What is Metabolic rate, allometry? — Biology

Definition 1.13 University Biology — Year 1 · Chapter 1 — The Organism: A System in Interaction with Its Environment

The metabolic rate $B$ of an organism is the rate at which it converts chemical energy, measured in watts as heat production or as oxygen consumption ( $1\,\mathrm{L}$ of $\mathrm{O_2}$ consumed $\approx 20\,\mathrm{kJ}$ ). The basal metabolic rate is that of a resting, fasting endotherm in its thermoneutral zone. A quantity $Y$ is said to scale allometrically with body mass $M$ when $Y = a\,M^{b}$ with an exponent $b \neq 1$ ; on a log–log plot the relation is a straight line of slope $b$ .

Kleiber’s law. Basal metabolic rate against body mass for six mammals on logarithmic axes: the points fall on a line of slope 3/4 over five orders of magnitude of mass. — Kleiber’s law. Basal metabolic rate against body mass for six mammals on logarithmic axes: the points fall on a line of slope $3/4$ over five orders of magnitude of mass.

Examples

Example 1.16 (Mouse and elephant)

A $20\,\mathrm{g}$ mouse: $B = 3.4\times 0.02^{0.75} = 0.18\,\mathrm{W}$ , or $9\,\mathrm{W}/\mathrm{kg}$ . A $4\,\mathrm{t}$ elephant: $B = 3.4\times 4000^{0.75} = 1700\,\mathrm{W}$ , or $0.43\,\mathrm{W}/\mathrm{kg}$ . The elephant burns ten thousand times more than the mouse, but each of its grams burns twenty-one times less: $(4000/0.02)^{-1/4} = 1/21$ . The mouse must eat a tenth of its mass every day; the elephant, a fiftieth. The mouse’s heart beats $600\,$ times a minute, the elephant’s $30\,$ : heart rate, like $B/M$ , scales as $M^{-1/4}$ , and both animals’ hearts beat about a billion times in a lifetime.

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