Theoretical and empirical derivation of cardiovascular allometric relationships in children.

Basic fluid dynamic principles were used to derive a theoretical model of optimum cardiovascular allometry, the relationship between somatic and cardiovascular growth. The validity of the predicted models was then tested against the size of 22 cardiovascular structures measured echocardiographically in 496 normal children aged 1 day to 20 yr, including valves, pulmonary arteries, aorta and aortic branches, pulmonary veins, and left ventricular volume. Body surface area (BSA) was found to be a more important determinant of the size of each of the cardiovascular structures than age, height, or weight alone. The observed vascular and valvar dimensions were in agreement with values predicted from the theoretical models. Vascular and valve diameters related linearly to the square root of BSA, whereas valve and vascular areas related to BSA. The relationship between left ventricular volume and body size fit a complex model predicted by the nonlinear decrease of heart rate with growth. Overall, the relationship between cardiac output and body size is the fundamental driving factor in cardiovascular allometry.     

Postnatal long bone growth in terrestrial placental mammals: Allometry,life history,and organismal traits

The ontogenetic allometry of long bone proportions is poorly understood in Mammalia. It has previously been suggested that during mammalian ontogeny long bone proportions grow more slender (positive allometry; length ∝ circumference^>1.0), although this conclusion was based upon data from a few small‐bodied taxa. It remains unknown how ontogenetic long bone allometry varies across Mammalia in terms of both taxonomy and body size. We collected long bone length and circumference data for ontogenetic samples of 22 species of mammals spanning six major clades and three orders of magnitude in body mass. Using reduced major axis bivariate regressions to compare bone length to circumference, we found that isometry and positive allometry are the most widespread patterns of growth across mammals. Negative allometry (i.e., bones growing more robust during ontogeny) occurs in mammals but is largely restricted to cetartiodactyls. Using regression slope as a proxy for long bone allometry, we compared long bone allometry to life history and organismal traits. Neonatal body mass, adult body mass, and growth rate have a negative relationship with long bone allometry. At an adult mass of roughly 15–20 kg, long bone growth shifts from positive allometry to mainly isometry and negative allometry. There were no significant relationships between ontogenetic long bone allometry and either cursoriality or basal metabolic rate. J. Morphol. © 2012 Wiley Periodicals, Inc.     

Size-dependent growth and the development of inequality in maize,sunflower and soybean

Links were investigated between allometry of plant growth and dynamics of size structure of well-fertilized, irrigated crops of soybean (Glycine max L.), sunflower (Helianthus annuus L.) and maize (Zea mays L.) grown at standard plant-population densities (D), as in commercial crops (D = 30, 6 and 8.5 plants m-2, respectively), and at high densities (2D). Patterns of size-dependent growth of shoot and seed mass accumulation were distinctly different among species. In soybean and sunflower, non-linear relationships between size and subsequent growth led to strong hierarchical populations in terms of both shoot and seed biomass. Curvilinear (soybean) and sigmoid (sunflower) size-dependent growth determined strongly asymmetrical (soybean) and bimodal (sunflower) frequency distributions of shoot biomass indicating predominantly size asymmetrical competition among individuals. In comparison, a lower plant-to-plant variation coupled with a typical linear allometry of growth to plant size indicated symmetrical two-sided plant interference in maize. Despite the weak development of hierarchies in shoot biomass, a strong inequality in reproductive output developed in crowded populations of maize indicating an apparent breakage of reproductive allometry.     

Statistical model of variable allometric growth: otolith growth in Micropogonias furnieri(Actinopterygii, Sciaenidae)

The main objective of this study was to develop a statistical model for accurate estimates of relative growth. The method was based on identifying patterns of the residuals obtained from the Huxley's allometric equation. Three different approaches were applied: (1) growth with variable proportionality and constant allometry coefficient, (2) growth with constant proportionality and variable allometry coefficient and (3) distinct growth phases in which proportionality and allometry coefficients remained constant. The proposed statistical models were applied to the relationship of the otolith size and fish size of whitemouth croaker Micropogonias furnieri . The best fit was obtained when using approach (3). A change in the growth parameters was associated with the attainment of sexual maturity.     

