Holocene stability: climate attractor, or lucky break?

Armstrong McKay, David Ian

doi:10.5194/egusphere-2026-3886

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https://doi.org/10.5194/egusphere-2026-3886

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10 Jul 2026

| 10 Jul 2026

Holocene stability: climate attractor, or lucky break?

David Ian Armstrong McKay

Abstract. Palaeorecords indicate that the average global temperature been relatively stable for the past ~10,000 years of the Holocene epoch, in contrast to cooling trends during previous interglacials and abrupt shifts during past Glacials. Hypotheses for this stability range from early anthropogenic emissions to orbital factors or the timing of carbon cycle feedbacks. An alternative suggestion grounded in dynamical systems theory is that Holocene stability reflects the Earth system residing near a climate “attractor”, with strong negative feedbacks acting to stabilise the climate’s state, and Glacial/Interglacial cycling representing either a limit cycle or tipping between Interglacial and Glacial basins of attraction. This in turn has led to the more recent hypothesis that human actions are eroding the resilience of the Earth system’s current state, and at some level could be sufficient to tip the whole Earth system towards a much warmer “Hothouse Earth” attractor. However, despite multiple hypotheses for Holocene stability, that the Earth system is close to the edge of a dynamical basin of attraction is often assumed rather than demonstrated. Here, I assess the basis for this hypothesis in the literature, finding that there is currently insufficient evidence to support this hypothesis over the alternatives of pseudo-stability from stable orbital forcing, lagged feedbacks, or more complex nonlinear dynamics. As such, more evidence is required to test these hypotheses, and in the meantime the presence of Holocene or Hothouse attractors should not be taken as a given. Given this, I outline some alternative frameworks for climate states and Earth system resilience that may be appropriate without strong attractors, centring adaptive capacity and stability through change.

Received: 30 Jun 2026 – Discussion started: 10 Jul 2026

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David Ian Armstrong McKay

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-3886', Anonymous Referee #1, 30 Jul 2026

This is a difficult paper for a climate scientist from the physical sciences realm to discuss because it is written from a completely different perspective, in an unfamiliar conceptual style, and with a different audience in mind. To the extent that it is discussing resilience and the likelihood that the Earth system will break completely free from its recent states it has some interest. However, the title, abstract and main hypothesis it discusses are amenable to statistical investigation, and these suggest that the whole concept is simply an incorrect strawman. On this basis I do not believe this paper is appropriate for ESD.
Basically, as can be seen from the title, the concept is that the Holocene is unusually stable compared to the 800 kyr of climate that the paper considers (eg Fig 1), and that this might be because there is some kind of unusual attractor that stabilises it (which anthropogenic action might breach). The problem, as indeed acknowledged in principle by the author around line 380, but never statistically tested, is that there is nothing very unusual about the Holocene, at least in the terms the author uses to describe it. If one takes the Antarctic temperature record (which I believe is what is plotted in Fig 1 despite it being labelled global temperature), or a genuine global mean surface temperature synthesis such as that of Clark et al 2024, one finds that there are numerous 10 kyr long periods in the last 800 kyr that have a similarly low variability. I used Clark et al’s GMST data, and the SD of the period 0-9 kyr is 0.14 degrees; the same low value occurs many other times in the last 800 kyr, including during periods generally considered interglacial, such as MIS 7c, 13 and 15. I found a similar result if I used Antarctic temperature from Jouzel et al 2008, or even if I used the concentration of CO2.
The Holocene is neither the coldest interglacial, the warmest interglacial (that would be MIS5e) or the longest lasting interglacial, though it is more than possible, because of the weak orbital forcing, that it would, excluding anthropogenic influence, have become that. It simply wasn’t that special until the last 200 years, so any paper that starts either by assuming it was, or by trying to prove that it wasn’t, is simply either incorrect, or proving what we already know.
I can see scope for a different paper that discusses why there have been lower and upper limits on climate and indeed CO2 over the past 800 kyr, and the consequences of breaching those limits, but that is not what this paper is. And for sure there is interesting work on the different states for glacials and interglacials that has been addressed in the literature by authors such as Crucifix and Paillard who are cited here. But again this paper is not about that. It specifically assumes some uniqueness about the Holocene, and without that, the rest of the arguments are too hypothetical for a journal such as ESD.

