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PubMed2001

Allometry of mammalian cellular oxygen consumption.

In the 1930s, Max Kleiber and Samuel Brody established that the interspecies correlation between mammalian body mass and metabolic rate (alphaM(0.75)) cannot be explained (solely) by whole body surface area (alphaM(0.66)) to volume ratios. Metabolic considerations must also be taken into account. Decreases in the proportion of visceral organ mass to whole body mass can account for some of the whole body metabolic differences. However, superimposed upon these anatomical differences, the metabolism of tissues and cells has been demonstrated to decrease with increasing body mass. These decreases in oxygen consumption rates (with increasing body mass) in cells and tissues can be explained by a decrease in ATP turnover and mitochondrial density and an increase in mitochondrial functional efficiency (decrease in proton leak). The majority of the proton leak differences reflect differences in mitochondrial inner membrane surface area. Indeed, liver metabolism correlates directly with liver mitochondrial inner membrane surface area. Apart from being a significant contributor (approximately 25%) to basal metabolism, mitochondrial proton leak is a major factor determining the differences in basal metabolism between mammals of different body mass.

Adenosine Triphosphate↗
PubMed1997

Immobilization distorts allometry of rat femur: implications for disuse osteoporosis.

It is inherent to mammalian limb bones that they tend to maintain the same relative proportions of bone mass with changing body mass. This assumption seemed not to comply with experimental data on bone mineral content (BMC) and areal density (BMD) we have previously observed with immobilized rat femora. Using allometric scaling (BMC = aWEIGHTb), we showed in this study that a 3-week period of unilateral immobilization of the left hindlimb of 27 Spraque-Dawley male rats at the age of 13 weeks resulted in disproportionate scaling between femoral BMC and body weight (range: 430-937 g) during subsequent 32 weeks. The allometric exponents (b) were 0.76 (95% confidence interval: 0.64-0.88) for the immobilized left femur and 0.62 (0.51-0.73) for the right intact femur, both of which were in significant contrast to the value of 0.99 (0.90-1.08) observed in 36 free-living control rats (410-910 g). For BMD, the corresponding exponent values were 0.52 (0.44-0.60), 0.44 (0.36-0.52), and 0.67 (0. 61-0.73), the values being significantly different from each other also. We conclude that a short period of immobilization significantly distorts the normal allometric scaling relationships between the body weight and femoral BMC and BMD in growing male rats. The obvious adverse effect on peak bone mass suggests that an immobilization period during growth may condemn the given bone to a lifetime of relative fragility. Therefore, further consideration of this issue is warranted.

Animals↗
PubMed2005

Tree allometry and improved estimation of carbon stocks and balance in tropical forests.

Tropical forests hold large stores of carbon, yet uncertainty remains regarding their quantitative contribution to the global carbon cycle. One approach to quantifying carbon biomass stores consists in inferring changes from long-term forest inventory plots. Regression models are used to convert inventory data into an estimate of aboveground biomass (AGB). We provide a critical reassessment of the quality and the robustness of these models across tropical forest types, using a large dataset of 2,410 trees >or= 5 cm diameter, directly harvested in 27 study sites across the tropics. Proportional relationships between aboveground biomass and the product of wood density, trunk cross-sectional area, and total height are constructed. We also develop a regression model involving wood density and stem diameter only. Our models were tested for secondary and old-growth forests, for dry, moist and wet forests, for lowland and montane forests, and for mangrove forests. The most important predictors of AGB of a tree were, in decreasing order of importance, its trunk diameter, wood specific gravity, total height, and forest type (dry, moist, or wet). Overestimates prevailed, giving a bias of 0.5-6.5% when errors were averaged across all stands. Our regression models can be used reliably to predict aboveground tree biomass across a broad range of tropical forests. Because they are based on an unprecedented dataset, these models should improve the quality of tropical biomass estimates, and bring consensus about the contribution of the tropical forest biome and tropical deforestation to the global carbon cycle.

Biomass↗
PubMed1980

Rethinking allometry.

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Animal Population Groups↗
PubMed1989

Interaction of allometry and development in the mouse Mus musculus: heart rate and hematology.

