Abstract
Kleiber's law, or the 3/4 -power law scaling of the metabolic rate with body mass, is considered one of the few quantitative laws in biology, yet its physiological basis remains unknown. Here, we report Kleiber's law scaling in the planarian Schmidtea mediterranea. Its reversible and life history-independent changes in adult body mass over 3 orders of magnitude reveal that Kleiber's law does not emerge from the size-dependent decrease in cellular metabolic rate, but from a size-dependent increase in mass per cell. Through a combination of experiment and theoretical analysis of the organismal energy balance, we further show that the mass allometry is caused by body size dependent energy storage. Our results reveal the physiological origins of Kleiber's law in planarians and have general implications for understanding a fundamental scaling law in biology.
Highlights
Body size varies strikingly across animal phylogeny
In spite of such tremendous variation in scale and physiology, the organismal metabolic rate (P; defined as the heat produced by the organism per unit time measured in Watts, which is related to the rate of oxygen consumption (McDonald, 2002)) follows a general scaling relationship with body mass (M)
Reported values of b vary somewhat between studies or specific animal species, a value of b » 3/4 is typically observed (Banavar et al, 2014; Blaxter, 1989; Brody, 1945; Calder, 1984; Hemmingsen, 1960; Kleiber, 1961; Peters, 1983; Schmidt-Nielsen, 1984; West and Brown, 2005; Whitfield, 2006) and this allometric relation between mass and metabolic rate is referred to as the ‘three-quarter’ or ‘Kleiber’s law’. This implies that the specific metabolic rate (P/M) decreases as body mass increases, which is commonly interpreted as reflecting a size-dependent decrease of cellular metabolic rates
Summary
Body size varies strikingly across animal phylogeny. From small crustaceans weighing a few ng to blue whales weighing in excess of 140 000 kg, body mass variations span more than 16 orders of magnitude (Makarieva et al, 2008; Sears and Calambokidis, 2002). Reported values of b vary somewhat between studies or specific animal species, a value of b » 3/4 is typically observed (Banavar et al, 2014; Blaxter, 1989; Brody, 1945; Calder, 1984; Hemmingsen, 1960; Kleiber, 1961; Peters, 1983; Schmidt-Nielsen, 1984; West and Brown, 2005; Whitfield, 2006) and this allometric relation between mass and metabolic rate is referred to as the ‘three-quarter’ or ‘Kleiber’s law’ This implies that the specific metabolic rate (P/M) decreases as body mass increases, which is commonly interpreted as reflecting a size-dependent decrease of cellular metabolic rates.
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