Kleiber's law

Kleiber's law, named after Max Kleiber for his biology 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 ~ M¾. Thus, over the same timespan, a cat having a mass 100 times that of a mouse will consume only about 32 times the energy the mouse uses.

The exact value of the exponent in Kleiber's law is unclear, in part because there is currently no completely satisfactory theoretical explanation for the law.

Kleiber's plot comparing body size to metabolic rate for a variety of species.[1]

Proposed explanations for the law

Kleiber's law, as many other biological allometric laws, is a consequence of the physics and/or geometry of animal circulatory systems.[2] Max Kleiber first discovered the law when analyzing a large number of independent studies on respiration within individual species.[3] Kleiber expected to find an exponent of ​23 (for reasons explained below), and was confounded by the exponent of ​34 he discovered.[4]

Heuristic explanation

One explanation for Kleiber's law lies in the difference between structural and growth mass. Structural mass involves maintenance costs, reserve mass does not. Hence, 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. Within each species, 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.[5]

Exponent ​2⁄3

Explanations for ​23-scaling tend to assume that metabolic rates scale to avoid heat exhaustion. Because bodies lose heat passively via their surface, but produce heat metabolically throughout their mass, the metabolic rate must scale in such a way as to counteract the square–cube law. The precise exponent to do so is ​23.[6]

Such an argument does not address the fact that different organisms exhibit different shapes (and hence have different surface-to-volume ratios, even when scaled to the same size). Reasonable estimates for organisms' surface area do appear to scale linearly with the metabolic rate.[5]

Exponent ​3⁄4

A model due to West, Enquist, and Brown (hereafter WEB) suggests that ​34-scaling arises because of efficiency in nutrient distribution and transport throughout an organism. In most organisms, metabolism is supported by a circulatory system featuring branching tubules (i.e., plant vascular systems, insect tracheae, or the human cardiovascular system). WEB claim that (1) metabolism should scale proportionally to nutrient flow (or, equivalently, total fluid flow) in this circulatory system and (2) in order to minimize the energy dissipated in transport, the volume of fluid used to transport nutrients (i.e., blood volume) is a fixed fraction of body mass.[7]

They then proceed by analyzing the consequences of these two claims at the level of the smallest circulatory tubules (capillaries, alveoli, etc.). Experimentally, the volume contained in those smallest tubules is constant across a wide range of masses. Because fluid flow through a tubule is determined by the volume thereof, the total fluid flow is proportional to the total number of smallest tubules. Thus, if B denotes the basal metabolic rate, Q the total fluid flow, and N the number of minimal tubules,

${\displaystyle B\propto Q\propto N}$.

Circulatory systems do not grow by simply scaling proportionally larger; they become more deeply nested. The depth of nesting depends on the self-similarity exponents of the tubule dimensions, and the effects of that depth depend on how many "child" tubules each branching produces. Connecting these values to macroscopic quantities depends (very loosely) on a precise model of tubules. WEB show that, if the tubules are well-approximated by rigid cylinders, then, in order to prevent the fluid from "getting clogged" in small cylinders, the total fluid volume V satisfies

${\displaystyle N^{4}\propto V^{3}}$.[8]

Because blood volume is a fixed fraction of body mass,

${\displaystyle B\propto M^{\frac {3}{4}}}$.[7]

Non-power-law scaling

Closer analysis suggests that Kleiber's law does not hold over a wide variety of scales. Metabolic rates for smaller animals (birds under 10 kg [22 lb], or insects) typically fit to ​23 much better than ​34; for larger animals, the reverse holds.[6] As a result, log-log plots of metabolic rate versus body mass appear to "curve" upward, and fit better to quadratic models.[9] In all cases, local fits exhibit exponents in the [​23,​34] range.[10]

Modified circulatory models

Adjustments to the WBE model that retain assumptions of network shape predict larger scaling exponents, worsening the discrepancy with observed data.[11] But one can retain a similar theory by relaxing WBE's assumption of a nutrient transport network that is both fractal and circulatory.[10] (WBE argued that fractal circulatory networks would necessarily evolve to minimize energy used for transport, but other researchers argue that their derivation contains subtle errors.[6][12]) Different networks are less efficient, in that they exhibit a lower scaling exponent, but a metabolic rate determined by nutrient transport will always exhibit scaling between ​23 and ​34.[10] If larger metabolic rates are evolutionarily favored, then low-mass organisms will prefer to arrange their networks to scale as ​23, but large-mass organisms will prefer to arrange their networks as ​34, which produces the observed curvature.[13]

