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Galapagos giant tortoise
Galapagos giant tortoise

Lifespans of animals

What is the relationship between the size of an animal and how long it lives? This interesting topic raises lots of questions, many quite pertinent to our modern lives. It begs for a bit of mathematical scaffolding.

In this step we

  • look at how long different species tend to live

  • summarize various theories that have been proposed over time to explain the differences

  • try to figure out which mammal lives the longest.

Big things live longer?

It has been well known for a long time that larger species tend, on average, to live longer. However there are also some anomalies—often birds, fish or tortoises. Let’s have a look at some data.

Lifespans of some animals

This table is taken from an article of Young Naturalist.

Animal Average Life Span of Animal (in years)
Antelope (Blackbuck) 15
Antelope (Pronghorn) 15
Badger 15
Bat (Guano) 15
Bear (Grizzly) 34
Beaver 20
Boa Constrictor 23
Buffalo 45
Bullfrog 15.5
Carp 50
Cat (Domestic) 30
Chameleon 3.5
Chickadee 7
Chimpanzee 50
Condor 52
Cottonmouth 21
Crappie 6
Crocodile 13.5
Deer (Fallow) 25
Deer (Mule) 20
Deer (Whitetail) 23
Dog (Domestic) 20
Donkey 50
Dove 12
Eagle (Golden) 80
Elephant (Indian) 70
Flounder 10
Fox 14
Frog (Leopard) 6
Garter Snake 6
Gila Monster 20
Giraffe 28
Goat 10
Goose (Canada) 32
Guinea Pig 5
Heron 24
Herring Gull 50
Horse 35
Javelina 20
Jay (Blue) 4
King Snake 14.5
Lion 35
Lizard (Anole) 6
Mole 3
Mountain Lion 18
Mule 37
Nutria 12
Opossum 8
Ostrick (African) 50
Owl (Snowy) 24
Penguin (King) 26
Perch 11
Pigeon 35
Pike 24
Porcupine 20
Porpoise 15
Python 20
Quail 10
Rabbit 10
Raccoon 13
Rattlesnake 18.5
Raven 69
Reindeer 15
Rhinoceros 40
Robin 12
Salamander (Spotted) 25
Seahorse 6
Seal (Common) 30
Sheep (Mouflon) 19
Shrew 2
Skunk 12
Skylark 24
Sparrow 20
Squirrel (Fox) 10
Squirrel (Gray) 18
Starling 15
Sturgeon 50
Trout (Rainbow) 4
Turkey 15
Turtle (Box) 123
Water Snake 7
Whale (Blue) 35
Wolf 16
Zebra 30

Q1 (M): Having studied the above list, you are now possibly an expert on lifespans of common animals. See if you can guess the life spans of the following: Alligator, Camel, African Elephant, Goldfish, Hippopotamus, Jaguar, Mouse, Otter, Pelican, Bighorn Sheep, Tiger.

pic of India Dove India Dove By Ashish Ghosh (Own work) CC BY-SA 3.0, via Wikimedia Commons

Aristotle’s explanation

The link between size and lifespan was first remarked on by Aristotle (350 BC). He made a connection between fire and life which was interestingly prescient:

A lesser flame is consumed by a greater one, for the nutriment, to wit the smoke, which the former takes a long period to expend is used up by the big flame quickly.


He argued that ageing and death were linked to the process of dehydration. For a long time, Aristotle’s explanation was accepted. However in the 1800s, people began to think of ageing more as a result of ‘wearing out’ the body.

The rate of living theory

In 1908 Max Rubner studied the energy metabolism and lifespans of five domestic animals: guinea pig, cat, dog, cow and horse, as well as man. The larger animals lived longer, and he observed that while the total metabolic rate of these animals increases with mass, it did so at a slower rate than mass (so a \(\normalsize 5000\) kilogram elephant will use less energy than \(\normalsize 5000\) kilograms of mice).

However it was also noticed that the product of energy expenditure by maximum lifespan was relatively independent of body size (with humans excluded from the comparison). So a gram of body tissue expends about the same amount of energy, over a lifetime, independent of whether the tissue is in a guinea pig, cat, dog, cow or horse.

The consequent idea that using energy up faster will hasten death is the ‘rate of living’ theory. In his 1922 book ‘The Biology of Death’, Raymond Pearl argued that genetic constitution and the rate of energy expenditure were the key factors in life expectancy. He observed that if accidents were excluded from the statistics, the rates at which males died after the age of 45 were directly related to the levels of energy expenditure in their occupations.

However more recent experiments involving birds have cast some doubt on the universality of this thesis: lifetime expenditures of energy per gram of bird tissue are on average substantially greater than the equivalent values in mammals.

Toxicity, metabolism and free-radicals

In the 1950s a different explanation gained traction: that ageing and death result from toxic by-products of metabolism. This idea is the `free-radical damage’ theory of ageing, in which oxidants and free radicals build up to cause damage to our system. The idea is that there is a direct relationship between oxygen consumption and generation of radical oxygen in our system.

So still there is a direct implication between metabolism and ageing, whether one favors the rate of living or the free-radical damage theory.

A billion heartbeats

Remarkably, biologists have discovered that on average most animals have a lifetime allocation of about a billion heartbeats. We might say that an elephant lives longer than a mouse because its heart beats slower, and so the elephant has more time to get its billion beats. But very possibly the increased metabolic rate of the mouse means that it is doing more living in any given day! There seems to be some glimmer of fairness in this idea.

Human Heart and Circulatory System Human Heart and Circulatory System By Bryan Brandenburg CC BY-SA 3.0, via Wikimedia Commons

Q2 (C): What mammal lives the longest? You should be able to make a pretty good guess, based on the evidence and discussion in this step. Hint: it is not on the list above, and it is not man. You know my methods, Watson.

A twist in the tail

There is an amusing twist on this theme. While it is certainly true that larger species tend to live longer, on average, it is also true that within a species, smaller individuals often live longer than bigger individuals. Perhaps it comes down once again to metabolic rate: larger individuals need a higher metabolism to keep up their energy levels, so perhaps they tend to clock through their allotted times a bit quicker??


A1. Here are the average lifespans of the animals:

Animal Average Life Span of Animal (in years)
Alligator 56
Camel 40
Elephant (African) 50
Goldfish 25
Hippopotamus 41
Jaguar 22
Mouse 4
Otter 15
Pelican 52
Sheep (Bighorn) 15
Tiger 25

A2. The longest living mammal is the bowhead whale, which can live up to 200 years. Also known as the Arctic whale, this animal is big, and lives in cold waters so its metabolism is slow. The record age for a bowhead is 211 years.

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Maths for Humans: Inverse Relations and Power Laws

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