The contribution of body mass changes to developmental adjustments in heart rate and hematology has been investigated in the mouse Mus musculus. Both resting heart rate (fH) and hematological variables including erythrocyte concentration, hemoglobin concentration, blood oxygen capacity, hematocrit, mean corpuscular hemoglobin and mean corpuscular volume, changed considerably during the increase in body mass from birth (1g) to adulthood (maximum of 50 g). There were two phases of change, one characteristic of preweaned mice (approximately less than 10 g) and the other of postweaned mice (approximately 10-50 g). In preweaned mice resting fH was about 1/2 of the value predicted on the basis of interspecific allometric data from mammals. fH increased steadily until body mass reached 10 g, then began to decrease with further mass increase at the same rate as predicted from interspecific allometric data. Erythrocyte concentration, hematocrit, hemoglobin concentration and blood oxygen capacity were all significantly lower in preweaned mice compared with postweaned mice. It is suggested that the progressive heart rate increase in very young mice may be to increase cardiac output to compensate for the neonatal anemia. After weaning, hematological variables showed little or no further change with increasing body mass. Collectively, these data indicate that during the early phases of postnatal growth, developmental factors other than body mass have the greatest influence on heart rate and hematology, and allometric data derived from interspecific studies on adults have little predictive value in neonates. After weaning, however, body mass is the major influence on these variables, and allometric data derived from interspecific studies on adults are reasonably accurate as predictors. We conclude that interspecific allometric studies must be properly regarded as the study of adult animals of different body sizes, and that untested assumptions about the applicability of these data to intraspecific studies of immature specimens should be made with extreme caution.

Animals↗
PubMed1989

Biochemical correlates of the structural allometry and site-specific properties of mammalian adipose tissue.

1. The maximum activities of the glycolytic enzymes hexokinase (HK) and phosphofructokinase (PFK) were measured in defatted homogenates of adipose tissue from nine homologous depots of 57 wild and captive mammals belonging to 17 species and eight orders and differing in body mass by six orders of magnitude. 2. Site-specific differences in the enzyme activities were similar in all terrestrial species and were not consistently related to adipocyte volume. 3. The specimen-mean maximum activities of HK and PFK did not correlate with body mass, body composition or natural diet. 4. When specimens of different body composition and body mass were compared, glycolytic enzyme activity per adipocyte was directly proportional to adipocyte volume. 5. Site-specific differences in collagen content of adipose tissue did not correspond to those adipocyte volume. When homologous depots of different specimens were compared, the collagen content of adipose tissue was directly proportional to body mass. 6. Adipose tissue of large cetaceans contains more collagen than predicted from the allometric equations fitted to the data from terrestrial mammals. 7. Neither the scaling of the collagen content with body mass nor the site-specific differences in its abundance are consistent with a role as protection or support for adjacent tissues. 8. There are consistent site-specific differences in the extracellular components of adipose tissue as well as in the structure and metabolism of the adipocytes. 9. Adipose tissue differs from most other tissues in that its maximum metabolic capacities do not scale to body mass. 10. Adjustment of the biochemical activity of adipose tissue to changes in body mass and body composition must depend upon neural and endocrine controls, not upon intrinsic differences in its metabolic capabilities.

Adipose Tissue↗
PubMed2004

The allometry and scaling of the size of vertebrate eyes.

We compiled data from the literature and colleagues to examine the relationship between eye axial length and body weight for vertebrates as well as birds, mammals, reptiles, and fishes independently. After fitting the data to logarithmic and semi-logarithmic models, we found that axial length of vertebrate eyes does obey a conventional logarithmic relationship with body weight rather than a semi-logarithmic relationship as suggested by the results of previous studies. The regression slopes and intercepts appear to be characteristic of various animal groups. The axial length of the eye is largest in birds and primates, smaller in other mammals (especially rodents) and reptiles, and widely varying in fishes.

Animals↗
PubMed2004

Allometry and scaling of wave aberration of eyes.

