Longevity quotient

How long an animal lives, against how long an animal of its size should live.

Body mass predicts lifespan. The 7,873 species in this model run from a rotifer at 0.5 µg to a blue whale at 150 tonnes, 14.5 orders of magnitude of body size. Across that whole range each tenfold increase in mass buys roughly a 1.5-fold increase in maximum lifespan. The relationship is strong enough to be worth dividing out. What remains is the longevity quotient:

LQ = observed lifespan ÷ lifespan predicted from body mass

Mass rises left to right and so does the prediction, because the fit can only go up. What the animals do is not monotonic, and the quotient is what is left once size has been divided out. This figure scores each animal against the fit across all animals; the rankings below and the visualiser score each against its own group, which for the human gives 5.0 rather than 4.0.

It is built by analogy with the encephalisation quotient¹, which does the same thing to brain size. A quotient of one means an animal lives exactly as long as its size predicts. The interesting animals are the ones far from one.

Lifespan against body mass. The dashed line is the fit across every animal in the table. Distance above or below that line, measured within a species' own class, is the quotient.

The twelve grade-A or B species furthest below their predicted lifespan and the eighteen furthest above, coloured by pool. The dashed line is parity, where an animal lives exactly as long as its mass predicts. Colonial animals are excluded, because a colony is not an individual; so are grade-C records, which is where the outlier rule below puts a compilation figure the fit cannot account for.

Comparing whole groups

The group view aggregates every species in a taxon and sets taxa against each other. The bar is the geometric mean quotient of the group's members, with a faint line spanning its lowest to its highest. The geometric mean is the correct average for ratios: a species at four times prediction and one at a quarter of it should average to one, not to 2.1.

Of the 81 orders holding four or more grade-A or B species, the egg-laying Monotremata top the list at 2.66 and the bats of Chiroptera follow at 2.53 — but one rests on a handful of species, 4, and a geometric mean over four animals is a claim about four animals. The large groups near the top are the ones worth the weight: the bats of Chiroptera at 2.53 across 261 species and the Primates at 2.06 across 346 species. At the bottom sit the tinamous of Tinamiformes at 0.32, the pangolins of Pholidota at 0.40, the tenrecs and golden moles of Afrosoricida at 0.47; the ground birds of Galliformes come in at 0.52 and the shrews, moles and hedgehogs of Eulipotyphla at 0.66. At family rank, among families with ten or more species, the evening bats of Vespertilionidae reach 3.25 over 122 species, the scorpionfishes of Scorpaenidae 3.16, the gibbons of Hylobatidae 3.01. Flight, burrowing, venom, armour and simply being difficult to swallow all register as raised quotients. Being a ground bird or a small terrestrial insectivore registers as the reverse.

All 81 orders holding four or more species, ranked by geometric mean quotient over their grade-A and B species and read left column first. The dashed line is parity with prediction: everything in the right-hand column falls short of what its members’ body masses predict.

Colonies are not individuals

Four entries are colonies rather than animals: a black coral aged at 4,265 years, a boulder star coral, a giant barrel sponge, and a glass sponge whose spicule growth rings have been read as eleven thousand years. Those are ages of the colony, and the polyps composing them live ordinary short lives. They are excluded from every regression, and hidden from the rankings by default, because an eleven-thousand-year colony sits at the top of every sort and buries whatever the data actually shows.

What comes out

The highest quotients against their own group, among the grade-A and B records, belong to an ocean quahog at 47×, a black garden ant queen at 29×, a cold-seep tubeworm at 23×, a freshwater pearl mussel at 16×, an olm at 15× and a rougheye rockfish at 13× its predicted lifespan. The lowest belong to a silkmoth at 0.04×, a common wasp at 0.05×, a common octopus at 0.07×, a longfin inshore squid at 0.07× and a toolache wallaby at 0.07×.

Three of those are worth a closer look. The honey bee worker and the honey bee queen carry the same genome and sit an order of magnitude apart in lifespan, because caste and diet decide the outcome rather than genetics. The giant Pacific octopus is large, capable, and dead in five years, because it breeds once and then stops eating. The chambered nautilus, a cephalopod that does not breed once and die, lives twenty. Labord's chameleon spends most of its existence inside an egg and then lives four or five months as an adult, the shortest life of any four-limbed vertebrate, in a body whose size predicts eight years. None of this is visible in a table of lifespans sorted by years. All of it appears the moment body mass is divided out.