Citation: https://doi.org/10.5194/egusphere-2026-3886-RC1
- AC1: 'Author's Reply on RC1', David Armstrong McKay, 28 Aug 2026
  
  Thank you for your review of this manuscript. I will write a full response including details of changes made to clarify the paper’s purpose and argument once all reviews are in, but for now I offer a brief initial response covering the main points raised.
  Firstly, the style and perspective of the paper was chosen as it was proposed and submitted as a Perspective piece (which per ESD’s manuscript instructions “provide a well-reasoned but potentially subjective view of a field relevant to ESD's scope, or seek to outline a new research direction. These peer-reviewed articles may address existing discussions in the literature, or originate new ones. Any arguments presented in a Perspective should be supported by existing literature”). In line with this, it explicitly takes a more conceptual and discursive approach, primarily using existing literature to respond to some common concepts in parts of the literature relevant to this Special Issue on “Earth [system] resilience in the Anthropocene". Given that ESD offer Perspectives as an option, that its topic relates to a key part of the conceptual underpinning of this Special Issue (i.e. the nature of Earth system resilience, which as discussed within & below has been commonly defined in a way that assumes Holocene uniqueness and stability), and that one of the SI editors expressed interest in receiving such a submission when first pitched, I believe this paper is therefore appropriate for publication in ESD, and will be of interest to the readers of this Special Issue.
  Secondly, this paper is not itself assuming or making the argument that the Holocene is uniquely stable, and that this therefore implies the existence of a climate attractor – it is to critically respond to that argument, which has been made and repeated elsewhere. I do not believe or posit that the Holocene is unusually stable, and I agree that this is already recognised within the palaeoclimate community in particular, but as summarised in the paper’s Introduction, the proposal that the Holocene is so and that this implies the climate system being in an attractor has nonetheless been stated or implied within the wider Earth system science literature on multiple occasions (and on the back of that, more widely within societal discourse). As such, the intended starting point of this paper (which likely needs some revision to make the arguments logic clearer) was to show this hypothesis has been commonly assumed in the literature, before exploring evidence from the literature and discussing the implications for conceptualising Earth system resilience, rather than assuming it to be correct from the outset.
  The reviewer’s proposed statistical analysis or analysis of climatic limits over the past 800 kyr would indeed be useful avenues for assessing these claims (and I agree the SD analysis contradicts the Holocene being uniquely stable amongst interglacials, although that does not directly refute the wider hypothesis of Holocene stability indicating an attractor, which relates more to the drivers of said stability rather than its uniqueness). However, the intention of this paper was not to provide an immediate quantitative disproof, but rather as a Perspective to provide a “well-reasoned but potentially subjective view of [this] field” and “outline a new research direction” for this field: in this case, critiquing a common assumption in several high profile Earth system resilience studies, and suggesting a new direction (of which the reviewer’s proposed analyses would be one potential approach). While direct quantitative analyses are of course critical to test these ideas, I believe there is also value in such Perspective or commentary pieces in this and other physical science journals in highlighting a potential problem in a field and outlining an alternative research direction, with analyses subsequently testing different approaches to that (or indeed challenging it).
  However, it is evident that the context, intention, and argument of this paper need to be made clearer, which I will endeavour to do during the paper’s revision. In particular, I will expand on the (non-)uniqueness aspect, more clearly demonstrating that the Holocene has been (incorrectly) assumed elsewhere to be uniquely stable within the cited literature (and is not simply a strawman set up in this paper), and that this has formed a key basis for the attractor model of Earth system resilience, as well as including some quantitative evidence of other interglacials being similarly stable as suggested. In addition, I will also address minor points too (e.g. on Figure 1, which is directly reproduced from one of the critiqued sources to exemplify how Holocene ‘stability’ is portrayed, but replotting from source data may indeed be preferable).
  
