In the 1930’s, Swiss-American animal metabolism pioneer Max Kleiber noticed that the metabolic rate of animals scales as the body mass to the three quarters power. There is still some controversy over whether the exponent is really three quarters or something else. Many theories have been proposed for why the exponent should be three quarters (or two thirds) but I won’t go into that here. The crucial thing is that it is less than one and that implies that a large animal is more efficient than a small one. This efficiency with size is not restricted to biological examples. As Steve Strogatz pointed out in a New York Times column last year, the number of gas stations doesn’t grow linearly with the population of a city but rather grows in proportion to the 0.77 power of the population. This sublinear scaling also goes for other city infrastructure like the total length of roads and electrical cables. Large cities may in fact be more efficient than small ones.

Now a mouse weighs about 20 to 30 grams so it is about a factor of 3500 times less massive than an average human. Metabolic rate scales as mass to the three quarters so power density ( e.g. Watts/gram) scales as mass to the minus one quarter. Hence, a mouse is or 7 to 8 times less metabolically efficient than a human. A colony of mice weighing as much as a human would have to eat 7 to 8 times as much food.

However, in terms of total energy utilized, first world humans are much less efficient than mice and perhaps all other organisms. The metabolic rate of an average person is about 10 megajoules per day or 115 watts but according to Wikipedia, the United States uses about 10,000 watts of power per capita. This is a factor of 90 over the metabolic rate implying that an average American is a factor of ten less efficient than a mouse. However, a very low energy use nation like Bangladesh only consumes about twice as much energy per capita as the human metabolic rate and thus an average Bangladeshi is more efficient than a mouse.

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