Metabolic theory of ecology

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Metabolic rate may relate to organismal temperature and dimensions

The metabolic theory of ecology is a theory that claims to explain the relationships between body mass and metabolic rate in organisms from unicellular microbes to plants and animals over 27 orders of magnitude, based on the physics and geometry of supply networks. The theory was developed by researchers at the Santa Fe Institute, including ecologists James Brown, Brian Enquist, Jamie Gillooly and Andrew Allen, and physicist Geoffrey West and Van Savage. This theory aims to explain the relationship between

metabolic rate and
the body size and temperature of animals, plants, and microbes.

The theory is actually not a theory of ecology but an application of Kleiber's Law, relating body mass to metabolic rate, that has been extrapolated to cover the mass of ecological systems. West, Brown, and Enquist hypothesized that the metabolic rate value for many biological allometries arises from the geometry of vascular networks and resource-exchange surfaces (e.g., cardiovascular or plant vascular systems). They are adamant about these values being related to geometry. The core assumption of this theory is that many organismic, anatomical, and physiological traits are linked mechanistically by how the geometry of vascular networks vary with the size of the organism. The WBE assert the equation applies over 27 orders of magnitude for living systems. When the organism is the size of a cell or a phage, the authors of the theory do not say how capillarity fits in. Gillooly et al. have elaborated upon the mathematics to include a term for temperature to model the affects of temperature on metabolism and growth. A key problem with the equation is its use by those who are not rigorously exclusive about what qualifies as metabolism^{[citation needed]}.

The theory (called metabolic scaling theory by some), involves numerous points of contention amongst life scientists. For example, some say complicated phenomena like those in ecology or biology require likewise complicated explanations, especially things like metabolism. Others, presumably including supporters of metabolic scaling theories of ecology, say a simpler explanation is not only possible, but preferable. Key problems include whether thermogenesis should be considered part of metabolism, what the affects of the organism's mass has on the metabolic rate of its basal constituents, and what the effects are on basal metabolic rate (BMR) of removing a cell from in vivo circumstances to in vitro ones^{[citation needed]}.

Simplification of the theory is introduced by the term metabolic efficiency (ME) to the exponent of biomass. This is done by Dr. Lloyd Demetrius of Harvard in attempts to understand the affects of caloric restriction on the longevity of mice [2004], in terms of changes in metabolic rates. ME is a ratio of rate of reduction reactions (in amperes) to rate of oxidation reactions (also in amperes), or a statement of the efficiency of redox coupling between an organism and the energy around it, usually available as food. Since every chemical reaction either takes energy or gives it off, the term ME gages the net balance at any particular moment. Metabolic rate is then expressed in watts, and is essentially the recharge rate at which the biomass is functioning at that moment. Redox coupling not only excludes thermogenesis as a metabolic consideration, but also introduces electrochemistry to considerations of biomass and MR. The longevity of the organism is dependent upon this recharge rate, and variations in ME are associated with perturbations in MR associated with growth and replication the way food availability is associated with reproductive strategies.

1 Implications of the theory
2 An alternative to the theory?
3 References
4 See also

[edit] Implications of the theory

The theory is alleged by some to have two notable implications, neither of which is supported by the very mathematics (Kleiber's Law) that the theory is based upon, but instead rests upon assumptions^{[citation needed]}. First, even a modest rise in the average temperature of Earth's atmosphere and oceans might increase the rate of metabolism of affected organisms. Metabolic rate, according to the mathematics of the theory, is related to the mass of the organism(s), and its ME, not its temperature. The importation of temperature considerations to the theory to justify this one of its implications is highly questionable^{[citation needed]}. Increased average temperatures may also reduce population densities. The reason for this is that if metabolic rate increases, resource consumption might rise, as well. This is a big 'if' given that the relation between temperature and metabolic rate is unarticulated. When consumption of a finite set of resources in an environment—in this case, planet Earth—rises, that environment becomes less capable of supporting the same population densities.

The second implication is, when Earth becomes warmer, pathogens and parasites on the planet may evolve and reproduce more rapidly, making it more difficult for humans and other animals to remain free of disease^{[citation needed]}. This is a completely fabricated implication, one that suggests that humans and other animals may be part of ecology, but parasites and microbes are not. The metabolic theory of ecology remains highly controversial in view of its incompleteness, lack of consistency, deviation from the math, and questionable relevance to nature^{[citation needed]}. To understand these criticisms, see below with regard to the math and the term for metabolic efficiency (ME), the ratio of the efficiency of redox coupling between an organism and an energy supply.

[edit] An alternative to the theory?

Metabolic scaling theory has been a source of disputation amongst life scientists. Its gain in acceptance has not been matched by corresponding increases in relevance at the field level where data is gathered^{[citation needed]}. Its triumph has been catechetical so far. The presumptions of the theory have not resulted in a single testable prediction or deductive inference from the math^{[citation needed]}. Criticisms of WBE stem in part from misconceptions regarding the scope and applicability of the model’s assumptions governing the role of network geometry, of temperature, and of additional factors/assumptions not specified in the core of the model. These misconceptions are fostered by the overriding presumptions of the WBE model that give primacy to geometry^{[citation needed]}. Scaling exponents in the WBE model originate from the geometry of the vascular network. When the vascular network is space-filling and minimizes transport times and or energy dissipation then the exponent should be 3/4. However, deviation from the 3/4 relationship is expected if the network is not space filling or minimizes energy. Building on the original model of WBE, Enquist et al. (2007) shows exponents of 1, for example, are even possible in small plants, where the branching geometry is not space-filling. As detailed by Price et al. (2007) the WBE model makes specific predictions for: (i) the origin of several allometric scaling exponents and how the specific value of these exponents is due to the geometry of the vascular network; and (ii) how covariation between allometric traits is related to the geometry of the network.

