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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↗
PubMed1987

Allometry of red cell oxygen binding and hematology in larvae of the salamander, Ambystoma tigrinum.

Very few studies have attempted to relate blood characteristics to body mass within, rather than between, species. Thus, respiratory and hematological properties of the blood of larval tiger salamanders (Ambystoma tigrinum) have been measured in animals ranging in body mass from approximately 2 to 112 g. This amphibian species was chosen because larvae of very different body mass may be of similar developmental stage, minimizing interference from ontogenetic factors. Mean corpuscular volume, mean corpuscular Hb, hematocrit, blood Hb concentration, blood O2 capacity and Hill's n were all positively correlated with body mass (P less than 0.005). Blood O2 affinity (P50) and Bohr shift were not significantly correlated with body mass (P greater than 0.20). The findings are discussed in the context of the general effect of body mass upon metabolic rate in vertebrates, as well as environmental and biological factors specific to larvae of the tiger salamander.

Animals↗
PubMed2001

Heart biometry and allometry in rats submitted to nitric oxide synthesis blockade and treatment with antihypertensive drugs.

Fifty mature male rats were separated into groups of ten rats each (control, L-NAME, spironolactone, enalapril and verapamil). On the 41st day of experimentation, animals were anesthetized, weighed and sacrificed. The tail blood pressure (TBP) was 76% higher in L-NAME group than in the control group. Spironolactone, enalapril and verapamil were efficient in reducing TBP in those respective groups of rats (spironolactone was less efficient in reducing TBP). The heart mass/body mass ratio (HBR) increased 24% in L-NAME group and spironolactone group. No differences in HBR were found when control animals and animals treated with enalapril and verapamil were compared. Heart volume (HV) was greater in L-NAME group than other groups, but it was not different comparing the L-NAME and the spironolactone groups. The left ventricle was responsible for the changes in the HV. The relationship between the HV and the body mass (BM) was not significant in the groups L-NAME and spironolactone. However, this relationship was significant and allometric in control, enalapril and verapamil groups. In control group, HV had a positive allometric tendency against the BM, but in the enalapril and verapamil groups this tendency was allometrically negative. Cardiac hypertrophy in rats under inhibition of NO synthesis was prevented by treatment with enalapril and verapamil more efficiently than spironolactone.

Animals↗
PubMed2001

Allometry and biomass of Korean pine (Pinus koraiensis) in central Korea.

Aboveground tree biomass of Korean pine (Pinus koraiensis Sieb. et Zucc.) was determined for a natural forest of Korean pine and mixed deciduous trees and seven age classes of plantation forests in central Korea. Regression analyses of the dry weights of stem wood, stem bark, branches, and needles versus diameter at breast height were used to calculate regression equations of the form of log Y = a + b log X. Biomass of Korean pine in the mixed forest was 118 Mg ha(-1), and biomass in the plantations was linearly related to stand age, ranging from 52.3 Mg ha(-1) in 11 to 20-year-old stands to 317.9 Mg ha(-1) in 71 to 80-year-old stands. The proportions of stem wood and stem bark in the total aboveground biomass decreased with stand age while those of branch and needle increased. Specific leaf area of Korean pine ranging from 35.2 to 52.1 cm2 g(-1) was significantly different among crown positions and needle ages; in general, lower crown position and current needles had the greatest surface area per unit dry weight.

Biomass↗
PubMed2001

Re-evaluation of the allometry of wet thermal conductance for birds.

