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No evidence for squaring the survival curve: lifespan-extending treatments increase variation in age- at-death.

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Title: No evidence for squaring the survival curve: lifespan-extending treatments increase variation in age- at-death.
Authors: Fulton TL; Charles Perkins Centre, University of Sydney, Camperdown, NSW2006, Australia.; School of Life and Environmental Sciences, University of Sydney, Sydney, NSW, Australia., Macartney EL; Charles Perkins Centre, University of Sydney, Camperdown, NSW2006, Australia.; School of Life and Environmental Sciences, University of Sydney, Sydney, NSW, Australia.; Institute of Organismic and Molecular Evolution, Johannes Gutenberg University Mainz, Mainz55122, Germany.; Evolution and Ecology Research Centre, School of Biological, Earth, and Environmental Sciences, University of New South Wales, Sydney, New South Wales2052, Australia., Senior AM; Charles Perkins Centre, University of Sydney, Camperdown, NSW2006, Australia.; School of Life and Environmental Sciences, University of Sydney, Sydney, NSW, Australia.; Sydney Precision Data Science Centre, University of Sydney, Camperdown2006, Australia.
Source: Biology letters [Biol Lett] 2026 Feb 25; Vol. 22 (2).
Publication Type: Journal Article
Language: English
Journal Info: Publisher: The Royal Society Country of Publication: England NLM ID: 101247722 Publication Model: Print Cited Medium: Internet ISSN: 1744-957X (Electronic) Linking ISSN: 17449561 NLM ISO Abbreviation: Biol Lett Subsets: MEDLINE
Imprint Name(s): Original Publication: London : The Royal Society, 2005-
MeSH Terms: Longevity*/drug effects , Metformin*/pharmacology , Sirolimus*/pharmacology , Geroscience*/methods , Caloric Restriction* , Aging* , Life Expectancy*, Animals
Abstract: Geroscience has the goal of extending lifespan through geroprotective interventions. These interventions are typically imparted on groups of individuals, with their efficacy judged by increases in the average age-at-death. A more equitable outcome, which looks beyond the average, is to attain a long life for all individuals, such that the average age-at-death is high while variability (e.g. standard deviation in age-at-death) is low. This goal of increasing the mean while reducing variation is sometimes referred to as 'squaring the survival curve'. A recent meta-analysis of vertebrate data found that dietary restriction (DR) and the DR-mimetic, rapamycin, generally increase the average age-at-death, while metformin (also considered a DR-mimetic) is less effective. We have re-analysed this recently published data to study the effects of lifespan-extending treatments on variation in the age-at-death. On average, all three treatments increase the variance in the age-at-death, but not the coefficient of variation (i.e. standard deviation relative to the mean). This suggests that lifespan-extending treatments do not reduce variance and 'square the survival curve'. Rather, any gains in mean age-at-death are matched by corresponding increases in variation. Interestingly, this result is consistent with the treatments proportionally reducing both the age-dependent and age-independent parameters in a Gompertz model of mortality.
(© 2026 The Authors.)
Grant Information: University of Sydney; Australian Research Council
Contributed Indexing: Keywords: ageing; calorie restriction; gerontology; life expectancy; lifespan extension; mTORC1; meta-regression; model organism; standard deviation; variance
Substance Nomenclature: 9100L32L2N (Metformin)
W36ZG6FT64 (Sirolimus)
Entry Date(s): Date Created: 20260227 Date Completed: 20260709 Latest Revision: 20260709
Update Code: 20260711
DOI: 10.1098/rsbl.2025.0651
PMID: 41759197
Database: MEDLINE
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  Data: No evidence for squaring the survival curve: lifespan-extending treatments increase variation in age- at-death.