Competitive regulation of plant allometry and a generalized model for the plant self-thinning process

Taking into account the individual growth form (allometry) in a plant population and the effects of intraspecific competition on allometry under the population self-thinning condition, and adopting Ogawa's allometric equation 1/y = 1/axb + 1/c as the expression of complex allometry, the generalized model describing the change mode of r (the self-thinning exponential in the self-thinning equation, log M = K + log N, where M is mean plant mass, K is constant, and N is population density) was constructed. Meanwhile, with reference to the changing process of population density to survival curve type B, the exponential, r, was calculated using the software MATHEMATICA 4.0. The results of the numerical simulation show that (1) the value of the self-thinning exponential, r, is mainly determined by allometric parameters; it is most sensitive to change of b of the three allometric parameters, and a and c take second place; (2) the exponential, r, changes continuously from about -3 to the asymptote -1; the slope of -3/2 is a transient value in the population self-thinning process; (3) it is not a 'law' that the slope of the self-thinning trajectory equals or approaches -3/2, and the long-running dispute in ecological research over whether or not the exponential, r, equals -3/2 is meaningless. So future studies on the plant self-thinning process should focus on investigating how plant neighbor competition affects the phenotypic plasticity of plant individuals, what the relationship between the allometry mode and the self-thinning trajectory of plant population is and, in the light of evolution, how plants have adapted to competition pressure by plastic individual growth.     

Postembryonic dimensional allometry of the human femur

Developmental constraints can affect evolution. McMahon's (1973, 1975a) hypothesis of elastic similarity is tested as an epigenetic rule. This is an ontogenetic hypothesis that previously has not been tested with ontogenetic data. Cross-sectional data from the human femur are analyzed. Length-diameter relationships for phases of growth and aging are calculated with bivariate allometry. McMahon's hypothesis cannot be rejected, although most of the calculations are not consistent with it. Ontogenetic skeletal allometry is complex because both material and geometric properties change during development.     

Dinosaur Metabolism and the Allometry of Maximum Growth Rate

The allometry of maximum somatic growth rate has been used in prior studies to classify the metabolic state of both extant vertebrates and dinosaurs. The most recent such studies are reviewed, and their data is reanalyzed. The results of allometric regressions on growth rate are shown to depend on the choice of independent variable; the typical choice used in prior studies introduces a geometric shear transformation that exaggerates the statistical power of the regressions. The maximum growth rates of extant groups are found to have a great deal of overlap, including between groups with endothermic and ectothermic metabolism. Dinosaur growth rates show similar overlap, matching the rates found for mammals, reptiles and fish. The allometric scaling of growth rate with mass is found to have curvature (on a log-log scale) for many groups, contradicting the prevailing view that growth rate allometry follows a simple power law. Reanalysis shows that no correlation between growth rate and basal metabolic rate (BMR) has been demonstrated. These findings drive a conclusion that growth rate allometry studies to date cannot be used to determine dinosaur metabolism as has been previously argued.     

ALLOMETRIC CONSTRAINTS AND THE EVOLUTION OF ALLOMETRY

Morphological traits often covary within and among species according to simple power laws referred to as allometry. Such allometric relationships may result from common growth regulation, and this has given rise to the hypothesis that allometric exponents may have low evolvability and constrain trait evolution. We formalize hypotheses for how allometry may constrain morphological trait evolution across taxa, and test these using more than 300 empirical estimates of static (within‐species) allometric relations of animal morphological traits. Although we find evidence for evolutionary changes in allometric parameters on million‐year, cross‐species time scales, there is limited evidence for microevolutionary changes in allometric slopes. Accordingly, we find that static allometries often predict evolutionary allometries on the subspecies level, but less so across species. Although there is a large body of work on allometry in a broad sense that includes all kinds of morphological trait–size relationships, we found relatively little information about the evolution of allometry in the narrow sense of a power relationship. Despite the many claims of microevolutionary changes of static allometries in the literature, hardly any of these apply to narrow‐sense allometry, and we argue that the hypothesis of strongly constrained static allometric slopes remains viable.     

