⚠️ Extracted by Claude on 2026-06-24 from the full open-access PDF (DOI 10.1038/s43587-026-01138-7), with a second-pass numeric re-check against the source text + figures (one correction made: removal/noise ratio is βX_c/ε, not βκ/ε). This is a single-agent extraction — an independent wiki-verifier adversarial pass has NOT run, because the paper is not yet in the local archive or on PMC. Treat quantitative claims as high-fidelity-but-not-independently-verified. gap/needs-verification

Raz et al. 2026 — A damage accumulation model identifies distinct aging regimes across species

One-line: Fitting the saturating-removal-model (a stochastic damage production + saturating-removal model) to high-quality survival data from nine well-studied species shows that the damage-production rate is the single best predictor of lifespan (spanning seven orders of magnitude), while removal, noise, and the death threshold are nearly invariant across mammals — and that species fall into two regimes, ballistic aging (Weibull-like; yeast, worms, flies, mice) versus quasi-steady-state aging (Gompertz-like; humans, dogs, cats, guinea pigs).

This is an Analysis article from Uri Alon’s lab (Weizmann Institute, Sagol Institute for Longevity Research; with Westlake University and UNIST). It is the comparative-across-species application of the Saturating Removal (SR) model first developed in Karin & Alon 2019 for senescent-cell dynamics. Received 21 June 2025, accepted 30 April 2026, published 9 June 2026. Open access (CC BY-NC-ND).

What they did

The SR model posits a single scalar damage variable x that drives aging, governed by a stochastic differential equation with three terms — linearly rising production, saturating removal, and Gaussian noise ¹²:

$\frac{d x}{d t} = η t - β \frac{x}{κ + x} + 2 ε ξ$

Death is a first-passage event: it occurs when x first crosses a death threshold X_c. An optional extrinsic-mortality (Makeham) term m_ex adds a constant age-independent death probability. The six parameters:

Parameter	Meaning	Units
η (eta)	rate of change (slope) of the damage-production rate — production grows as ηt	damage·time⁻²
β (beta)	maximum removal rate at saturation	damage·time⁻¹
κ (kappa)	removal half-saturation point (Michaelis–Menten constant)	damage
ε (epsilon)	noise amplitude (effective diffusion coefficient)	damage²·time⁻¹
X_c	death threshold (robustness to damage)	damage
m_ex	extrinsic mortality	time⁻¹

Production rises linearly with age (required to produce Gompertz-law mortality); removal saturates at high damage (a Michaelis–Menten form, a common feature of biological removal processes). The authors distinguish removal (processes that specifically clear damage x — e.g., immune clearance of senescent/damaged cells in mammals) from repair (intracellular processes that lower the production rate η — e.g., DNA repair preventing a cell from becoming damaged).

They assembled high-quality mortality datasets for nine species spanning ~four orders of magnitude in median lifespan and fit the SR parameters per species via a Bayesian / MCMC approach (simulating ~20,000 individual organisms per parameter set and matching the simulated death-time distribution to the data) ¹:

Species	Dataset (source)	n	Notes
Saccharomyces cerevisiae (BY4742)	McCormick 2015	24,512	replicative aging (mother-cell divisions)
Caenorhabditis elegans (QZ0 Bristol)	Stroustrup 2016	2,908	”lifespan machine”
Drosophila melanogaster (4 genotypes)	McCracken 2020	~1,000–1,117 each	strains 217 / 441 / 707 / 853
E. coli (MG1655 PrrnB2)	Yang 2019	4,744	survival under starvation
Mus musculus (UM-HET3)	ITP, Miller 2024	F 3,701 / M 2,746	genetically heterogeneous controls
Cavia porcellus (guinea pig)	O’Neill 2024	674	UK veterinary data
Felis catus (cat)	Teng 2024	F 2,702 / M 2,746	neutered animals only
Canis familiaris (dog)	Teng 2022	1,049–2,427 / breed	Jack Russell, Labrador, Staffy, German Shepherd
Homo sapiens	Human Mortality Database	~80,000 / cohort	Denmark 1890/1900 + Sweden 1910 cohorts

Key findings

1. Damage-production rate (η) is the best single predictor of lifespan

Across species, η varies by ~seven orders of magnitude and is inversely related to lifespan — the longer the lifespan, the lower the η ¹. The other parameters (β, ε, X_c) vary much less and generally decrease only mildly with lifespan.