Modified thermodynamic models

An alternative model notes that metabolic rate does not solely serve to generate heat. Metabolic rate contributing solely to useful work should scale with power 1 (linearly), whereas metabolic rate contributing to heat generation should be limited by surface area and scale with power ​23. Basal metabolic rate is then the convex combination of these two effects: if the proportion of useful work is f, then the basal metabolic rate should scale as

${\displaystyle B=f\cdot kM+(1-f)\cdot k'M^{\frac {2}{3}}}$

where k and k are constants of proportionality. k in particular describes the surface area ratio of organisms and is approximately 0.1 ​kJhr·g-​23[4]; typical values for f are 15-20%.[14] The theoretical maximum value of f is 21%, because the efficiency of Glucose oxidation is only 42%, and half of the ATP so produced is wasted.[4]

Experimental support

Analyses of variance for a variety of physical variables suggest that although most variation in basal metabolic rate is determined by mass, additional variables with significant effects include body temperature and taxonomic order.[15][16]

A 1932 work by Brody calculated that the scaling was approximately 0.73.[5][17]

A 2004 analysis of field metabolic rates for mammals conclude that they appear to scale with exponent 0.749.[13]

Criticism of the law

Kozlowski and Konarzewski (hereafter "K&K") have argued that attempts to explain Kleiber's law via any sort of limiting factor is flawed, because metabolic rates vary by factors of 4-5 between rest and activity. Hence any limits that affect the scaling of basal metabolic rate would in fact make elevated metabolism — and hence all animal activity — impossible.[18] WEB conversely argue that animals may well optimize for minimal transport energy dissipation during rest, without abandoning the ability for less efficient function at other times.[19]

Other researchers have also noted that K&K's criticism of the law tends to focus on precise structural details of the WEB circulatory networks, but that the latter are not essential to the model.[8]

Kleiber's law only appears when studying animals as a whole; scaling exponents within taxonomic subgroupings differ substantially.[20][21]

Generalizations

Kleiber's law only applies to interspecific comparisons; it (usually) does not apply to intraspecific ones.[22]

In other kingdoms

A 1999 analysis concluded that biomass production in a given plant scaled with the ​34 power of the plant's mass during the plant's growth,[23] but a 2001 paper that included various types of unicellular photosynthetic organisms found scaling exponents intermediate between 0.75 and 1.00.[24]

A 2006 paper in Nature argued that the exponent of mass is close to 1 for plant seedlings, but that variation between species, phyla, and growth conditions overwhelm any "Kleiber's law"-like effects.[25]

Intra-organismal results

Because cell protoplasm appears to have constant density across a range of organism masses, a consequence of Kleiber's law is that, in larger species, less energy is available to each cell volume. Cells appear to cope with this difficulty via choosing one of the following two strategies: a slower cellular metabolic rate, or smaller cells. The latter strategy is exhibited by neurons and adipocytes; the former by every other type of cell.[26] As a result, different organs exhibit different allometric scalings (see table).[5]

Allometric scalings for BMR-vs.-mass in human tissue
Organ Scaling Exponent
Brain 0.7
Kidney 0.85
Liver 0.87
Heart 0.98
Muscle 1.0
Skeleton 1.1

