Here we derive conditions on p and π in correlated vs. anticorrelated environments. We will make repeated use of the following general result. Proposition1. Let ωABbeajointprobabilitydistributionover two binary random variables:A with outcomes{1, 2} and B with outcomes {↓, ↑}. If the marg...

    work page

  76. [76]

    1 − x∗ 2, ⇝⇝e−λ X∅| ⇝⇝(λ) # b, (B23) q2| ⇝(b, λ) ≈ x ⇝ 2,∅(b, λ) X∅| ⇝(λ) =

    Best achievable strategy In order to study the best achievable strategy, we recall from our main result, Eq. (23), that all the dependence on the strategy q is encoded in our information-theoretic cost Cπ,q(R|Y ), given in Eq. (28). In our example introduced in Sec. III, the parameters that control q are {b, λ}, i.e., q = q(b, λ). In general, there may no...

    work page