Shapley additive explanations (SHAP) analysis on the 19 independently calibrated parameter sets ranked global importance for predicting log median lifespan ¹:

Parameter	Mean \|SHAP\| (log-scaled input)
log(η) production	2.85
log(X_c) threshold	1.53
log(β) removal	1.38
log(ε) noise	0.33

η’s importance (2.85) effectively matches the summed importance of the next two parameters; noise ε is least important. Robust to ANOVA and single-parameter substitution. Conclusion: evolution appears to tune lifespan primarily by changing the damage-production rate — i.e., enhanced molecular accuracy / reduced error rates — rather than by changing removal or the death threshold.

2. Two aging regimes: ballistic vs quasi-steady-state

Because η varies widely while β and ε are conserved, the ratio of production to removal (ηt vs β) defines two behaviors ¹:

Ballistic aging — production outpaces removal over most of life. Mean damage rises quadratically like a free-falling object, ⟨x⟩ ~ ½ηt², giving an inverse-quadratic production–lifespan relation η ~ 2X_c/L² (i.e., η ~ 1/L²). Hazard curves are Weibull-like (power-law). Found in yeast, C. elegans, most Drosophila strains, and mice.
Quasi-steady-state aging — production is balanced by removal (dx/dt ≈ 0), so damage tracks a slowly rising moving set-point until very old age, giving η ~ 1/L (inverse-linear). Hazard curves are Gompertz-like (exponential rise that slows at very old age). Found in humans, dogs, guinea pigs, and cats.

Each organism lies on a continuum between the regimes, defined by the fraction of lifespan in which production exceeds removal. Most studied species sit squarely in one regime; female mice spend their first ~2 years in quasi-steady-state and the remainder in ballistic aging (≈ half the population dying in each regime).

3. Removal, noise, and threshold are nearly invariant across mammals

Two conserved parameter combinations emerge across mammals ¹:

Noise→threshold timescale T_c = X_c²/ε ≈ 600 days (within a factor of ~3) — the time it would take noise alone to drive damage to the death threshold. Close to the ~2-year timescale of mice; in longer-lived mammals this noise timescale is shorter than the lifespan.
Removal-to-noise timescale ratio βX_c/ε ≈ 10 (to a factor of ~2) — i.e., removal working at full speed clears a threshold’s worth of damage ~10× faster than noise alone would reach the threshold.

The death threshold X_c is at least ~10× larger than the removal saturation point κ in every organism — removal saturates in youth/reproductive age, well before death. The near-constancy of the noise/removal ratio raises the possibility that biological noise in mammals arises from systemic fluctuations in removal — one hypothesis being circadian fluctuations in immune clearance of damaged/senescent cells.

4. Which species best resemble human aging

Plotting species in the space of dimensionless parameters (relative noise vs production; determinism), the species closest to humans are dogs (except the largest breed, German Shepherd), cats, guinea pigs, starving E. coli, and Drosophila strain 853 — all with Gompertz-like hazard that slows only at very old age ¹. Mice, C. elegans, and Drosophila strains 707/441/217 are closer to the ballistic regime and have mortality patterns less like humans. Female mice are closer to human-like aging than male mice. This directly informs model-organism choice for human-aging questions — see _extrapolation-guide.

5. Yeast replicative aging has negligible removal

Yeast replicative aging is an extreme case of ballistic aging: the best-fit removal β is very small and can be neglected. Damage accumulates in the mother cell with essentially no opposing removal process; an analytical β=0 approximation gives an asymptotic hazard that rises quadratically with time, h(t) ∝ t² (prefactor ∝ a power of η/ε), in agreement with the observed yeast hazard ¹. Candidate non-removed damage: disrupted mitochondria, DNA, epigenetic (histone) states, and alkaline vacuoles retained in the mother cell.

