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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 Propel Steps.

Animal Average Life Span of Animal (in years)
African Grey Parrot 50
Amazon Parrot 80
Angleworm 15
Ant (Queen) 3
Ant (Worker) 1.5
Asian elephant 40
Cockatoo 40
Bat 24
Bear 40
Beaver 20
Bison 30
Blackbird 18
Boa Constrictor 23
Bottlenose Dolphin 20
Box Turtle 123
Bull 28
Bull Snake 18
Canada Goose 33
Carp 100
Cat 25
Catfish 60
Chicken 15
Chimpanzee 40
North American Cicada 13-17
Cow 22
Crocodile 45
Deer 35
Dog 22
Eagle 55
Elephant 70
Elk 22
English Sparrow 23
Fence Lizard 4
Ferret 12
Fox 14
Galapagos Land Tortoise 193
Giant Tortoise 152
Goat 15
Golden Hamster 4
Gorilla 20
Great Horned Owl 68
Green Frog 10
Hog 18
Horse 40
Human 70-80
Humming Bird 8
Kangaroo 9
Koala 8
Lion 35
Lobster 15
Macaw 50
Mountain Lion 20
Mouse 4
Newt 7
Opossum 4
Parrot 80
Polar bear 20
Porcupine 20
Quail 6
Rhinoceros 40
Salamander 11
Sea Lion 14
Tasmanian Tiger 7
Wombat 15
Wolf 18

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, Bee (Queen), Bee (Worker), Camel, Cow, Domestic Pigeon, Eel, Hippopotamus, Leopard, Mongoose, Ox, Platypus, Rabbit, 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.

Aristotle

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 1800’s, people began to think of ageing more as a result of `wearing out’ the body.

http://www.impactaging.com/papers/v5/n4/full/100551.html

The rate of living theory

In 1908 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 kilogram elephant will use less energy than 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’, Pearl argued that genetic constitution and the rate of energy expenditure were the key factors in life expectancy. He observed that 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 1950’s 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.

Here is an article that explains the work: http://hep.ucsb.edu/courses/ph6b_99/0111299sci-scaling.html

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??

Answers

A1. Here are the average lifespans of the animals:

Animal Average Life Span of Animal (in years)
Alligator 68
Bee (Queen) 5
Bee (Worker) 1.5
Camel 50
Cow 22
Domestic Pigeon 26
Eel 55
Hippopotamus 45
Leopard 17
Mongoose 12
Ox 20
Platypus 10
Rabbit 9
Sheep 15
Tiger 22

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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This article is from the free online course:

Maths for Humans: Linear, Quadratic & Inverse Relations

UNSW Sydney

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