  Citation: https://doi.org/10.5194/egusphere-2026-3886-AC1
RC2:
'Comment on egusphere-2026-3886', Michel Crucifix, 07 Sep 2026

The manuscript assesses what McKay terms the "Heterostatic Holocene" hypothesis: the idea that Holocene stability reflects the Earth system sitting in a dynamical basin of attraction, with a possible cascade toward a "Hothouse Earth" attractor. This heterostatic framing builds on the potential-landscape metaphor used in the Hothouse narrative of Steffen et al. (2018). McKay concludes that there is insufficient evidence to defend the hothouse-attractor framing, or to choose between it and alternatives such as pseudo-stability from stable orbital forcing.
There are ample reasons to be concerned with Steffen et al. (2018): their Figure 1 is ambiguous and relies on loose semantics (it in fact depicts the attractor landscape of a *governed* Earth, implicitly folding in socio-economic stabilising feedbacks), and dynamical-systems framing is poorly quantified. McKay seems to share these concern in principle, but its own treatment does not correct these flaws. It arguably replicates and exacerbates them through a narrative that leans heavily on rhetorical framing, loosely defined concepts, mixed frameworks, and abundant conditional verbs.
A few concrete examples:
- ll. 121-130 (glacial-interglacial cycle theories): this section mixes modern references with ones fifty years old, from authors of very different vintages of expertise, without proper contextualisation. This exaggerates the impression of non-consensus. There is, in fact, a current expert consensus that G-IG cycles involve an orbitally-paced ramp-up and instability of glacial conditions, enabled by CO2 and topographic conditions that are favourable at Cenozoic scale. What remains debated is the precise role of carbon cycle, sea-level, and ice physics in that instability. Unforced glacial-interglacial cycles under constant orbital forcing remain a theoretical possibility, but several of the older references cited in support of this possibility do not engage carefully with the constraint posed by the Mid-Pleistocene transition, unlike the more recent ones. The sawtooth character of the last four glacial-interglacial cycles was already established by Broecker and Van Donk (1970).
- Multistability in models (l. 160 onward): the models discussed here (atmosphere-ocean) operate in a specifically restricted context that excludes sea-level and biosphere dynamics. Connecting this work to "climate system attractors" more broadly is therefore a rhetorical move.
- Overreliance on the potential-landscape metaphor: a potential landscape is specific to gradient systems, which effectively behave as 1-dimensional systems. This restricts the range of possible behaviours considerably, and the metaphor becomes misleading if followed too closely, both for past climates (diagnosing topological properties of basins of attraction in a non-autonomous, aperiodically-forced context is difficult, conceptually and in practice) and for the future. The phrase "limit cycle" is invoked at several points and not well connected to its standard dynamical-systems definition. For example, the long warm Holocene excursion depicted by Steffen is referred to as a "limit cycle" while this is clearly a non-autonomous transient trajectory.
- From l. 360 onward, the informal wording increases toward what reads as loose, under-defined language for a scientific text: attractor basins "rendered obsolete," "orbital quietude," "reduced buffering," the Earth system able to "defy" the landscape, "maintaining the Earth system in some degree of dynamical stability *despite* the landscape," and Holocene quasi-stability attributed to the biosphere "keeping the Earth system seemingly stable" in an interglacial state "even if there was no Interglacial attractor".
More broadly, the objective of the article is unclear. The title's dichotomy is never actually resolved. Addressing Steffen et al.'s flaws requires a rigorous scientific framework, with the system domain clearly specified, mathematically anchored, and organised around clearly framed questions.(disclaimer: some rewording / polishing with LLM but arguments are mine)

Citation: https://doi.org/10.5194/egusphere-2026-3886-RC2
- RC3: 'Reply on RC2', Michel Crucifix, 07 Sep 2026
  
  one element I forgot to add, though this is not a critique to the paper per se : if anything, inspection of the Pleistocene records (CO2, d18O) suggests that the glacial boundary is much more constrained than the interglacial one.
  