Temperature-mediated transitions between isometry and allometry in a colonial, modular invertebrate

The evolutionary success of animal design is strongly affected by scaling and virtually all metazoans are constrained by allometry. One body plan that appears to relax these constraints is a colonial modular (CM) design, in which modular iteration is hypothesized to support isometry and indeterminate colony size. In this study, growth rates of juvenile scleractinians (less than 40mm diameter) with a CM design were used to test this assertion using colony diameters recorded annually for a decade and scaling exponents (b) for growth calculated from double logarithmic plots of final versus initial diameters. For all juvenile corals, b differed significantly among years, with isometry (b=1) in 4 years, but positive allometry (b>1) in 5 years. The study years were characterized by differences in seawater temperature that were associated significantly with b for growth, with isometry in warm years but positive allometry in cool years. These results illustrate variable growth scaling in a CM taxon and suggest that the switch between scaling modes is mediated by temperature. For the corals studied, growth was not constrained by size, but this outcome was achieved through both isometry and positive allometry. Under cooler conditions, positive allometry may be beneficial as it represents a growth advantage that increases with size.     

Carica papaya (Caricaceae): a case study into the effects of domestication on plant vegetative growth and reproduction

Few studies have quantitatively evaluated the gender specific effects of cultivation on plant growth and reproduction. The availability of cultivated and wild populations of different genders of Carica papaya L. (Caricaceae) on Guam provided an opportunity to study these effects quantitatively. We compared the gender specific allometry of height vs. basal stem diameter (H vs. D), stem slenderness ratio (H/D), and the height at first flowering (H(fl)) of carpellate and staminate plants growing under natural conditions (N = 150 each) with those of carpellate and hermaphroditic plants (N = 250 each) from two cultivars (Sunrise and Tainung 2). These comparisons indicated that (1) wild carpellate and staminate plants are significantly taller than either gender of the two cultivars with equivalent D; (2) the scaling exponent governing the H vs. D relationship of both genders of wild plants is significantly higher than that of either cultivated gender; (3) cultivar type does not affect the H vs. D exponent, but gender expression does; (4) gender expression (but not cultivar-type) also affects H(fl) (cultivation substantially reduces carpellate plant H(fl)); and (5) the onset of sexual maturity is associated with a dramatic reversal in H/D ontogeny. Cultivation therefore has "condensed" patterns of vegetative growth in a gender specific manner, whereas gender expression alters both vegetative and reproductive growth significantly more so than does cultivar-type.     

Do mating strategies determine genital allometry in African mole rats (Bathyergidae)?

Allometry describes the relationship of components of an organism with change in overall body size and has become the focus of numerous studies on the evolution of genitalia. Typically, negative allometry is observed in insects and is explained by stabilizing selection whereas the very few studies on mammals have shown a positive allometric relationship of genitalia in the body size, thought to have arisen as a result of sexual selection. However, all mammal species studied to date are thought to use mainly post-copulatory mating strategies. Across mammals, however, both pre-and post-copulatory strategies occur (although the two are not mutually exclusive). We propose that where pre-copulatory strategies are mainly used, no reproductive benefits would result from evolving positively allometric genitalia. As such, mammal genitalia are not typically positively allometric but rather allometry will, to a certain degree, be determined by mating strategy. We tested this prediction using four species of African mole rats (Bathyergidae) exhibiting variation in their life histories and mating strategies. Although generally supported, in that positive allometry did not occur in species that we assumed use mainly pre-mating strategies, positive allometry did not occur in either of the promiscuous species thought to use post-copulatory strategies. We suggest, therefore, that while mating strategies may tentatively determine genital allometry, whether positively allometric genitalia occur also depends on a number of complex interacting factors. In addition, this study provides further evidence and empirical support for the co-evolution of male and female genitalia in mammals.     

