Life as a Categorical Information-Handling System: An Evolutionary Information-Theoretic Model of the Holobiont

Round 1

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

Summary of the Work

This study frames life and evolution as information-handling processes, proposing that living entities, from genes to holobionts, can be understood as systems that capture, transform, and reproduce information to persist and multiply. By reformulating classical evolutionary dynamics (e.g., replicator equations, group selection, symbiosis) in information-theoretic terms, the study shows that evolutionary change corresponds to measures such as Jeffreys divergence, which quantify information generated through selection. Using category theory, the author introduces abstract Information Handlers (IH), a unified framework that accommodates both gene-centric and holistic perspectives and represents evolutionary processes across hierarchical levels. This categorical approach naturally extends to holobionts, providing an informational decomposition that generalizes earlier models of non-random mating and systemic evolution.

Main Findings in the Bullet Form

This study introduced a unified Information Handler (IH) framework that integrates replication, transmission, reproduction, and symbiosis within a single categorical model.

i) It showed that each evolutionary process naturally generates an information-theoretic measure, expressed as a Jeffreys divergence, without additional assumptions.

ii) It demonstrated that evolutionary change can be quantified in terms of both magnitude and the functional nature of information produced.

iii) Developed a new informational decomposition for holobionts, separating host, microbial, and association contributions.

iv) Generalized previous information-theoretic results for non-random mating, which emerge as a special case of the framework.

v) Establishes the IH approach as a coherent, multi-level framework for analyzing evolutionary dynamics from genes to holobionts.

General Comments

- This study offers an unifying framework that successfully connects evolutionary dynamics across multiple biological levels using a consistent information-theoretic and categorical formalism.

- The automatic emergence of Jeffreys divergence as a measure of evolutionary change provides clear conceptual and analytical value.

However,

- The categorical formulation, while powerful, is presented at a high level of abstraction, which may limit accessibility for readers without a strong background in category theory.

- The biological interpretation of “information” could be clarified further to distinguish functional meaning from purely statistical measures.

- The framework would benefit from additional concrete examples or empirical case studies to demonstrate its operational applicability.

- The relationship between the proposed IH framework and existing evolutionary models could be discussed more explicitly to better delineate its novelty and limitations.

- Some points require clarification. The following suggestions may be helpful.

Suggestions

1) How robust is the reliance on Jeffreys divergence when evolutionary dynamics deviate from frequency-based descriptions, for example, in systems with strong epigenetic inheritance or developmental constraints?

2) To what extent does the categorical abstraction preserve causal and mechanistic biological detail, especially when modeling interactions between evolutionarily distant taxa within holobionts?

2) How is the functorial mapping from population-state spaces to informational measures defined explicitly, and under which conditions is the Jeffreys divergence invariant under the composition of IH morphisms?

3) Can the author clarify whether the Jeffreys divergence arises uniquely from the categorical structure, or whether alternative f-divergences could satisfy the same axioms within the IH framework?

4) In the holobiont decomposition, what assumptions ensure the additivity of host, microbial, and association information terms, and how are cross-level correlations treated formally?

5) How does the IH formalism distinguish between informational change due to selection versus that induced by stochastic transmission processes such as drift or migration?

6) Is there a well-defined notion of causal closure or feedback at the categorical level, and how is it represented in terms of endomorphisms or higher-order morphisms of IHs?

7) To what extent does the framework depend on replicator-type dynamics, and can it be generalized to non-replicator evolutionary processes while preserving the informational interpretation?

Conclusions

The study is good, and I enjoyed reading it. The introduction of Information Handlers and the systematic emergence of Jeffreys divergence as a measure of evolutionary change are original and potentially impactful contributions, particularly in their extension to holobiont dynamics and multi-level selection. At the same time, several aspects would benefit from further clarification and development. In particular, the high level of abstraction introduced by the categorical formalism raises questions about accessibility and biological interpretability, especially regarding the preservation of causal and mechanistic detail. A more explicit discussion of the assumptions under which Jeffreys' divergence is unique or preferred, as well as its robustness beyond frequency-based dynamics, would strengthen the theoretical foundations of the approach. Likewise, the holobiont decomposition would benefit from a clearer treatment of cross-level correlations and from concrete examples illustrating how the framework can be operationalized in realistic biological systems.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