  Citation: https://doi.org/10.5194/egusphere-2026-3886-RC3
- AC2:
  'Reply on RC2', David Armstrong McKay, 22 Sep 2026
  
  Thank you Michel for your thoughtful comments. A detailed response to all of your points will come in due course during the revision process, but for now here is a brief initial response.
  On the general style of the manuscript, it was written and submitted as a Perspective piece, following the ESD guidelines for such an article type (namely to “provide a well-reasoned but potentially subjective view of a field relevant to ESD's scope, or seek to outline a new research direction... Any arguments presented in a Perspective should be supported by existing literature”). In line with this, and as noted in response to Reviewer 1 too, the article takes a more conceptual and discursive approach, using existing literature to help make its case (rather than undertaking a new empirical analysis), aiming to be evidence-based while also taking a subjective view (much like Steffen et al’s original piece). Deeper empirical analysis of Steffen et al. would indeed be worthwhile, but I think is likely beyond the scope of a single paper (and author). Instead, the goal is in part to call attention to the surprising lack of such analysis or critique in the scientific literature of this scenario and its basis, despite its substantial interdisciplinary & societal impact in the eight years since publication, and call for research in the emerging ‘Earth resilience’ field (the topic of this special issue, which as described tends to adopt this framework as its basis) to more explicitly interrogate it in order to drive new research.
  As such, a Perspective felt like the most appropriate choice for this article. This choice may also help explain why some aspects appear more subjective or briefly argued than a normal ESD paper, but I believe is line with ESD’s requirements and intentions for this article type. However, I agree that in responding to some of the confused basis for Steffen et al, any critique of it should avoid creating new confusions in turn. This in part relates to limited wordcount (with this submission already somewhat over guidelines), leading to an initial approach of briefly highlighting examples from across various relevant frameworks to illustrate how the current literature does not yet clearly support Holocene/Hothouse attractors, as well as attempting to make this Perspective accessible to the wider interdisciplinary audience who might find a response to Steffen et al useful. I agree though that this conceptual tour approach has led to some parts being not so clear or fully representative, for example around the usage of potential landscapes and limit cycles, or the current state of Glacial/Interglacial cycle research (although for example on AOGCM multistability, I note that at least some existing literature do attribute results to climate system attractors, e.g. https://link.aps.org/doi/10.1103/PhysRevE.107.054214, so is not just a move made here).
  In revising the manuscript then, I will endeavour to clarify and refine discussion of the underlying conceptual frameworks, making sure they are theoretically robust (which I think will strengthen the argument being made) while also trying to maintain accessibility for an interdisciplinary audience. I will also review some of the informal phrasing used in places – while I would argue that particularly in a Perspective aimed at a broader audience, some metaphorical language can better express some points (and reflects a tradition of scientific metaphor usage for both pedagogic and epistemic purposes), I do not wish for it distract from the wider points being made, and will better define, modify, or remove unclear instances. Finally, I will clarify the goal of the article too, which overall is to offer a perspective highlighting some of the issues with the Holocene/Hothouse attractor hypothesis for an interdisciplinary audience influenced by Steffen et al, and on that basis calling for more research on this within the Earth resilience field that this special issue focuses on.
  
  Citation: https://doi.org/10.5194/egusphere-2026-3886-AC2
  - RC4: 'Reply on AC2', Michel Crucifix, 22 Sep 2026
    
    Thanks David for this constructive answer to my somewhat critical review. I will read the revised version with interest.
    
    Citation: https://doi.org/10.5194/egusphere-2026-3886-RC4
RC5: 'Comment on egusphere-2026-3886', Raphael Hébert, 30 Sep 2026

Review of "Holocene stability: climate attractor, or lucky break?" by D. I. Armstrong McKay (egusphere-2026-3886)

GENERAL COMMENTS
I think that this Perspective is quite interesting and timely, warning against overconfidence in frameworks assuming the existence of attractors stabilizing the current Holocene climate and potentially tipping the future into a Hothouse climate. It then outlines alternative ways of conceptualising Earth system resilience, including a "messy landscape" of weak attractors in which resilience is tied to adaptive capacity.
I have read the two previous referee reports (RC1 and RC2, M. Crucifix) and the author's initial replies (AC1, AC2), and I have tried to avoid repeating the points made there.
1. How exceptional is Holocene stability?