For example, these debates included:

Jan Kozlowski of the Jagiellonian University is a main developer of an alternative theory that relates metabolic rate to cell dimensions and amount of DNA^{[citation needed]}. But it is unclear if this correlative model, that lacks the firm mathematical footing of Kleiber, can actually account for the patterns allegedly covered by the theory of West, Brown, and Enquist (WBE) .

Lloyd Demetrius's mathematical refinement takes as the exponent of mass (4ME - 1)/4ME, where ME or metabolic efficiency. Demetrius implies that the version favored by West et al., where the exponent is 3/4, does not describe efficiency, but assumes it. The numerator of the ratio ME is the rate, in amperes, of all reduction reactions involving such disparate things as ATP synthesis, glycogenesis, anaerobic protein synthesis, things which apply to behavior, growth, and replication.

Demetrius's claims his work supports the conclusions of others that despite the alleged role of fractality, and increasing nutrient delivery to the cell, either the equation must be given up as irrelevant to biology, or else it must restrict itself to consideration of the efficiency of redox coupling, and has nothing to do with the Euclidean geometry of capillary branching or fluid dynamics. Enquist et al.[2007], purports to show how efficiency can easily be detailed in the original WBE model.

WBE and Savage [PNAS, 2007] claim that the field metabolic rate (FMR) of an organism is the product of the average basal metabolic rate of its cells, and the number of cells. FMR includes but is not limited to BMR, and includes the metabolism necessary for motor behavior. The implication is that the nature of the organization of the cells has no affect on the metabolic rate or ME of the organism. WBE & Savage [PNAS, 2007] relate the mass of the organism to affects on basal metabolic rate when the equation, according to Demetrius, shows the two are unrelated by mass, but are related by ME, with the ME of the organism being the same as it is for the cells of that organism.

Jan Kozlowski and colleagues in addition to Chaui-Berlinck have made the serious claim that the original WBE model is mathematically flawed. However, West, Brown, Enquist and colleagues have argued that their critics are incorrect in their original statements (see Brown et al. 2005 and Savage et al. 2007).

Another prominent alternative has been proposed by Charles Darveau (Now at University of Ottawa) and colleagues, that postulates that the 0.75 scaling exponent arises as an organismal sum of varying scaling exponents of biochemical and other processes. However, their approach has been shown to be mathematically incorrect (West et al. 2003). The empirical foundations of Darveau's argument (originally proposed as evidence against metabolic theory) has been shown by Gillooly and Allen (2007) to be entirely consistent with WBE metabolic scaling theory, though Gillooly and Allen and West simultaneously assert Darveau's criticism is based upon flawed math.

[edit] References

Brown, J. H., West, G. B., & B. J. Enquist (2005) Yes, West, Brown and Enquist's model of allometric scaling is both mathematically correct and biologically relevant. Functional Ecology 19:735-738.
Chaui-Berlinck, J. G. (2006) A critical understanding of the fractal model of metabolic scaling. Journal of Experimental Biology 209:3045-3054.
Darveau, C. A., Suarez, R. K., Andrews, R. D., & Hochachka, P. W. (2002) Allometric cascade as a unifying principle of body mass effects on metabolism Nature417:166-170.
Enquist, B.J., Kerkhkoff, A.J., Stark, S.C., Swenson, N.G., McCarthy, M.C. and C.A. Price (2007)). A general integrative model for scaling plant growth and functional trait spectra "Nature" (In Press).
Gillooly, J. F. and A. P. Allen. (2007). Changes in body temperature influence the scaling of VO_2_max and aerobic scope in mammals. "Biology Letters", 3: 99-102.
Kozlowski, J. & Konarzewski, M. (2004) Is West, Brown and Enquist's model of allometric scaling mathematically correct and biologically relevant? Functional Ecology 18:283-289.
Kozlowski, J. & Konarzewski, M. & Gawelczyk, A. T. (2003) Cell size as a link between noncoding DNA and metabolic rate scaling. Proc Natl Acad Sci U S A 100:14080-14085.
Makarieva, A. M., V. G. Gorshkov, & B. L. Li. (2005) Revising the distributive networks models of West, Brown and Enquist (1997) and Banavar, Maritan and Rinaldo (1999): Metabolic inequity of living tissues provides clues for the observed allometric scaling rules. Journal of Theoretical Biology 237:291-301.
Makarieva, A. M., V. G. Gorshkov, & B. L. Li. (2005) Biochemical universality of living matter and its metabolic implications. Functional Ecology 19:547-557.
Price, C.P., Enquist, B.J. & V. M. Savage (2007) A general model for allometric covariation in botanical form and function. PNAS 104:13204-13209.
Robinson, D. Biology's Big Idea. "Nature" 444:272.
Savage, V.M., Enquist, B.J. & G.B. Weset (2007) Comment on Chaui-Berlinck (2006) A Critical understanding of the fractal model of metabolic scaling. Journal of Experimental Biology. 209:3045-3054. "Journal of Experimental Biology" (In Press).

West, G. B., Brown, J. H. & B. J.Enquist (1997) A general model for the origin of allometric scaling laws in biology. Science 276:122-126.
West, G.B., Savage, V.M., Gillooly, J., Enquist, B.J., Woodruff, W.H. & J.H. Brown (2007) Response to Darveau et al.: Why does metabolic rate scale with body size? "Nature" 421:713.
Whitfield, J. (2001) All creatures great and small. Nature 413:342-344.
Whitfield, J. (2004). Ecology's big, hot idea. PLoS Biol 2(12):e440.
Whitfield, J. (2006). In the Beat of a Heart: Life, energy, and the unity of nature. The National Academies Press, New York.