References

1. ^ Kleiber M (October 1947). "Body size and metabolic rate". Physiological Reviews. 27 (4): 511–41. doi:10.1152/physrev.1947.27.4.511. PMID 20267758.
2. ^ Schmidt-Nielsen, Knut (1984). Scaling: Why is animal size so important?. NY, NY: Cambridge University Press. ISBN 978-0521266574.
3. ^ Kleiber M (1932). "Body size and metabolism". Hilgardia. 6 (11): 315–351. doi:10.3733/hilg.v06n11p315.
4. ^ a b c Ballesteros FJ, Martinez VJ, Luque B, Lacasa L, Valor E, Moya A (January 2018). "On the thermodynamic origin of metabolic scaling". Scientific Reports. 8 (1): 1448. Bibcode:2018NatSR...8.1448B. doi:10.1038/s41598-018-19853-6. PMC 5780499. PMID 29362491.
5. ^ a b c d Hulbert, A. J. (28 April 2014). "A Sceptics View: "Kleiber's Law" or the "3/4 Rule" is neither a Law nor a Rule but Rather an Empirical Approximation". Systems. 2 (2): 186–202. doi:10.3390/systems2020186.
6. ^ a b c Dodds PS, Rothman DH, Weitz JS (March 2001). "Re-examination of the "3/4-law" of metabolism". Journal of Theoretical Biology. 209 (1): 9–27. arXiv:physics/0007096. doi:10.1006/jtbi.2000.2238. PMID 11237567.
7. ^ a b West GB, Brown JH, Enquist BJ (April 1997). "A general model for the origin of allometric scaling laws in biology". Science. 276 (5309): 122–6. doi:10.1126/science.276.5309.122. PMID 9082983.
8. ^ a b Etienne RS, Apol ME, Olff HA (2006). "Demystifying the West, Brown & Enquist model of the allometry of metabolism". Functional Ecology. 20 (2): 394–399. doi:10.1111/j.1365-2435.2006.01136.x.
9. ^ Kolokotrones T, Deeds EJ, Fontana W (April 2010). "Curvature in metabolic scaling". Nature. 464 (7289): 753–6. Bibcode:2010Natur.464..753K. doi:10.1038/nature08920. PMID 20360740.
But note that a quadratic curve has undesirable theoretical implications; see MacKay NJ (July 2011). "Mass scale and curvature in metabolic scaling. Comment on: T. Kolokotrones et al., curvature in metabolic scaling, Nature 464 (2010) 753-756". Journal of Theoretical Biology. 280 (1): 194–6. doi:10.1016/j.jtbi.2011.02.011. PMID 21335012.
10. ^ a b c Banavar JR, Moses ME, Brown JH, Damuth J, Rinaldo A, Sibly RM, Maritan A (September 2010). "A general basis for quarter-power scaling in animals". Proceedings of the National Academy of Sciences of the United States of America. 107 (36): 15816–20. Bibcode:2010PNAS..10715816B. doi:10.1073/pnas.1009974107. PMC 2936637. PMID 20724663.
11. ^ Savage VM, Deeds EJ, Fontana W (September 2008). "Sizing up allometric scaling theory". PLoS Computational Biology. 4 (9): e1000171. doi:10.1371/journal.pcbi.1000171. PMC 2518954. PMID 18787686.
12. ^ Apol ME, Etienne RS, Olff H (2008). "Revisiting the evolutionary origin of allometric metabolic scaling in biology". Functional Ecology. 22 (6): 1070–1080. doi:10.1111/j.1365-2435.2008.01458.x.
13. ^ a b Savage VM, Gillooly JF, Woodruff WH, West GB, Allen AP, Enquist BJ, Brown JH (April 2004). "The predominance of quarter-power scaling in biology". Functional Ecology. 18 (2): 257–282. doi:10.1111/j.0269-8463.2004.00856.x. The original paper by West et al. (1997), which derives a model for the mammalian arterial system, predicts that smaller mammals should show consistent deviations in the direction of higher metabolic rates than expected from M34 scaling. Thus, metabolic scaling relationships are predicted to show a slight curvilinearity at the smallest size range.
14. ^ Zotin, A. I. (1990). Thermodynamic Bases of Biological Processes: Physiological Reactions and Adaptations. Walter de Gruyter. ISBN 9783110114010.
15. ^ Clarke A, Rothery P, Isaac NJ (May 2010). "Scaling of basal metabolic rate with body mass and temperature in mammals". The Journal of Animal Ecology. 79 (3): 610–9. doi:10.1111/j.1365-2656.2010.01672.x. PMID 20180875.
16. ^ Hayssen V, Lacy RC (1985). "Basal metabolic rates in mammals: taxonomic differences in the allometry of BMR and body mass". Comparative Biochemistry and Physiology. A, Comparative Physiology. 81 (4): 741–54. doi:10.1016/0300-9629(85)90904-1. PMID 2863065.
17. ^ Brody, S. (1945). Bioenergetics and Growth. NY, NY: Reinhold.
18. ^ Kozlowski J, Konarzewski M (2004). "Is West, Brown and Enquist's model of allometric scaling mathematically correct and biologically relevant?". Functional Ecology. 18 (2): 283–9. doi:10.1111/j.0269-8463.2004.00830.x.
19. ^ Brown JH, West GB, Enquist BJ (2005). "Yes, West, Brown and Enquist's model of allometric scaling is both mathematically correct and biologically relevant". Functional Ecology. 19 (4): 735–738. doi:10.1111/j.1365-2435.2005.01022.x.
20. ^ White CR, Blackburn TM, Seymour RS (October 2009). "Phylogenetically informed analysis of the allometry of Mammalian Basal metabolic rate supports neither geometric nor quarter-power scaling". Evolution; International Journal of Organic Evolution. 63 (10): 2658–67. doi:10.1111/j.1558-5646.2009.00747.x. PMID 19519636.
21. ^ Sieg AE, O'Connor MP, McNair JN, Grant BW, Agosta SJ, Dunham AE (November 2009). "Mammalian metabolic allometry: do intraspecific variation, phylogeny, and regression models matter?". The American Naturalist. 174 (5): 720–33. doi:10.1086/606023. PMID 19799501.
22. ^ Heusner, A. A. (1982-04-01). "Energy metabolism and body size I. Is the 0.75 mass exponent of Kleiber's equation a statistical artifact?". Respiration Physiology. 48 (1): 1–12. doi:10.1016/0034-5687(82)90046-9. ISSN 0034-5687. PMID 7111915.
23. ^ Enquist BJ, West GB, Charnov EL, Brown JH (28 October 1999). "Allometric scaling of production and life-history variation in vascular plants". Nature. 401 (6756): 907–911. doi:10.1038/44819. ISSN 1476-4687.
Corrigendum published 7 December 2000.
24. ^ Niklas KJ (2006). "A phyletic perspective on the allometry of plant biomass-partitioning patterns and functionally equivalent organ-categories". The New Phytologist. 171 (1): 27–40. doi:10.1111/j.1469-8137.2006.01760.x. PMID 16771980.
25. ^ Reich PB, Tjoelker MG, Machado JL, Oleksyn J (January 2006). "Universal scaling of respiratory metabolism, size and nitrogen in plants". Nature. 439 (7075): 457–61. Bibcode:2006Natur.439..457R. doi:10.1038/nature04282. PMID 16437113.
For a contrary view, see Enquist BJ, Allen AP, Brown JH, Gillooly JF, Kerkhoff AJ, Niklas KJ, Price CA, West GB (February 2007). "Biological scaling: does the exception prove the rule?" (PDF). Nature. 445 (7127): E9–10, discussion E10–1. doi:10.1038/nature05548. PMID 17268426. and associated responses.
26. ^ Savage VM, Allen AP, Brown JH, Gillooly JF, Herman AB, Woodruff WH, West GB (March 2007). "Scaling of number, size, and metabolic rate of cells with body size in mammals". Proceedings of the National Academy of Sciences of the United States of America. 104 (11): 4718–23. Bibcode:2007PNAS..104.4718S. doi:10.1073/pnas.0611235104. PMC 1838666. PMID 17360590.