I agree with RC1 that the premise that the Holocene is exceptionally stable is not generally agreed upon, and RC1 explains well why. I would add that the view of an exceptionally stable Holocene could be said to have been fostered, to a large extent, by the Greenland ice cores, and GRIP in particular (Dansgaard et al., 1993; GRIP Project Members, 1993). Rehfeld et al. (2018) showed that the temperature variance ratio between the LGM and the Holocene is an order of magnitude greater for Greenland than elsewhere. Also, looking at a comprehensive database of pollen reconstructions, we have shown that there is large regional variability in the Holocene (Hébert et al., 2022). This is not apparent in stacks of such records (e.g. Marsicek et al., 2018) because stacking records with time-uncertainty leads to smoothing and effectively only captures the lower-frequency trend.

The Holocene temperature conundrum is also relevant here and not settled (Kaufman and Broadman, 2023). Osman et al. (2021) is currently cited at L44-47 in support of a Holocene Thermal Maximum peak, whereas they argued that data assimilation solves the conundrum and practically erases the HTM; Marsicek et al. (2018) also argued the HTM was amplified by seasonality biases in the reconstructions. All that to say that the current text is a bit too assertive, also regarding the Little Ice Age, whose existence as a globally coherent cold period has been disputed (Neukom et al., 2019). Note that the reconstruction on Fig 1 also doesn't show the HTM, it's not global temperature right but an Antarctic record and the HTM might be a northern hemisphere signal; it is somewhat confusing to discuss the HTM and then show a figure in which it does not appear.

2. The messy landscape

I found quite interesting the "messy landscape" view of weak attractors in a dynamic stability landscape (Sect. 4, Fig. 4b). I would encourage the author to explain further the messy landscape, as this would make the manuscript a more positive contribution, proposing a framework rather than mainly criticising previous arguments, and to also propose ways that it could be probed (maybe in model worlds) if not verified. If the author can make connections to past states from Sect. 2 (snowball Earth, Phanerozoic climate states), that would also be interesting. There should still be some limits to the messy landscape on Fig. 4 though right, such as the Planck feedback at least. I'll be looking forward to the revised figure.
3. Biosphere and adaptive capacity

I'm a bit confused by the discussion L360-364, as life is framed as able to defy the stability landscape, but on Fig. 4, it is also included as part of the stability landscape, and so does it defy the forcing and climate stability landscape by introducing the biosphere dimension in the landscape?

Relatedly, the author may be interested in Spiridonov and Lovejoy (2022), who address a similar question on much longer timescales, examining the relative roles of climate and biotic dynamics (in terms of the Court Jester and Red Queen hypotheses) in Phanerozoic diversity fluctuations.

Overall, I think this Perspective addresses a question that is relevant to ESD and to this Special Issue and that following revision it could be published.
Recommendation: major revisions.

SPECIFIC COMMENTS (Largely the product of an LLM)
L30-32: The 6-7°C LGM-to-Holocene global warming is at the upper end of published estimates, and the two cited studies (Tierney et al., 2020; Osman et al., 2021) share authors, model prior (iCESM) and data assimilation approach, so they are not independent. Other estimates are lower, e.g. ~4.5 ± 0.9°C (Annan et al., 2022), and IPCC AR6 gives 5-7°C. I suggest giving a range (e.g. ~4.5-7°C) with citations reflecting this spread.
L85: "12000 Kya" should be ~12 ka (11.7 ka).
L95-96: The paragraph describes warming beyond the basin edge towards a hotter attractor, but the example given ("orbital forcing initiating reglaciation") is a cooling transition. Please correct or clarify.
L103: "Rockström et al., 2024b, a" are cited, but the reference list does not distinguish a and b entries.
L136: "coldhouse" should be "coolhouse", consistent with Westerhold et al. (2020) and with L141 and Figure 3.
L138: The Phanerozoic began ~539 Ma, not 485 Ma. Judd et al. (2024) cover the last 485 Myr, i.e. from the Ordovician.
L146: The Cryogenian begins ~720 Ma, not ~760 Ma.
L174 (Figure 3a caption): Zachos et al. (2008) is a benthic δ18O compilation rather than a global temperature reconstruction. Please state how temperature was derived.
L349-350: "Dissipative systems" is Prigogine's later terminology; Schrödinger (1944) discussed life in terms of "negative entropy". Consider rephrasing or adding an appropriate reference.
L356: Through the Looking-Glass was published in 1871 (title page dated 1872), not 1873.
References:

- Cited in the text but missing from the reference list: Börner et al. (2026), Bertolami and Nyström (2026), GLOBAÏA (2026), Günther et al. (2003), Carroll (1873), Schrödinger (1944).

- Incorrect DOIs: Broecker (1987) and Walker et al. (2004), whose DOI points to a Physical Review Letters article.

- Incomplete entries: Edwards et al. (2010) lacks journal and volume; Dakos (2008) refers to the Supporting Information and lists a single author; Kaufhold et al. (2025) lacks journal details.

TECHNICAL CORRECTIONS
L18: "the average global temperature been" -> "has been".

L40: "milestones(bottom)" -> "milestones (bottom)".

L48: "in to" -> "into".

L120 (Figure 2 caption): "Proceedings of the National Academies of Sciences" -> "Proceedings of the National Academy of Sciences".

L258: "relatively stability" -> "relative stability".

L283-285: stray line break between "In" and "Figure 4".

L319: "the time taken for to bounce back" -> "the time taken to bounce back".

L357: "species most constantly adapt" -> "species must constantly adapt".

L374: "antisyzgy" -> "antisyzygy".

REFERENCES CITED IN THIS REVIEW (not in the manuscript)
Annan, J. D., Hargreaves, J. C., and Mauritsen, T.: A new global surface temperature reconstruction for the Last Glacial Maximum, Clim. Past, 18, 1883-1896, https://doi.org/10.5194/cp-18-1883-2022, 2022.
GRIP Project Members: Climate instability during the last interglacial period recorded in the GRIP ice core, Nature, 364, 203-207, https://doi.org/10.1038/364203a0, 1993.
Hébert, R., Herzschuh, U., and Laepple, T.: Millennial-scale climate variability over land overprinted by ecosystem dynamics, Nat. Geosci., 15, 899-905, https://doi.org/10.1038/s41561-022-01056-4, 2022.
Marsicek, J., Shuman, B. N., Bartlein, P. J., Shafer, S. L., and Brewer, S.: Reconciling divergent trends and millennial variations in Holocene temperatures, Nature, 554, 92-96, https://doi.org/10.1038/nature25464, 2018.
Neukom, R., Steiger, N., Gómez-Navarro, J. J., Wang, J., and Werner, J. P.: No evidence for globally coherent warm and cold periods over the preindustrial Common Era, Nature, 571, 550-554, https://doi.org/10.1038/s41586-019-1401-2, 2019.
Rehfeld, K., Münch, T., Ho, S. L., and Laepple, T.: Global patterns of declining temperature variability from the Last Glacial Maximum to the Holocene, Nature, 554, 356-359, https://doi.org/10.1038/nature25454, 2018.
Spiridonov, A. and Lovejoy, S.: Life rather than climate influences diversity at scales greater than 40 million years, Nature, 607, 307-312, https://doi.org/10.1038/s41586-022-04867-y, 2022.

Citation: https://doi.org/10.5194/egusphere-2026-3886-RC5

David Ian Armstrong McKay

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Short summary

Global temperature in the Holocene has been remarkably stable compared to the Glacials and Interglacials before it. This is often interpreted as evidence for the Holocene being in a self-stabilising “attractor” climate state, implying a potentially imminent tipping point to a much hotter state instead. However, while there is some evidence in support of a Holocene attractor, it is insufficient to rule out several other potential explanations, and more evidence is needed to test these hypotheses.


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