Biological interpretation

What is damage x? In mammals the leading candidate is senescent cells — a broad class of damaged cells that enter growth arrest and drive inflammation and stem-cell exhaustion, with a damage half-life of ~days plausible and supported experimentally in mice (the SR model’s original calibration in Karin & Alon 2019) ². In yeast the non-removed damage is intracellular (mitochondria, epigenetic states, vacuolar pH).
Production vs removal vs repair. Reduced production (better repair fidelity) corresponds to the documented inverse relationship between somatic mutation / epigenetic-drift / translation-error rates and mammalian lifespan; removal rates seem roughly constant across mammals.
Origin of biological noise. The conserved noise/removal timescale ratio suggests noise is linked to the removal machinery — plausibly circadian rhythm in immune function.

Implications for interventions

The analysis frames a clear lever hierarchy ¹:

Production (η) is the knob evolution uses to set lifespan, so it is the natural target for large lifespan extension.
But reducing production alone stretches both lifespan and sickspan by the same factor (per Yang 2023’s compression-of-morbidity analysis). To extend life and compress sickspan, interventions must also raise the threshold X_c, reduce noise ε, and/or boost removal β.
Practically: future longevity interventions aimed at large extension should focus on the production parameter (molecular-accuracy / damage-prevention) rather than exclusively on removal (e.g., senolytics) or threshold.

Limitations & caveats

The SR parameters are mathematical constructs inferred from survival curves, not directly measured biological quantities. The model shows how theoretical variables track lifespan; it is not independent validation of unique biological causation — these are “mathematically grounded hypotheses that await experimental verification” (the authors’ own framing).
Both lifespan and the parameters are estimated from the same survival data, so the inferred η/β/etc. are not independent measurements.
An identifiability issue: best-fit parameter sets form elongated valleys in parameter space; X_c in particular is weakly constrained, so some confidence intervals are large. Normalizing by X_c resolves much of this.
The model misses the decrease in mortality at very old ages in C. elegans (possibly phenotypic heterogeneity between plates/individuals).
Human data are historical Danish/Swedish birth cohorts (1890–1910); extrinsic mortality was handled with a Makeham term + age cutoffs.

Why this matters for the wiki

This paper is the quantitative spine for the saturating-removal-model frame and bears on several recurring questions:

“Does this model-organism result extrapolate to humans?” — gives a principled, mortality-dynamics answer (regime classification). See _extrapolation-guide.
“What interventions target the rate of aging?” — production-rate primacy reframes the senolytic (removal) vs damage-prevention (production) debate.
It connects mechanistically to cellular-senescence (the proposed substrate of damage x) and to demographic frames like negligible-senescence (Gompertz/Weibull hazard shapes).

Footnotes

raz-2026-sr-model-aging-regimes (this page) · Raz N et al. · Nat Aging 6:1330–1340 (2026) · doi:10.1038/s43587-026-01138-7 · multi-species Bayesian/MCMC fit of the SR model to survival data (yeast, C. elegans, Drosophila, E. coli, mouse, guinea pig, cat, dog, human); n ranged 674 to ~80,000 per species · design: in-silico modeling of observational mortality data · open access. ↩ ↩² ↩³ ↩⁴ ↩⁵ ↩⁶ ↩⁷ ↩⁸ ↩⁹
karin-2019-senescent-cell-turnover-gompertz · Karin O, Agrawal A, Porat Z, Krizhanovsky V, Alon U. “Senescent cell turnover slows with age providing an explanation for the Gompertz law.” Nat Commun 10:5495 (2019) · doi:10.1038/s41467-019-13192-4 · origin of the Saturating Removal model; calibrated against senescent-cell turnover dynamics in mice · model: mouse senescent-cell imaging. ↩ ↩²

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A damage accumulation model identifies distinct aging regimes across species