This article was taken from the November 2011 issue of Wired magazine. Be the first to read Wired's articles in print before they're posted online, and get your hands on loads of additional content by subscribing online.
If a mouse gains three kilocalories of energy a day from its food, how much does an elephant gain? (A kilocalorie is the scientific unit; diet books call it a Calorie with a capital C.)
Hint: a mouse weighs 25g. An elephant weighs about four tonnes, depending on size and species -- that's 160,000 times more. So does the elephant get 160,000 times as much energy? That would be 480,000kcal. Actually it's about 25,000kcal. What we're talking about is technically called the basal metabolic rate -- the amount of energy that a resting animal requires. On the whole, a big animal needs more energy than a small one -- but not in direct proportion to its mass. The precise relationship is governed by Kleiber's Law: the metabolic rate is proportional to mass raised to the power of three-quarters, or 0.75. This means that the elephant's metabolic rate ought to be 160,0000. 75 times that of a mouse, which is 8,000 times as big. That's 25,120 -- spot on.
Swiss zoologist Max Kleiber derived his equation in the US in the 30s. He originally thought the power was 0.66, based on how animals lose heat via surface area, but he came to prefer 0.75. Biologists Geoffrey West, Brian Enquist and James Brown deduced 0.75 as a consequence of fractal branching of blood vessels. Fractals, introduced by Benoît Mandelbrot in the 80s, are geometric shapes that reproduce their form on smaller scales. The fractal model is controversial, in part because Kleiber's Law works for everything between bacteria and whales -- but bacteria don't have blood.
To work out your own metabolic rate, take your mass in kilograms, raise it to the power of 0.75 and multiply by 50 (the constant of proportionality as a round figure). For instance, a weight of 80kg gives a basal metabolic rate of 1,337kcal per day.
This article was originally published by WIRED UK