This manuscript presents an ambitious theoretical framework that unifies information theory, category theory, and evolutionary biology to model living systems (including holobionts) as “Information Handlers” (IHs). The author starts by contrasting gene-centric (reductionist) versus holistic (systems/relational) views of life and evolution, then introduces an abstract categorical architecture where an IH is an entity that absorbs and processes information from its environment with the aim of persistence and reproduction. Using category theory formalisms, the paper shows how classical evolutionary scenarios,from allele frequency change in populations to multi-level selection, symbiosis, and holobiont dynamics,can be represented within a single hierarchical information-centric model. A notable result is that evolutionary changes at different levels can be quantified by an information metric (Jeffreys divergence), offering a novel measure of “information production” by evolutionary processes. The framework is presented as general enough to encompass known models (e.g. non-random mating as a special case) and to bridge reductionist and holistic perspectives.
Overall, the manuscript introduces a fresh formalism to synthesize diverse evolutionary phenomena, and does so by leveraging sophisticated mathematics (category theory) in a way that could yield new insights. The work’s strength lies in its integrative approach,it attempts to reconcile gene-level and system-level evolution by viewing organisms, genomes, and even holobionts through a unifying lens of information handling. The formal development appears sound and is supplemented by a “toy model” illustration for a holobiont.
However, major revisions are needed before acceptance. In particular, the manuscript would benefit from improvements in conceptual clarity (especially definitions and scope), stronger connection to existing literature (to properly ground and differentiate this work), and more discussion on how this abstract model might connect to empirical biology. I outline below the key strengths to preserve and the main areas requiring revision, followed by specific suggestions (including additional references) to help the authors enhance the manuscript.
Some key concepts would benefit from clearer definition and consistency of use throughout the manuscript:
•    “Information Handler”: This is a central concept, yet it could be explained more thoroughly. The Simple Summary provides one sentence on IHs (entities that absorb/process information for persistence and multiplication). The manuscript should explicitly define an IH early in the main text (perhaps in the Introduction or at the start of the Methods/Theory section) in both intuitive and formal terms. For example, how exactly do IHs relate to standard biological entities? Are all organisms IHs? Are genes or symbiotic units also considered IHs? It seems so, since later the holobiont is a composite IH. Making this explicit would help readers. Additionally, clarifying what counts as information in this context (genetic information? environmental cues? any data influencing fitness?) would strengthen the conceptual framing. The authors might draw on existing literature where life is described in terms of information processing,e.g., Paul Davies and Sara Walker’s work on life as an information system (see Walker & Davies 2013, already cited as ref. 112, and other discussions of information in biology). Another highly relevant source is the recent Astrobiology Primer 3.0 chapter by Colón-Santos et al. (2024), “What Is Life?”, which highlights the information storage and processing view of life and gives historical context to defining life. 
•    The manuscript touches on individual vs. group vs. holobiont selection, but the framework’s stance on units of evolution could be clearer. For instance, in the IH model, an individual organism is an IH, a holobiont is a higher-order IH. Does the framework allow for multiple nested levels of IH hierarchies (e.g., genes as IHs inside cells as IHs, etc.)? It would help to clarify this hierarchy explicitly. Since category theory naturally handles hierarchies, a brief discussion would reassure readers that the model can accommodate, say, cells within organisms within ecosystems, if that is the case. Relating this to classic debates on units of selection (e.g., referencing Lewontin 1970 or Okasha 2006 which are already in the references) could be useful to position the work. In particular, the notion of “causal closure” in living systems is mentioned,consider elaborating how the IH framework addresses or requires causal closure at each level.
•    The use of Jeffreys divergence as the measure of evolutionary change is intriguing. The manuscript should ensure readers understand why Jeffreys (a symmetrized Kullback-Leibler divergence) is used and what it signifies biologically. A bit more intuition here would help. For example, you might explain that as population state frequencies change from one generation to the next, the Jeffreys divergence $J$ quantifies how much “information” (in bits or nats) is gained about the system’s adaptive fit to the environment. This links to earlier literature where natural selection is framed as an information gain process. Indeed, classic work by Fisher, Frank, Kimura, and others have noted connections between selection and information (e.g., Fisher’s Fundamental Theorem can be seen as an information increase statement, Kimura (1961) described natural selection as accumulating information[9], and more recently Steven Frank has written a series on selection and information,some of which you cite). By explicitly referencing these connections, the paper can strengthen its theoretical foundation. For instance, you might cite Frank (2012) who interprets Fisher’s theorem in information terms or Kimura (1961) on selection as information gain to show precedence for your information-based approach.
•When introducing the holobiont model, be sure to define holobiont for readers who may not be familiar. You should clarify that in your usage it means a host plus its associated microbiome considered as an evolutionary individual. The manuscript already does a nice job explaining the model (host IH + monoidal product of microbial IHs). I encourage the authors to also connect this with existing definitions from the literature. For example, quoting a definition from Theis et al. (2016) or Zilber-Rosenberg & Rosenberg (2008) (both cited in your ref. list) could help. Moreover, acknowledging the ongoing discussion about whether holobionts qualify as units of selection would be wise. The manuscript could mention that its framework provides a formal way to analyze holobiont selection vs. selection on partners, which addresses some controversies (like the extent of vertical transmission needed for a holobiont to be an evolutionary individual). There is a very recent Science perspective by Bordenstein et al. (2024) that underscores the importance of holobiont thinking. Bordenstein and colleagues introduce “holobiont biology” as a holistic view uniting life’s “seen and unseen realms,” arguing that microbes can drive trait variation and evolution as much as genes do. This paper is worth citing to show that the importance of host–microbiome interactions in evolution is widely recognized, and your model provides a timely formal tool to investigate it.
I recommend the authors bolster all key definitions and conceptual explanations, ensuring that a broad Biology readership can grasp the framework. Introduce IH clearly; explain how categories map to biology; define holobiont and its components. Wherever possible, tie these definitions to existing concepts in the literature,this not only aids understanding but also situates your work within the ongoing scientific conversation 
•    Colón-Santos, S., et al. (2024). “What Is Life?” Astrobiology 24(S1): S-40–S-56.,This work provides an updated perspective on defining life, emphasizing information, complexity, and is a key reference for framing your introduction
•    Bordenstein, S.R., et al. (2024). “The disciplinary matrix of holobiont biology.” Science 386: 731–732.,This short article advocates a holistic understanding of host–microbiome systems in evolution. It will support the relevance of your holobiont approach
•    Sherwin, W.B. (2024). “Pan-Evo: The Evolution of Information and Biology’s Part in This.” Biology 13(7): 507.,Introduces a framework unifying information processes in living and non-living systems, resonating with your information-centric model
•    Maruyama, Y. (2021). “Category theory and foundations of life science: a structuralist perspective on cognition.” BioSystems 203: 104376.,Highlights the current state (and limitations) of category theory applications in life sciences, providing philosophical support for your use of category theory
•    Laland, K.N., et al. (2015). “The extended evolutionary synthesis: its structure, assumptions and predictions.” Proc. R. Soc. B 282: 20151019.,Key paper outlining the need for an extended framework beyond gene-centrism, which your work supplies in a formal way
Minor comments 
Ensure consistent use of terms like “holobiont”, “hologenome”, “microbiome”, etc. At times, authors mix “symbiont” vs “microbial partner”,stick to one set of terms for clarity. Also, when referring to information measures, sometimes “information gain” is used, other times “entropy” or “divergence”,just be sure the reader knows these all connect (perhaps clarify that in information theory, a change in entropy or a divergence is a way to quantify information gained or lost).
The manuscript’s writing is generally good. I did not focus on style, as requested, since there are no egregious errors impeding understanding. (One tiny note: “Jeffreys” divergence is sometimes spelled “Jeffrey’s” in error; ensure the spelling “Jeffreys” is consistent as it’s named after Harold Jeffreys.)