Bacterivore

Bacterivores are free-living, generally heterotrophic organisms, exclusively microscopic, which obtain energy and nutrients primarily or entirely from the consumption of bacteria. Many species of amoeba are bacterivores, as well as other types of protozoans. Commonly, all species of bacteria will be prey, but spores of some species, such as Clostridium perfringens, will never be prey, because of their cellular attributes.

Copiotroph

A copiotroph is an organism found in environments rich in nutrients, particularly carbon. They are the opposite to oligotrophs, which survive in much lower carbon concentrations.

Copiotrophic organisms tend to grow in high organic substrate conditions. For example, copiotrophic organisms grow in Sewage lagoons. They grow in organic substrate conditions up to 100x higher than oligotrophs.

Decomposer

Decomposers are organisms that break down dead or decaying organisms, and in doing so, they carry out the natural process of decomposition. Like herbivores and predators, decomposers are heterotrophic, meaning that they use organic substrates to get their energy, carbon and nutrients for growth and development. While the terms decomposer and detritivore are often interchangeably used, detritivores must ingest and digest dead matter via internal processes while decomposers can directly absorb nutrients through chemical and biological processes hence breaking down matter without ingesting it. Thus, invertebrates such as earthworms, woodlice, and sea cucumbers are technically detritivores, not decomposers, since they must ingest nutrients and are unable to absorb them externally.