Trade-off between height growth and stem diameter growth for an evergreen Oak, Quercus glauca, in a mixed hardwood forest

1. Patterns of stem growth of a mid-successional evergreen Oak species ( Quercus glauca ) in a mixed hardwood forest were examined to explore the trade-off relationship between stem-diameter growth and height growth.
2. The mean cross-sectional area (and the corresponding mean diameter) of a stem at a point in time was defined as the stem volume divided by tree height. Based on this definition, a simple equation representing the trade-off relationship between the height growth and mean diameter growth was formulated.
3. In the long term, allocation to height growth was encouraged at the seedling stage and it gradually declined with time, with the decline in the suppressed seedlings being more pronounced than in the dominant trees.
4. However, both the suppressed and the dominant trees showed acceleration of height growth at various ages. Such a fluctuation in the allocation of biomass to height growth is likely to have been caused by chronological changes in light conditions, and meandered the trajectory of allometry between the height and mean diameter.
5. The observed stem growth patterns of the individual trees could explain the chronological changes in the diameter–height relationship of the population.     

The ontogeny of sexual dimorphism in the cranium of Bornean orang-utans (Pongo pygmaeus pygmaeus) as detected by principal-components analysis

The ontogeny of cranial sexual dimorphism in the Bornean orang-utan (Pongo pygmaeus pygmaeus) is examined by means of principal-components analysis (PCA). Normalized first components are called allometry vectors or vectors of relative growth and show that sexual dimorphism is present at all stages of growth. Two patterns of sexual dimorphism are present: (1) sexual differences at age groups 2 and 3 are the result primarily of differences in principal component II scores, reflecting mainly shape-related differences, and (2) age groups 5, 6, and 7 show a trend of stronger size-related shape differences with increasing age in the allometry vector along with decreasing differences in principal component II scores, reflecting an increase in size-related shape differences between the sexes. Age group 4 shows a combination of both patterns. Our results support Shea's hypothesis (1985a) that when using multigroup PCAs in closely related taxa, the allometry vector will generally estimate the shape variation resulting from the extension of common growth allometry patterns (ontogenetic scaling). The second and subsequent components summarize shape variation from slope and intercept differences between the groups, provided that ontogenetic scaling is not solely responsible for all the shape differences present. Subanalyses of those dimensions previously found to show ontogenetic scaling and acceleration follow this pattern well. The total sample provides a pattern whereby ontogenetically scaled dimensions possess a stronger influence over accelerated dimensions but still generally follow Shea's hypothesis. Finally, variously derived coefficients provided several interesting findings: (1) strong evidence was found against multivariate isometry for both the pooled and the separate samples, (2) multivariate allometric coefficients for both sexes follow the general growth pattern of negative scaling in neurocranial dimensions and positive scaling in the viscerocranium, and (3) multivariate slopes have a very high correlation with bivariate slopes relative to the same independent X variable, thereby lending further support to Jolicoeur's (1963a, b) allometry generalization.     

The evolution of static allometry in sexually selected traits

Although it has been the subject of verbal theory since Darwin, the evolution of morphological trait allometries remains poorly understood, especially in the context of sexual selection. Here we present an allocation trade-off model that predicts the optimal pattern of allometry under different selective regimes. We derive a general solution that has a simple and intuitive interpretation and use it to investigate several examples of fitness functions. Verbal arguments have suggested cost or benefit scenarios under which sexual selection on signal or weapon traits may favor larger individuals with disproportionately larger traits (i.e., positive allometry). However, our results suggest that this is necessarily true only under a precisely specified set of conditions: positive allometry will evolve when the marginal fitness gains from an increase in relative trait size are greater for large individuals than for small ones. Thus, the optimal allometric pattern depends on the precise nature of net selection, and simple examples readily yield isometry, positive or negative allometry, or polymorphisms corresponding to sigmoidal scaling. The variety of allometric patterns predicted by our model is consistent with the diversity of patterns observed in empirical studies on the allometries of sexually selected traits. More generally, our findings highlight the difficulty of inferring complex underlying processes from simple emergent patterns.     

