Kleiber's law,^[1] named after Max Kleiber's biological work in the early 1930s, is the observation that, for the vast majority of animals, an animal's metabolic rate scales to the ¾ power of the animal's mass. Symbolically: if q₀ is the animal's metabolic rate, and M the animal's mass, then Kleiber's law states that q₀ ~ M^¾. Thus a cat, having a mass 100 times that of a mouse, will have a metabolism roughly 31 times greater than that of a mouse. In plants, the exponent is found to be close to 1.

Figure 1. Body size versus metabolic rate for a variety of species^[2]. Originally published in Kleiber (1947).

[edit] Biography

Max Kleiber^[3] was born and educated in Zurich, Switzerland. He graduated from the Federal Institute of Technology as an Agricultural Chemist in 1920, earned the ScD degree in 1924, and became a private dozent after publishing his thesis The Energy Concept in the Science of Nutrition.

He came to the Animal Husbandry Department of UC Davis in 1929 to construct respiration chambers and conduct research on energy metabolism in animals. Among his many important achievements, two are especially noteworthy. In 1932 he came to the conclusion that the ¾ power of body weight was the most reliable basis for predicting the basal metabolic rate (BMR) of animals and for comparing nutrient requirements among animals of different size. He also provided the basis for the conclusion that total efficiency of energy utilization is independent of body size. These concepts and several others fundamental for understanding energy metabolism are discussed in Kleiber's book, The Fire of Life published in 1961 and subsequently translated into German, Polish, Spanish, and Japanese.

[edit] Reasoning behind the law

Kleiber's law, as many other biological allometric laws, is a consequence of the physics and geometry of animal circulatory systems, according to some authors. Young (i.e., small) organisms respire more per unit of weight than old (large) ones of the same species because of the overhead costs of growth, but small adults of one species respire more per unit of weight than large adults of another species because a larger fraction of their body mass consists of structure rather than reserve; structural mass involves maintenance costs, reserve mass does not.

[edit] Value of the exponent

Kleiber's law is a power law. The exponent of this power law was a matter of dispute for many decades. It is still claimed by a diminishing number to ⅔ rather than the more widely accepted ¾. An exponent of ⅔ would be expected if metabolic rate were proportional to surface area. Kleiber himself came to favor ¾, and that is the number favored today.

Theoretical models presented by Geoffrey West, Brian Enquist, and James Brown,^[4] derive the ¾ exponent from assumptions about the hierarchical branching of the vascular system. This treatment assumes that metabolic rate is determined by the ability of the vascular system to deliver resources. Their claims have been criticized on the grounds that fractal capillary branching is not demonstrated to be fundamental to the exponent ¾, and that arguments based on vascular systems do not apply organisms smaller than e ^{- 6} (≈ 0.0025) grams and yet the equation is claimed to apply to organisms as small as bacteria.

Attempts to understand the metabolic rate of a multi-cellular organism (field metabolic rate, which includes the activity of the organism) are couched in terms of the product of average basal metabolic rate and number of cells.^[5] This, plus capillary terminal size invariance, leaves the equation open to the criticism that it cannot account for spikes in metabolic rate needed for motor activity: too much blood flow would be required.

In plants, according to a paper in 2006 in Nature, the exponent of mass is found to be close to 1.^[6][7].

[edit] Current debate

Some biologists [e.g., Kozlowski and Konarzewski, John Speakman] have criticized West, Brown, and Enquist on the grounds that the size-invariance of capillaries, which applies to systems as diverse as mammals and vascular plants, dooms attempts to account for motor activity as part of metabolism.^[8][9] This is why metabolic rates are almost always associated with the organism at rest, where metabolic rate is figured to be the basal rate rather than the rate for the organism in its day-to-day life in the field. West et al. claim that Kleiber's law refers to the basal metabolic rate of an organism's cells, not the field metabolic rate of the organism, and regard field metabolic rate as the product of the average basal metabolic rate and number of cells in the organism. Critics respond that BMR cannot account for motor activity even by this reckoning, so the equation is nonetheless of limited value.

[edit] See also

• Allometric law
• Constructal law
• Evolutionary physiology
• Metabolic theory of ecology
• Scaling law

[edit] References

[edit] External links

• Kleiber bio - UC Davis
• Wang Z, O'Connor TP, Heshka S, Heymsfield SB (November 2001). "The reconstruction of Kleiber's law at the organ-tissue level". J Nutr. 131 (11): 2967–70. PMID 11694627. 
• Rau AR (September 2002). "Biological scaling and physics". J Biosci. 27 (5): 475–8. doi:10.1007/BF02705043. PMID 12381870. 
• Of Mice and Elephants
• New Clues to Why Size Equals Destiny