Sizing Up Allometric Scaling Theory

Metabolic rate, heart rate, lifespan, and many other physiological properties vary with body mass in systematic and interrelated ways. Present empirical data suggest that these scaling relationships take the form of power laws with exponents that are simple multiples of one quarter. A compelling explanation of this observation was put forward a decade ago by West, Brown, and Enquist (WBE). Their framework elucidates the link between metabolic rate and body mass by focusing on the dynamics and structure of resource distribution networks—the cardiovascular system in the case of mammals. Within this framework the WBE model is based on eight assumptions from which it derives the well-known observed scaling exponent of 3/4. In this paper we clarify that this result only holds in the limit of infinite network size (body mass) and that the actual exponent predicted by the model depends on the sizes of the organisms being studied. Failure to clarify and to explore the nature of this approximation has led to debates about the WBE model that were at cross purposes. We compute analytical expressions for the finite-size corrections to the 3/4 exponent, resulting in a spectrum of scaling exponents as a function of absolute network size. When accounting for these corrections over a size range spanning the eight orders of magnitude observed in mammals, the WBE model predicts a scaling exponent of 0.81, seemingly at odds with data. We then proceed to study the sensitivity of the scaling exponent with respect to variations in several assumptions that underlie the WBE model, always in the context of finite-size corrections. Here too, the trends we derive from the model seem at odds with trends detectable in empirical data. Our work illustrates the utility of the WBE framework in reasoning about allometric scaling, while at the same time suggesting that the current canonical model may need amendments to bring its predictions fully in line with available datasets

Consistency in approximate entropy given by a volumetric estimate

Non-linear methods for estimating variability in time-series are currently of widespread use. Among such methods are approximate entropy (ApEn) and sample approximate entropy (SampEn). The applicability of ApEn and SampEn in analyzing data is evident and their use is increasing. However, consistency is a point of concern in these tools, i.e., the classification of the temporal organization of a data set might indicate a relative less ordered series in relation to another when the opposite is true. As highlighted by their proponents themselves, ApEn and SampEn might present incorrect results due to this lack of consistency. In this study, we present a method which gains consistency by using ApEn repeatedly in a wide range of combinations of window lengths and matching error tolerance. The tool is called volumetric approximate entropy, vApEn. We analyze nine artificially generated prototypical time-series with different degrees of temporal order (combinations of sine waves, logistic maps with different control parameter values, random noises). While ApEn/SampEn clearly fail to consistently identify the temporal order of the sequences, vApEn correctly do. In order to validate the tool we performed shuffled and surrogate data analysis. Statistical analysis confirmed the consistency of the method. (C) 2008 Elsevier Ltd. All rights reserved.FAPESP[06/02120-0]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP[06/02377-0]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP[06/02176-5]FAPESP[06/05490-2]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP[06/02171-3]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP[06/01955-0]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Moving towards acceleration for estimates of activity-specific metabolic rate in free-living animals: The case of the cormorant

1. Time and energy are key currencies in animal ecology, and judicious management of these is a primary focus for natural selection. At present, however, there are only two main methods for estimation of rate of energy expenditure in the field, heart rate and doubly labelled water, both of which have been used with success; but both also have their limitations. 2. The deployment of data loggers that measure acceleration is emerging as a powerful tool for quantifying the behaviour of free-living animals. Given that animal movement requires the use of energy, the accelerometry technique potentially has application in the quantification of rate of energy expenditure during activity. 3. In the present study, we test the hypothesis that acceleration can serve as a proxy for rate of energy expenditure in free-living animals. We measured rate of energy expenditure as rates of O2 consumption (√O2 ) and CO2 production (√CO2 ) in great cormorants (Phalacrocorax carbo) at rest and during pedestrian exercise. √O2 and √CO2 were then related to overall dynamic body acceleration (ODBA) measured with an externally attached three-axis accelerometer. 4. Both √O2 and √CO2 were significantly positively associated with ODBA in great cormorants. This suggests that accelerometric measurements of ODBA can be used to estimate √O2 and √CO2 and, with some additional assumptions regarding metabolic substrate use and the energy equivalence of O2 and CO2, that ODBA can be used to estimate the activity specific rate of energy expenditure of free-living cormorants. 5. To verify that the approach identifies expected trends in √O2 from situations with variable power requirements, we measured ODBA in free-living imperial cormorants (Phalacrocorax atriceps) during foraging trips. We compared ODBA during return and outward foraging flights, when birds are expected to be laden and not laden with captured fish, respectively. We also examined changes in ODBA during the descent phase of diving, when power requirements are predicted to decrease with depth due to changes in buoyancy associated with compression of plumage and respiratory air. 6. In free-living imperial cormorants, ODBA, and hence estimated √O2, was higher during the return flight of a foraging bout, and decreased with depth during the descent phase of a dive, supporting the use of accelerometry for the determination of activity-specific rate of energy expenditure.Fil: Wilson, Rory P.. Swansea University; Reino UnidoFil: White, Craig R.. University of Birmingham. School of Biosciences. Centre for Ornithology; Reino UnidoFil: Quintana, Flavio Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Centro Nacional Patagónico; ArgentinaFil: Halsey, Lewis G.. University of Birmingham. School of Biosciences. Centre for Ornithology; Reino UnidoFil: Liebsch, Nikolai. Swansea University; Reino UnidoFil: Martin, Graham R.. University of Birmingham. School of Biosciences. Centre for Ornithology; Reino UnidoFil: Butler, Patrick. University of Birmingham. School of Biosciences. Centre for Ornithology; Reino Unid

Determinants of inter-specific variation in basal metabolic rate

Basal metabolic rate (BMR) is the rate of metabolism of a resting, postabsorptive, non-reproductive, adult bird or mammal, measured during the inactive circadian phase at a thermoneutral temperature. BMR is one of the most widely measured physiological traits, and data are available for over 1,200 species. With data available for such a wide range of species, BMR is a benchmark measurement in ecological and evolutionary physiology, and is often used as a reference against which other levels of metabolism are compared. Implicit in such comparisons is the assumption that BMR is invariant for a given species and that it therefore represents a stable point of comparison. However, BMR shows substantial variation between individuals, populations and species. Investigation of the ultimate (evolutionary) explanations for these differences remains an active area of inquiry, and explanation of size-related trends remains a contentious area. Whereas explanations for the scaling of BMR are generally mechanistic and claim ties to the first principles of chemistry and physics, investigations of mass-independent variation typically take an evolutionary perspective and have demonstrated that BMR is ultimately linked with a range of extrinsic variables including diet, habitat temperature, and net primary productivity. Here we review explanations for size-related and mass-independent variation in the BMR of animals, and suggest ways that the various explanations can be evaluated and integrated