Phyletic size change and brain/body allometry: A consideration based on the African pongids and other primates

A problematic aspect of brain/body allometry is the frequency of interspecific series which exhibit allometry coefficients of approximately 0.33. This coefficient is significantly lower than the 0.66 value which is usually taken to be the interspecific norm. A number of explanations have been forwarded to account for this finding. These include (1) intraspecificallometry explanations, (2) nonallometric explanations, and (3) Jerison’s “extraneurons” hypothesis, among others. The African apes, which exhibit a lowered interspecific allometry coefficient, are used here to consider previous explanations. These are found to be inadequate in a number of ways, and an alternative explanation is proposed. This explanation is based on patterns of brain and body size change during ontogeny and phytogeny. It is argued that the interspecific allometry coefficient in African apes parallels the intraspecific one because similar ontogenetic modifications of body growth separate large and small forms along each curve. In both cases, body size differences are produced primarily by growth in later postnatal periods, during which little brain growth occurs. Data on body growth, neonatal scaling, and various lifehistory traits support this explanation. This work extends previous warnings that sizecorrected estimates of relative brain size may not correspond very closely to our understanding of the behavioral capacities of certain species in lineages characterized by rapid change in body size.     

Is non‐loglinear allometry a statistical artifact?

The allometric equation, y = ax^b, is commonly fitted to data indirectly by transforming predictor (x) and response (y) variables to logarithms, fitting a straight line to the transformations, and then back‐transforming (exponentiating) the resulting equation to the original arithmetic scale. Sometimes, however, transformation fails to linearize the observations, thereby giving rise to what has come to be known as non‐loglinear allometry. A smooth curve for observations displayed on a log–log plot is usually interpreted to mean that the scaling exponent in the allometric equation is a continuously changing function of body size, whereas a breakpoint between two (or more) linear segments on a log–log plot is typically taken to mean that the exponent changes abruptly, coincident with some important milestone in development. I applied simple graphical and statistical procedures in re‐analyses of three well‐known examples of non‐loglinear allometry, and showed in every instance that the relationship between predictor and response can be described in the original scale by simple functions with constant values for the exponent b. In no instance does the allometric exponent change during the course of development. Transformation of data to logarithms created new distributions that actually obscured the relationships between predictor and response variables in these investigations, and led to erroneous perceptions of growth. Such confounding effects of transformation are not limited to non‐loglinear allometry but are common to all applications of the allometric method. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, ?? , ??–??.     