The scaling of root mean square (RMS) wave aberration in an isometrically growing eye is investigated, along with changes due to measurements made at different relative pupil sizes. It is found that, relative to an initial state, if an eye expands in all directions by the factor k, and the wave aberration is then measured at a relative pupil size which has changed over the pupil size used for the original measurement by a factor b, the new wave aberration will be increased or decreased by a factor kb(n), where n is the exponent relating RMS wave aberration, to pupil radius, r, in the equation: RMS=qr(n) in the initial eye. This implies that, if wave aberration is measured in a growing eye with a constant measurement pupil size, the measured RMS will decrease by the factor 1/k(n-1).

Eye↗
PubMed1998

Host cell allometry and regulation of the symbiosis between pea aphids, Acyrthosiphon pisum, and bacteria, Buchnera.

The symbiotic bacteria Buchnera in aphids are borne in cells, called bacteriocytes, in the insect haemocoel. The number and median volume of bacteriocytes in pre-reproductive adult insects varied significantly among 14 parthenogenetic clones of the pea aphid Acyrthosiphon pisum. After logarithmic transformation of the data, the relationship of both number and median volume of bacteriocytes with aphid weight for the clones could be described by common regression lines with slopes significantly greater than zero. The allometric slope for median bacteriocyte volume was calculated as 1.06, by model I regression and 1.94 by model II regression; and the equivalent values of the allometric slope for total volume of bacteriocytes were 1.51 and 2.50, suggesting that the total volume of bacteriocytes increases disproportionately with aphid body weight. The partial correlation coefficient between the number and median volume of bacteriocytes was +0.07, with body weight held constant. It is proposed that the regulation of number and size of bacteriocytes is not linked and that bacteriocytes may not exhibit compensatory changes in size, in response to alteration in number. Experimental manipulation of the rates of bacteriocyte differentiation and division could therefore perturb the total volume of the symbiosis, on which aphid pests depend for normal growth and reproduction.

Journal Article↗
PubMed1984

Determination of relative size: the "criterion of subtraction" problem in allometry.

By providing a predicted value against which to judge observed values, allometric equations are often used as a "criterion of subtraction" to calculate measurements corrected for the effects of overall size. The observed and predicted values have been used to calculate several different versions of a size-adjusted measurement; two of the more common being (observed/predicted) and (log observed-log predicted). Using data on brain size, tooth size, metabolic rate, and long bone shape, it is found that the manner in which the relative size value is calculated can alter interpretations and statistical results. Some of the assumptions underlying use of a criterion of subtraction calculated from empirical data are reviewed. It is suggested that predicted values determined from a priori theoretical equations often have several advantages over those from empirical equations.

Anatomy↗
PubMed1985

The relationship between growth and allometry.

The asymptotic allometric equations are derived by considering the relative growth of different physiological and anatomical quantities. The growth rate is assumed to be proportional to the value of the quantity, where the proportion coefficient depends on time. The allometric exponents are calculated for some organs of man and compared with the experimental values for primates. The exponents are generally time-dependent during the growth. The effect of the choice of the origin of time axis on the asymptotic allometric exponents is studied.

Biometry↗
PubMed1989

Fitting bent lines to data, with applications to allometry.

Change-point models, in which a linear or non-linear relation is generalized by allowing it to change at a point not fixed in advance, are of growing importance in allometric and other types of modeling. Frequently, the change-point is picked "by eye" and separate regressions are run for each resultant subdomain. This procedure is deficient, however, for the following reasons: first, a repeatable and objective procedure for estimating the change-point has not been used; second, the subsequent analysis usually does not take into account the fact that the change-point is estimated from the data; and last, the usually desirable requirement of continuity at the change-point is ignored. This paper describes various methods for jointly estimating linear relations and the intervening change-point from the data. In the simplest case, with normal errors and a linear relation of one variable upon another, this amounts to fitting a "bent line" via least squares techniques. In addition, tests and graphical diagnostics for the presence of change-points are presented. An example is given where a change-point and slopes are estimated for the relation of running speed with size among land mammals. In the past, these data have been fit with a straight line or a parabola. It is shown here that superior fit and interpretability are achieved using a change-point model.

Animals↗