Why big animals live slow

A mouse's heart beats around 600 times a minute and it lives about two years. An elephant's beats about 30 times a minute and it lives around 70. Both get roughly a billion heartbeats. Body size turns out to predict an extraordinary amount about an animal, and the relationships are not proportional but follow consistent powers.

The three-quarters law

If metabolism were simply about keeping a body running, you might expect an animal twice the mass to need twice the energy. It does not. It needs about 1.68 times as much. Metabolic rate scales with mass raised to roughly the power of three quarters, a relationship Max Kleiber established in the 1930s that holds from bacteria to whales, across more than twenty orders of magnitude.

The consequence is that a gram of elephant is much cheaper to run than a gram of mouse. Large animals are more energy-efficient per unit of mass, which is a large part of why being large is worth the trouble.

Why three quarters, and the argument about it

A tidy geometric story says surface area scales as the two-thirds power of volume, so heat loss should too. That predicts an exponent of two thirds, and the data say three quarters, so the tidy story is not sufficient.

The leading explanation is about distribution rather than surface. Bodies are supplied by branching networks, blood vessels or airways or plant vasculature, and if such a network is space-filling, ends in units of a fixed size (capillaries are much the same everywhere), and is optimised to minimise the energy of pumping, then three quarters falls out of the geometry. That is the West, Brown and Enquist model from the 1990s.

It is worth flagging that this is contested. Critics argue the exponent varies more between groups than a universal law implies, and that some datasets sit closer to two thirds. What is not in dispute is that metabolism scales sublinearly with mass, and that the consequences below follow from it.

What follows from one exponent

Because metabolic rate per gram falls with size, everything downstream of metabolism slows down in a predictable way. Heart rate, breathing rate and the pace of development all scale with mass to about the power of minus a quarter. Lifespan scales positively, at roughly a quarter power.

Combine those two and the famous result appears: heart rate falls at the same rate lifespan rises, so total heartbeats per life are approximately constant across mammals, somewhere around a billion. A mouse and an elephant live very different lives at very different speeds and get a similar number of beats to do it in.

Humans are a conspicuous exception, living roughly three times longer than our size predicts, which is one of the more interesting unexplained facts about our species. And the biological clock that matters is not the calendar: a mouse at two years and an elephant at seventy are both old, and both are old at about the same point in metabolic time.

Size as a gene, with a cost that scales

Body size is one of the nineteen genes an organism carries here, inherited and mutable, and it is load-bearing in the cost model rather than cosmetic.

Movement costs the square of speed multiplied by body size and by terrain resistance, so a larger organism pays more to move and pays more the faster it goes. Metabolic efficiency and energy storage are separate genes, so the trade-off between what a body costs and what it can hold is something the population explores rather than something set by the designer. Lifespan is a further gene again. The cost table is on energy, metabolism and death.