Modes of ontogenetic allometric shifts in crocodylian vertebrae

During postnatal ontogeny of vertebrates, allometric trends in certain morphological units or dimensions can shift drastically among isometry, positive allometry, and negative allometry. However, detailed patterns of allometric transitions in certain timings have not been explored well. Identifying the presence and nature of allometric shifts is essential for understanding the patterns of changes in relative size and shape and the proximal factors that are controlling these changes mechanistically. Allometric trends in 10 selected vertebrae (cervical 2–caudal 2) from hatchlings to very mature individuals of Alligator mississippiensis (Archosauria, Crocodylia) are reported in the present study. Allometric coefficients in 12 vertebral dimensions are calculated and compared relative to total body length, including centrum, neural spine, transverse process, zygapophysis, and neural pedicle. During the postnatal growth, positive allometry is the most common type of relative change (10 of the 12 dimensions), although the diameter of the neural canal shows a negative allometric trend. However, when using spurious breaks (i.e. allometric trends subdivided into growth stages using certain growth events, and key body sizes and/or ages), vertebral parts exhibit various pathways of allometric shifts. Based on allometric trends in three spurious breaks, separated by the end of endochondral ossification (body length: approximnately 0.9 m), sexual maturity (1.8 m), and the stoppage of body size increase (2.8 m), six types of ontogenetic allometric shifts are established. Allometric shifts exhibit a wide range from positive allometry restricted only in the early postnatal stage (Type I) to life‐long positive allometry (Type VI). This model of ontogenetic allometric shifts is then applied to interpret potential mechanisms (causes) of allometric changes, such as (1) growth itself (when allometric trend gradually decreases to isometric or negative allometric change: Type II–IV allometric shift); (2) developmental constraint (when positive allometry is limited only in the early growth stage: Type I allometric shift); and (3) functional or biomechanical drive (when positive allometry continues throughout ontogeny: Type VI allometric shift).     

How liana loads alter tree allometry in tropical forests

Intense competition with lianas (wood climbers) can limit tree growth, reproduction, and survival. However, the negative effects of liana loads on tree allometry have not yet been addressed. We investigated the hypothesis that liana loading on tree crown alters tree’s allometry, expressed through slenderness (height–diameter ratio). The relationship between trunk slenderness and percentage of tree crown covered by lianas was investigated for 12 tree species from 10 fragments of the Semideciduous Seasonal Forest in Southeastern Brazil. We also tested whether the relationship between slenderness and wood density differ between trees without lianas and trees heavily infested. Liana loads significantly altered tree allometry by decreasing slenderness, even when lianas covered less than 25% of tree crown. Heavy-wood species decreased their trunk slenderness in a greater ratio than light-wood species. Our findings indicate that liana infestation shifts tree allometry, and these effects are stronger on heavy-wood tree species.     

Ontogenetic and interspecific organ weight allometry in Old World monkeys

The importance of allometry as an analytic tool is well recognized in the literature of primate morphology. However, a number of recent studies have illustrated how interpretive difficulties can arise when researchers confound different types of allometric data. Such confusion is due less to carelessness than to uncertainty about how different types of allometry are related. The present study examines the relationship between two types—ontogenetic and interspecific allometry–in the case of organ weight scaling in six species of Old World monkeys. Accepting the interpretation of interspecific allometry as a reflection of functional scaling constraints, the results of this analysis indicate how ontogenetic patterns have been modified in different-sized species to maintain compliance with these constraints. Specifically, for the heart and lungs it appears that vertical transpositions of individual species' ontogenies are dictated by isometric interspecific allometry, while in the case of the kidneys and liver, the relation of negative allometry across species entails alteration of the relative growth coefficients of the individual species. While these conclusions can at present only be applied to organ weight scaling, the approach of examining interspecific patterns in light of developmental differences between species should prove very helpful in our efforts to understand the phenomena of size and scaling.     

The developmental basis for allometry in insects

Within all species of animals, the size of each organ bears a specific relationship to overall body size. These patterns of organ size relative to total body size are called static allometry and have enchanted biologists for centuries, yet the mechanisms generating these patterns have attracted little experimental study. We review recent and older work on holometabolous insect development that sheds light on these mechanisms. In insects, static allometry can be divided into at least two processes: (1) the autonomous specification of organ identity, perhaps including the approximate size of the organ, and (2) the determination of the final size of organs based on total body size. We present three models to explain the second process: (1) all organs autonomously absorb nutrients and grow at organ-specific rates, (2) a centralized system measures a close correlate of total body size and distributes this information to all organs, and (3) autonomous organ growth is combined with feedback between growing organs to modulate final sizes. We provide evidence supporting models 2 and 3 and also suggest that hormones are the messengers of size information. Advances in our understanding of the mechanisms of allometry will come through the integrated study of whole tissues using techniques from development, genetics, endocrinology and population biology.