Wild against captive, sorted by the size of the gap. Where protection helps most, and where it does not help at all.

Fitting the baseline

An ordinary least squares regression of log lifespan on log body mass, run globally and within each group. Fitting inside a group matters. Birds come out about 2.2 times longer-lived than mammals of equal mass, which matches what the comparative literature reports, so a single fit across every animal charges every bird a bonus it did not earn and every mammal a penalty it does not deserve. Fish classes are pooled together, and the many small invertebrate classes are pooled into one baseline, because separately they are too thin to fit.

The amphibian regression returns an r² of 0.04 across 83 species, which is not a relationship. Any group fit with a non-positive slope or an r² below 0.15 is rejected, and that group falls back to the global baseline. The model reports which groups were rejected and why. Amphibians are currently the only one.

Data

7,873 species spanning 10 phyla, 32 classes, 199 orders, 764 families and 2,921 genera. Every record carries full taxonomy, an adult body mass, at least one maximum lifespan, a quality grade and its provenance. 2,905 have a maximum their source labeled wild, 1,795 one it labeled captive, and 309 have both — the comparison this project was built around, and the reason the merge keeps the hand-checked table at the top of the precedence order rather than letting a bulk source overwrite it. The largest set, 3,482 species, carries a maximum whose source did not say where the animal lived: the Amniote and AmphiBIO compilations report one figure per species with no origin, FishBase population maxima do the same, and 90 AnAge rows list the specimen origin as unknown. A captive maximum runs longer than a wild one, so a record whose origin is not stated is carried, drawn and counted as a maximum of unrecorded origin rather than as a wild one.

Disputed records lose to verified ones: the 226-year koi and the 120-year cockatoo are both out. Grade C records appear in the table and in the visualiser, with their grade shown, but are held out of every regression, so a weak record can be looked at without being allowed to move the baseline that judges it.

Where the data comes from

Six databases carry a maximum lifespan. They overlap heavily and they disagree, so a species found in more than one takes its numbers from the best source available and records the others as corroboration. Averaging a careful record against a careless one produces a number that belongs to neither.

Body-mass databases are a separate matter and they are much larger. AVONET alone has measured masses for 14,673 species, mostly birds. None of them create a record: a species with a mass and no lifespan is not an observation of anything this model can use. They only rescue a species that has been aged and never weighed, which they did 524 times.

8,583 distinct species carried a lifespan after the merge. 710 of them were dropped for having no body mass in any source — mostly reptiles and amphibians, which are routinely measured snout to vent and never put on a scale. 641 fish were kept with a mass computed from maximum length through FishBase's own length–weight relationship; those are modeled, not measured, and are marked and graded accordingly. What survives is 7,873 species, graded A 149 · B 6,250 · C 1,474 as they arrive from their sources. The outlier rule described under the arithmetic then demotes 57 grade-B records to C, so the model runs on A 149 · B 6,192 · C 1,528 (the four colonies are counted separately).

This is the ceiling, and it is worth being clear about why. About 2.24 million species have been described. Fewer than nine thousand have ever been both aged and weighed, because a maximum lifespan requires somebody to have watched an animal until it died. The limit here is not access to data. It is that the observations were never made. Wikidata, which is the aggregate of individual species pages rather than a compiled table, holds 1,147 taxa with a recorded maximum lifespan and 259 with a lifespan and a mass together — less than a twentieth of what the compiled databases give, which is the answer to whether scraping species pages one at a time would do better.

The arithmetic, written out

One ordinary least squares regression per baseline, unweighted, of log₁₀ maximum lifespan in years on log₁₀ adult body mass in grams, over the grade-A and grade-B records. Grade C is held out of every fit and scored against the result. Nothing is weighted. The simulation in test_fit_strategy.py is why — a thin record is biased short, not merely noisy, and down-weighting a bias still lets it through where dropping it does not. The count beside each baseline above is the number of records in that fit. The sample spans 14.5 orders of magnitude of body mass, from 0.5 µg to 150 tonnes.