Dominance (ecology)

Ecological dominance is the degree to which a taxon is more numerous than its competitors in an ecological community, or makes up more of the biomass.

Most ecological communities are defined by their dominant species.

In many examples of wet woodland in western Europe, the dominant tree is alder (Alnus glutinosa).

In temperate bogs, the dominant vegetation is usually species of Sphagnum moss.

Tidal swamps in the tropics are usually dominated by species of mangrove (Rhizophoraceae)

Some sea floor communities are dominated by brittle stars.

Exposed rocky shorelines are dominated by sessile organisms such as barnacles and limpets.

Ecological threshold

Ecological threshold is the point at which a relatively small change or disturbance in external conditions causes a rapid change in an ecosystem. When an ecological threshold has been passed, the ecosystem may no longer be able to return to its state by means of its inherent resilience . Crossing an ecological threshold often leads to rapid change of ecosystem health. Ecological threshold represent a non-linearity of the responses in ecological or biological systems to pressures caused by human activities or natural processes.Critical load, tipping point and regime shift are examples of other closely related terms.

Feeding frenzy

In ecology, a feeding frenzy occurs when predators are overwhelmed by the amount of prey available. For example, a large school of fish can cause nearby sharks, such as the lemon shark, to enter into a feeding frenzy. This can cause the sharks to go wild, biting anything that moves, including each other or anything else within biting range. Another functional explanation for feeding frenzy is competition amongst predators. This term is most often used when referring to sharks or piranhas. It has also been used as a term within journalism.

Herbivore

A herbivore is an animal anatomically and physiologically adapted to eating plant material, for example foliage or marine algae, for the main component of its diet. As a result of their plant diet, herbivorous animals typically have mouthparts adapted to rasping or grinding. Horses and other herbivores have wide flat teeth that are adapted to grinding grass, tree bark, and other tough plant material.

A large percentage of herbivores have mutualistic gut flora that help them digest plant matter, which is more difficult to digest than animal prey. This flora is made up of cellulose-digesting protozoans or bacteria.

Jarman-Bell principle

The Jarman-Bell principle, coined by P.J Jarman (1968.) and R.H.V Bell (1971), is a concept in ecology offering a link between a herbivore's diet and their overall size. It operates by observing the allometric (non- linear scaling) properties of herbivores. According to the Jarman-Bell principle, the food quality of a herbivore's intake decreases as the size of the herbivore increases, but the amount of such food increases to counteract the low quality foods.Large herbivores can subsist on low quality food. Their gut size is larger than smaller herbivores. The increased size allows for better digestive efficiency, and thus allow viable consumption of low quality food. Small herbivores require more energy per unit of body mass compared to large herbivores. A smaller size, thus smaller gut size and lower efficiency, imply that these animals need to select high quality food to function. Their small gut limits the amount of space for food, so they eat low quantities of high quality diet. Some animals practice coprophagy, where they ingest fecal matter to recycle untapped/ undigested nutrients.However, the Jarman-Bell principle is not without exception. Small herbivorous members of mammals, birds and reptiles were observed to be inconsistent with the trend of small body mass being linked with high-quality food. There have also been disputes over the mechanism behind the Jarman-Bell principle; that larger body sizes does not increase digestive efficiency.The implications of larger herbivores ably subsisting on poor quality food compared smaller herbivores mean that the Jarman-Bell principle may contribute evidence for Cope's rule. Furthermore, the Jarman-Bell principle is also important by providing evidence for the ecological framework of "resource partitioning, competition, habitat use and species packing in environments" and has been applied in several studies.

Kleiber

Kleiber is a German surname. Notable people with the surname include:

Erich Kleiber (1890–1956), Austrian-German conductor

Max Kleiber (1893–1976), Swiss agricultural biologist, known for Kleiber's law

Carlos Kleiber (1930–2004), Austrian conductor

Günther Kleiber (born 1931), German communist politician

Stanislava Brezovar or Stanislava Kleiber (1937–2003), Slovenian ballerina

Jolán Kleiber-Kontsek (born 1939), Hungarian athlete

Dávid Kleiber (born 1990), Hungarian football player

Max Kleiber

Max Kleiber (4 January 1893 – 5 January 1976) was a Swiss agricultural biologist, born and educated in Zurich, Switzerland.

Kleiber 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.