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  Data: <searchLink fieldCode="AU" term="%22Fulton+TL%22">Fulton TL</searchLink>; Charles Perkins Centre, University of Sydney, Camperdown, NSW2006, Australia.; School of Life and Environmental Sciences, University of Sydney, Sydney, NSW, Australia.<br /><searchLink fieldCode="AU" term="%22Macartney+EL%22">Macartney EL</searchLink>; Charles Perkins Centre, University of Sydney, Camperdown, NSW2006, Australia.; School of Life and Environmental Sciences, University of Sydney, Sydney, NSW, Australia.; Institute of Organismic and Molecular Evolution, Johannes Gutenberg University Mainz, Mainz55122, Germany.; Evolution and Ecology Research Centre, School of Biological, Earth, and Environmental Sciences, University of New South Wales, Sydney, New South Wales2052, Australia.<br /><searchLink fieldCode="AU" term="%22Senior+AM%22">Senior AM</searchLink>; Charles Perkins Centre, University of Sydney, Camperdown, NSW2006, Australia.; School of Life and Environmental Sciences, University of Sydney, Sydney, NSW, Australia.; Sydney Precision Data Science Centre, University of Sydney, Camperdown2006, Australia.
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  Data: <searchLink fieldCode="JN" term="%22101247722%22">Biology letters</searchLink> [Biol Lett] 2026 Feb 25; Vol. 22 (2).
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  Data: <searchLink fieldCode="MM" term="%22Longevity%22">Longevity*</searchLink>/<searchLink fieldCode="MM" term="%22Longevity+drug+effects%22">drug effects</searchLink> <br /><searchLink fieldCode="MM" term="%22Metformin%22">Metformin*</searchLink>/<searchLink fieldCode="MM" term="%22Metformin+pharmacology%22">pharmacology</searchLink> <br /><searchLink fieldCode="MM" term="%22Sirolimus%22">Sirolimus*</searchLink>/<searchLink fieldCode="MM" term="%22Sirolimus+pharmacology%22">pharmacology</searchLink> <br /><searchLink fieldCode="MM" term="%22Geroscience%22">Geroscience*</searchLink>/<searchLink fieldCode="MM" term="%22Geroscience+methods%22">methods</searchLink> <br /><searchLink fieldCode="MM" term="%22Caloric+Restriction%22">Caloric Restriction*</searchLink> <br /><searchLink fieldCode="MM" term="%22Aging%22">Aging*</searchLink> <br /><searchLink fieldCode="MM" term="%22Life+Expectancy%22">Life Expectancy*</searchLink><br /><searchLink fieldCode="MH" term="%22Animals%22">Animals</searchLink>
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  Data: Geroscience has the goal of extending lifespan through geroprotective interventions. These interventions are typically imparted on groups of individuals, with their efficacy judged by increases in the average age-at-death. A more equitable outcome, which looks beyond the average, is to attain a long life for all individuals, such that the average age-at-death is high while variability (e.g. standard deviation in age-at-death) is low. This goal of increasing the mean while reducing variation is sometimes referred to as 'squaring the survival curve'. A recent meta-analysis of vertebrate data found that dietary restriction (DR) and the DR-mimetic, rapamycin, generally increase the average age-at-death, while metformin (also considered a DR-mimetic) is less effective. We have re-analysed this recently published data to study the effects of lifespan-extending treatments on variation in the age-at-death. On average, all three treatments increase the variance in the age-at-death, but not the coefficient of variation (i.e. standard deviation relative to the mean). This suggests that lifespan-extending treatments do not reduce variance and 'square the survival curve'. Rather, any gains in mean age-at-death are matched by corresponding increases in variation. Interestingly, this result is consistent with the treatments proportionally reducing both the age-dependent and age-independent parameters in a Gompertz model of mortality.<br /> (© 2026 The Authors.)
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  Data: University of Sydney; Australian Research Council
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  Data: <i>Keywords: </i>ageing; calorie restriction; gerontology; life expectancy; lifespan extension; mTORC1; meta-regression; model organism; standard deviation; variance
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  Data: 9100L32L2N (Metformin)<br />W36ZG6FT64 (Sirolimus)
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              Text: 2026 Feb 25
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