All animals:    log10 L = +0.583 +0.188 log10 M
Mammals:        log10 L = +0.357 +0.215 log10 M
Birds:          log10 L = +0.706 +0.216 log10 M
Reptiles:       log10 L = +0.605 +0.211 log10 M
Fish:           log10 L = +0.379 +0.240 log10 M
Invertebrates:  log10 L = +0.593 +0.256 log10 M

predicted lifespan  =  10 ^ (a + b * log10(mass in grams))
LQ                  =  observed maximum lifespan / predicted

One rule runs before the final fit. A preliminary fit per group flags any grade-B record more than 3 residual standard deviations from it, in either direction, and demotes it to grade C: 57 records here (31 mammals, 10 birds, 8 fish, 8 reptiles). The Amniote compilation grades as B by construction and carried twenty-eight mammals, birds and reptiles with maximum lifespans of one to three months at body masses up to five kilograms — a 2.2 kg hare at one month — which are unit or field errors, not observations, and which sat at the bottom of every ranking on this page. The rule is symmetric so that it cannot be accused of only removing what hurts, it never touches a grade-A record (each of those was checked by hand against a citation), and it deletes nothing: a demoted record keeps its row, its note says why, and the visualiser shows it under Include C.

The slope is the interesting parameter. At 0.188 it says a tenfold increase in mass buys a 1.54-fold increase in maximum lifespan — lifespan goes roughly as the 5th root of mass. This is why the prediction is so hard to escape by growing: an animal a thousand times heavier than another is predicted to live only about 3.7 times longer.

An honourable mention

Steven Austad’s Methuselah’s Zoo: What Nature Can Teach Us About Living Longer, Healthier Lives (MIT Press, 2022) is the book behind the question this page asks. It is a working comparative biologist’s tour of the animals that outlive their size — the bats, the naked mole-rat, the quahog, the bowhead — and the argument that the interesting cases are precisely the ones a body-mass expectation fails to explain. The quotient computed here is a way of putting a number on that observation; the observation, and the case for taking it seriously, are his. It is worth reading whether or not you care about the arithmetic.

Sources

1. Jerison, Evolution of the Brain and Intelligence, Academic Press, 1973.The quotient construction this model borrows.
2. Wilkinson & Adams, Biology Letters, 2019 - recent advances in the biology of bat ageing.Why flight and longevity travel together.
3. Nielsen et al., Science 353:702, 2016 (Greenland shark, eye-lens radiocarbon); Cailliet et al., Experimental Gerontology 36:739, 2001 (rockfish otolith ageing).The extreme fish lifespans, and the dating methods behind them.
4. Butler et al., Palaeogeography, Palaeoclimatology, Palaeoecology, 2013 - the 507-year Arctica islandica.The longest-lived non-colonial animal recorded.
5. Tacutu et al., Nucleic Acids Research 46:D1083, 2018 - the AnAge database of animal ageing and longevity.Maximum lifespan and adult body mass for most species in the table.
6. Myhrvold et al., Ecology 96:3109, 2015 - an amniote life-history database for comparative analyses with birds, mammals and reptiles.Lifespan and body mass for most birds, mammals and reptiles here.
7. Jones et al., Ecology 90:2648, 2009 - PanTHERIA, a species-level database of life history, ecology and geography of extant and recently extinct mammals.Mammalian maximum longevity and adult body mass.
8. Oliveira et al., Scientific Data 4:170123, 2017 - AmphiBIO, a global database for amphibian ecological traits.Amphibian longevity and body mass.
9. Froese & Pauly (eds.), FishBase, v25.04 snapshot, distributed as parquet by rOpenSci. CC BY-NC.Maximum age and weight for fish, graded C throughout.
10. Tobias et al., Ecology Letters 25:581, 2022 - AVONET, morphological, ecological and geographical data for all birds.Body mass used only to fill gaps for birds already aged.

Animal icons in the margin scene: OpenMoji, licensed CC BY-SA 4.0, recoloured to this page’s own palette. The chameleon and the tubeworm have no emoji and are drawn by hand to match. Every quotient beside a creature is that species’ own figure from the table above.