Kleiber joined 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.

He is credited with the description of the ratio of metabolism to body mass, which became Kleiber's law.

Mesotrophic soil

Mesotrophic soils are soils with a moderate inherent fertility. An indicator of soil fertility is its base status, which is expressed as a ratio relating the major nutrient cations (calcium, magnesium, potassium and sodium) found there to the soil's clay percentage. This is commonly expressed in hundredths of a mole of cations per kilogram of clay, i.e. cmol (+) kg−1 clay.

Metabolic theory of ecology

The metabolic theory of ecology (MTE) is an extension of Kleiber's law and posits that the metabolic rate of organisms is the fundamental biological rate that governs most observed patterns in ecology. MTE is part of a larger set of theory known as metabolic scaling theory that attempts to provide a unified theory for the importance of metabolism in driving pattern and process in biology from the level of cells all the way to the biosphere.

MTE is based on an interpretation of the relationships between body size, body temperature, and metabolic rate across all organisms. Small-bodied organisms tend to have higher mass-specific metabolic rates than larger-bodied organisms. Furthermore, organisms that operate at warm temperatures through endothermy or by living in warm environments tend towards higher metabolic rates than organisms that operate at colder temperatures. This pattern is consistent from the unicellular level up to the level of the largest animals and plants on the planet.

In MTE, this relationship is considered to be the single constraint that defines biological processes at all levels of organization (from individual up to ecosystem level), and is a macroecological theory that aims to be universal in scope and application.

Mycotroph

A mycotroph is a plant that gets all or part of its carbon, water, or nutrient supply through symbiotic association with fungi. The term can refer to plants that engage in either of two distinct symbioses with fungi:

Many mycotrophs have a mutualistic association with fungi in any of several forms of mycorrhiza. The majority of plant species are mycotrophic in this sense. Examples include Burmanniaceae.

Some mycotrophs are parasitic upon fungi in an association known as myco-heterotrophy.

Organotroph

An organotroph is an organism that obtains hydrogen or electrons from organic substrates. This term is used in microbiology to classify and describe organisms based on how they obtain electrons for their respiration processes. Some organotrophs such as animals and many bacteria, are also heterotrophs. Organotrophs can be either anaerobic or aerobic.

Overpopulation

Overpopulation occurs when a species' population exceeds the carrying capacity of its ecological niche. It can result from an increase in births (fertility rate), a decline in the mortality rate, an increase in immigration, or an unsustainable biome and depletion of resources. When overpopulation occurs, individuals limit available resources to survive.

The change in number of individuals per unit area in a given locality is an important variable that has a significant impact on the entire ecosystem.

Planktivore

A planktivore is an aquatic organism that feeds on planktonic food, including zooplankton and phytoplankton.

Rate-of-living theory

The rate of living theory postulates that the faster an organism’s metabolism, the shorter its lifespan. The theory was originally created by Max Rubner in 1908 after his observation that larger animals outlived smaller ones, and that the larger animals had slower metabolisms. After its inception by Rubner, it was further expanded upon through the work of Raymond Pearl. Outlined in his book, The Rate of Living published in 1928, Pearl conducted a series of experiments in drosophilia and cantaloupe seeds that corroborated Rubner’s initial observation that a slowing of metabolism increased lifespan.

Further strength was given to these observations by the discovery of Max Kleiber’s law in 1932. Colloquially called the “mouse-to-elephant” curve, Kleiber’s conclusion was that basal metabolic rate could accurately be predicted by taking 3/4 the power of body weight. This conclusion was especially noteworthy because the inversion of its scaling exponent, between 0.2 and 0.33, was the scaling for lifespan and metabolic rate.

Recruitment (biology)

In biology, especially marine biology, recruitment occurs when a juvenile organism joins a population, whether by birth or immigration, usually at a stage whereby the organisms are settled and able to be detected by an observer.There are two types of recruitment: closed and open.In the study of fisheries, recruitment is "the number of fish surviving to enter the fishery or to some life history stage such as settlement or maturity".

Relative abundance distribution

In the field of ecology, the relative abundance distribution (RAD) or species abundance distribution describes the relationship between the number of species observed in a field study as a function of their observed abundance. The graphs obtained in this manner are typically fitted to a Zipf–Mandelbrot law, the exponent of which serves as an index of biodiversity in the ecosystem under study.

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