Wet thermal conductance is an important thermoregulatory parameter for birds and mammals. It is generally calculated as C(wet) (ml O2 g(-1) h(-1) degrees C(-1)) = VO2/(T(b)-T(a)), where VO2 is metabolic rate measured in ml O2 g(-1) h(-1), T(b) is body and T(a) is ambient temperature measured in degrees C. Minimum C(wet) is measured at T(a) at or below the lower critical temperature (T(lc)) of the thermoneutral zone, and is strongly influenced by time of day (rest or activity phase) and body mass [J. Aschoff, Comp. Biochem. Physiol. 69A (1981) 611]. Allometric analyses indicate differences in C(wet) for passerine and non-passerine birds, in their rest and active phases (Aschoff, 1981). The allometric slope for non-passerine rest-phase (-0.583) is lower than that for non-passerine active-phase (-0.484), and passerine rest-phase (-0.461) and active-phase (-0.463), although none of these slopes are significantly different. This different-sloped relationship for non-passerine rest-phase C(wet) extrapolates to lower-than-expected values at high body mass, and so this allometric relationship may be inappropriate for predictive purposes. Consequently, we have reanalysed Aschoff's (1981) data, as well as more recent compilations, to determine a more useful allometric relationship for C(wet) of non-passerine rest-phase birds. Re-analyses of minimum thermal conductance data from Drent and Stonehouse [Comp. Biochem. Physiol. 40A (1971) 689], Aschoff (1981) and Gavrilov and Dolnik [Acta XVIII Congressus Internationalis Ornithologici Moscow (1982) 421] indicate that the most appropriate regressions for predicting C(wet) (ml O2 g(-1) h(-1) degrees C(-1)) of birds from body mass (M; g) are the pooled regressions for non-passerine and passerine birds, in the active (alpha) and resting (rho) phases, using data tabulated by Aschoff (1981): alpha, C(wet)=0.994M(-0.509); rho, C(wet)=0.702M(-0.519). C(wet) is approximately 40% higher in the active phase than the rest phase. Regressions of various data sets for C(wet) of birds and mammals indicate a similar slope of approximately -0.5 for the allometric relationship, but significantly higher elevations for mammals compared to birds. The approximately 50% higher C(wet) for mammals than birds indicates a better physical insulation for birds than mammals of the same body mass. The general scaling of C(wet) with M(-0.5) indicates that (T(b)-T(lc)) should scale with M(0.22), if mass-specific metabolic rate scales with M(-0.28) [Reynolds and Lee, Am. Nat. 147 (1996) 735]. The observed scaling for (T(b)-T(lc)) of M(0.183) (calculated from Gavrilov and Dolnik, 1985) is consistent with this expectation.

Animals↗
PubMed2003

Intraspecific allometry of standard metabolic rate in green iguanas, Iguana iguana.

To study the allometric relationship between standard metabolic rate and body mass (mass range 16-3627 g) in green iguanas, Iguana iguana (n=32), we measured rates of oxygen consumption (V(O(2))) at 30 degrees C during scotophase. The relationship could be described as: V(O(2))(ml h(-1))=0.478W(0.734). The resulting mass exponent was similar to the 3/4 power commonly used in interspecific curves (P>0.05), but differed from a proposed intraspecific value of 2/3 (P<0.05). The mass exponents of male (n=8) and female (n=11) iguanas did not differ (P>0.05). The mass adjusted V(O(2)) was higher than predicted from generalized squamate curves. The mean mass exponent of intra-individual allometric equations of iguanas (n=7) at varying masses during ontogeny did not differ from that of the pooled equation, indicating that scaling of V(O(2)) is similar for both between and within individuals. Thermal acclimation, compensatory changes in V(O(2)) with prolonged exposure to a constant temperature, was not observed in juvenile iguanas (n=11) between 1 and 5 weeks of acclimation at 30 degrees C.

Acclimatization↗
PubMed2003

Morphometry and allometry of the postnatal lung development in the quokka wallaby (Setonix brachyurus): a light microscopic study.

The postnatally developing lungs of the quokka wallaby, Setonix brachyurus, were investigated macroscopically and by light microscopic morphometry. Lung, parenchymal and non-parenchymal volumes as well as the components of the latter two were analysed by regression analysis. The lungs comprised a single undivided left lung and a right lung with an adherent accessory lobe. Septal tissue growth was most remarkable in the canalicular and saccular stages. Between mid-canalicular stage and the saccular stage, the lung volume increased 2-fold, mainly due to airspace expansion, coupled with septal tissue thinning. The non-parenchymal vascular volume increase accelerated in the successive developmental stages while the airway and connective tissue volumes progressed in a decreasing order, being highest in the canalicular and saccular stages and lowest in the alveolar stage. Growth and remodelling of the alveolar septa occurred simultaneously with airspace subdivision. Airspace expansion accelerated during the stage of microvascular maturation, when most other parameters showed the least rate of increase.