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

With regard to my previous comments, I note that the author has carefully and comprehensively addressed all the issues and concerns raised in my earlier report. The revisions have clarified the points in question and have significantly improved the overall quality and coherence of the manuscript. I therefore confirm that the study is sound, well presented, and scientifically robust, and in my opinion, it fully meets the standards required for publication.

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

Dear Author,

Thank you for the revised version of the manuscript. I am satisfied with the nature and quality of the additions and modifications, which adequately address the points raised during review. The manuscript is now clear and well supported, and I believe it is suitable for publication.

Best regards,

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Living systems can be understood as organized entities that capture, transform, and reproduce information. In this paper, the authors claimed that they proposed a Categorical Model of Information Handlers (IH), entities capable of self-maintenance, mutation, and combination. I spent a lot of time to try to capture the key new findings of the paper, but failed. So that I can not suggest the acceptance.

(1) To me, the first five sections are summaries about known results, but not in a clear form.

(2) In Section 6, the authors claimed that evolution is categories of information, but lack enough details. Furthermore, I didn't see new findings but only an interpretation of limited known results in a different form. This greatly weakens the usage of category theory.

Author Response

Please see the attached file.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper reviews evolutionary frameworks, from the replicator equation to group selection and holobiont dynamics. The following suggestions should be addressed to consider the manuscript for publication.

1. The Abstract is not written in a proper manner. It should be re-written by highlighting the major contributions of the study.
2. Why there is a section called simple summary before the Abstract? If needed, it can be added towards the end of the paper.
3. The Introduction section should be rewritten with the initial two paragraphs introducing the problem statement. Followed by the Literature Review section with proper citation on this work.
4. A proper academic tone should be maintained throughout the manuscript.
5. The Literature review should include more recent works on this domain. Adequate literature review is lacking in the entire manuscript.
6. The titles of sections are very vague. Section 2.1 and 3.1 are having same titles. It should be changed.
7. The organization of the paper should be given at the end of the Introduction.
8. Proper punctuations should be added at the end of all equations. It’s missing for all equations.
9. How is Equation (1) obtained? Provide a reference to it.
10. Why certain lines are shown in italic?
11. Can the categorical IH model be compared with any existing mathematical modeling techniques? Justify.
12. Section 6 is lacking proper sub section alignments.
13. Mathematical expressions in lines 736, 737 are not clearly written.
14. How is the value of sexual isolation factor ( I_xy) always positive?
15. The Reference styling is not proper, and recent and updated works in these domains are not listed properly. Unnecessary bulk citations are seen throughout the paper. This should be limited to maximum 60 – 70 important works.
16. In total, this work lacks academic clarity in its present form. Issues regarding mathematical expressions and grammatical errors should be rectified.

 

This work requires a Major Revison.

  Comments on the Quality of English Language

A proper academic tone should be maintained throughout the manuscript.

Author Response

Please see the attached file.

Author Response File: Author Response.pdf