Animals↗
PubMed2003

Morphometry and allometry of the postnatal marsupial lung development: an ultrastructural study.

An utrastructural morphometric study of the postnatally remodelling lungs of the quokka wallaby (Setonix brachyurus) was undertaken. Allometric scaling of the volumes of the parenchymal components against body mass was performed. Most parameters showed a positive correlation with body mass in all the developmental stages, except the volume of type II pneumocytes during the alveolar stage. The interstitial tissue and type II cell volumes increased slightly faster than body mass in the saccular stage, their growth rates declining in the alveolar stage. Conversely, type I pneumocyte volumes increased markedly in both the saccular and alveolar stages. Both capillary and endothelial volumes as well as the capillary and airspace surface areas showed highest rates of increase during the alveolar stage, at which time the rate was notably higher than that of the body mass. The pulmonary diffusion capacity increased gradually, the rate being highest in the alveolar stage and the adult values attained were comparable to those of eutherians.

Aging↗
PubMed1996

Allometry and simple epidemic models for microparasites.

Simple mathematical models for microparasites offer a useful way to examine the population dynamics of different viral and bacterial pathogens. One constraint in applying these models in free-living host populations is the paucity of data with which to estimate transmission rates. Here we recast a standard epidemiological model by setting the birth and death rates of the host population and its density as simple allometric functions of host body weight. We then use standard threshold theorems for the model in order to estimate the minimum rate of transmission for the parasite to establish itself in a mammalian host population. Transmission rates that produce different comparable values of the parasites' basic reproductive number, RO, are themselves allometric functions of host body size. We have extended the model to show that hosts having different body sizes suffer epidemic outbreaks whose frequency scales with body size. The expected epidemic periods for pathogens in different mammalian populations correspond to cycles observed in free-living populations.

Animals↗
PubMed2005

Evolution through genetically controlled allometry space.

Understanding evolutionary change requires phenotypic differences between organisms to be placed in a genetic context. However, there are few cases where it has been possible to define an appropriate genotypic space for a range of species. Here we address this problem by defining a genetically controlled space that captures variation in shape and size between closely related species of Antirrhinum. The axes of the space are based on an allometric model of leaves from an F2 of an interspecific cross between Antirrhinum majus and Antirrhinum charidemi. Three principal components were found to capture most of the genetic variation in shape and size, allowing a three-dimensional allometric space to be defined. The contribution of individual genetic loci was determined from QTL analysis, allowing each locus to be represented as a vector in the allometric space. Leaf shapes and sizes of 18 different Antirrhinum taxa, encompassing a broad range of leaf morphologies, could be accurately represented as clouds within the space. Most taxa overlapped with, or were near to, at least one other species in the space, so that together they defined a largely interconnected domain of viable forms. It is likely that the pattern of evolution within this domain reflects a combination of directional selection and evolutionary tradeoffs within a high dimensional space.

Antirrhinum↗
PubMed1984

Snail shape and growth rates: Evidence for plastic shell allometry in Littorina littorea.

The periwinkle Littorina littorea exhibits morphological variation among southern New England populations that appear to be genetically continuous. In dense populations, individuals have relatively elongate shells in comparison to individuals in sparse populations, which have rounder, globose shells. We experimentally demonstrate that this shell variation is a function of snail growth rate. Rapidly growing snails develop thin, globose shells that accommodate more body mass than thicker, more elongate shells. The implications of these results are discussed in relation to interpreting morphological variation in extant gastropods and in the molluscan fossil record.

Journal Article↗
PubMedDate not supplied

Short-term pharmacologically induced growth study of ontogenetic allometry of oxygen uptake in children.

BACKGROUND: A range of allometric coefficients have been proposed in describing the maximal oxygen uptake (VO2max): body mass relation in children using weight-bearing ergometry. However, a wide deviation in the allometric coefficients for VO2max may be apparent when selected pediatric cohorts are studied in conjunction with clinical intervention for growth abnormalities. AIM: The purpose of this study was to determine the allometric coefficients for VO2max after short-term pharmacologically induced growth in pre- and early pubescent children. SUBJECTS AND METHODS: The treatment group consisted of nine subjects with non-growth hormone (GH)-deficient short stature and one with GH-deficient short stature (mean age: 13.7+/-1.7 years). Ten pre- and early pubescent children matched for age, height, weight, VO2max and body mass index (BMI) were controls. The treatment group were evaluated before (Pre-GH) and after (Post-GH) 4 months of subcutaneous GH therapy (0.05 mgkg(-1)day(-1) x 6 days week(-1)). RESULTS: The mean ontogenetic coefficient for the treatment group was 1.50+/-0.20 and for the control group was 0.77+/-0.34. The mean allometric coefficient for body mass relative to VO2max was significantly higher in the treatment group compared with the control group (p<0.05). Height, weight, fat free mass (FFM), VO2max indexed to body mass (mLkg(-1)min(-1)) and FFM (mLkgFFM(-1)min(-1)) increased (p<0.05) with GH therapy. GH therapy also increased insulin-like growth factor-I (IGF-I) and served as a biochemical marker of GH therapy (p<0.05). The control group had no significant differences in all the variables tested (p<0.05). CONCLUSION: The scaling for oxygen uptake (VO2) for body mass varies with GH treatment and the increase in VO2max that commonly occurs in conjunction with physical growth in the pre-and early pubescent individual may be linked to an increase in FFM and linear size.

Adolescent↗
PubMedDate not supplied

Subspecies and body size allometry affect milk production and composition, and calf growth in red deer: comparison of Cervus elaphus hispanicus and Cervus elaphus scoticus.

Studies comparing lactation in wild mammals have shown that maternal weight scales with offspring weight, milk production, or its energy. However, no study appears to have scaled milk composition with maternal or offspring weight. Although diet affects milk composition and production, their effects in biological studies have almost never seemed to be controlled. In this study, we compare two subspecies of red deer, Scottish deer, Cervus elaphus scoticus (10 lactations), and Iberian deer, Cervus elaphus hispanicus (14 lactations), kept under the same diet and housing to assess differences in hind and calf weights and their trends, milk production and composition, and their allometric relationships. Scottish hinds were heavier, and calf weight and gains were greater than Iberian ones, with greater milk production and milk protein content, but they did not differ in fat or lactose content. Calf birth weight, milk production, and protein content showed significant allometric relationships with maternal weight, but no relationship was found for fat, lactose, or any of these variables with calf birth weight. Protein content correlated with calf birth weight, and calf weight trend depended on milk protein production rather than on that of fat or lactose. Protein may be the most important milk component to explain growth and milk composition differences between closely related mammals.

Animals↗
PubMedDate not supplied

Does basal metabolic rate contain a useful signal? Mammalian BMR allometry and correlations with a selection of physiological, ecological, and life-history variables.

Basal metabolic rate (BMR, mL O2 h(-1)) is a useful measurement only if standard conditions are realised. We present an analysis of the relationship between mammalian body mass (M, g) and BMR that accounts for variation associated with body temperature, digestive state, and phylogeny. In contrast to the established paradigm that BMR proportional to M3/4, data from 619 species, representing 19 mammalian orders and encompassing five orders of magnitude variation in M, show that BMR proportional to M2/3. If variation associated with body temperature and digestive state are removed, the BMRs of eutherians, marsupials, and birds do not differ, and no significant allometric exponent heterogeneity remains between orders. The usefulness of BMR as a general measurement is supported by the observation that after the removal of body mass effects, the residuals of BMR are significantly correlated with the residuals for a variety of physiological and ecological variables, including maximum metabolic rate, field metabolic rate, resting heart rate, life span, litter size, and population density.

Animals↗