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Empirical evidence refutes the theory that sexually selected traits usually exhibit positive static allometries. It suggests that very few sexual traits exhibit positive allometry and directional sexual selection does not always produce positive allometry.

We give a functional generalization of fractal scaling laws applied to response problems as well as to probability distributions. We consider excitations and responses, which are functions of a given state vector. Based on scaling arguments, we derive a general nonlinear response functional scaling law, which expresses the logarithm of a response at a given state as a superposition of the values of the logarithms of the excitations at different states, Such a functional response law may result from the balance of different growth processes, characterized by variable growth rates, and it is the first order approximation of a perturbation expansion similar to the phase expansion. Our response law is a generalization of the static fractal scaling law and can be applied to the study of various problems from physics, chemistry, and biology. We consider some applications to heterogeneous and disordered kinetics, organ growth (allometry), and population genetics. Kinetics on inhomogeneous reconstructing surfaces leads to rate equations described by our nonlinear scaling law. For systems with dynamic disorder with random energy barriers, the probability density functional of the rate coefficient is also given by our scaling law. The relative growth rates of different biological organs (allometry) can be described by a similar approach. Our scaling law also emerges by studying the variation of macroscopic phenotypic variables in terms of genotypic growth rates. We study the implications of the causality principle for our theory and derive a set of generalized Kramers-Kronig relationships for the fractal scaling exponents.

Sleep is one of the most noticeable and widespread phenomena occurring in multicellular animals. Nevertheless, no consensus for a theory of its origins has emerged. In particular, no explicit, quantitative theory exists that elucidates or distinguishes between the myriad hypotheses proposed for sleep. Here, we develop a general, quantitative theory for mammalian sleep that relates many of its fundamental parameters to metabolic rate and body size. Several mechanisms suggested for the function of sleep can be placed in this framework, e.g., cellular repair of damage caused by metabolic processes as well as cortical reorganization to process sensory input. Our theory leads to predictions for sleep time, sleep cycle time, and rapid eye movement time as functions of body and brain mass, and it explains, for example, why mice sleep [approximately equal to] 14 hours per day relative to the 3.5 hours per day that elephants sleep. Data for 96 species of mammals, spanning six orders of magnitude in body size, are consistent with these predictions and provide strong evidence that time scales for sleep are set by the brain's, not the whole-body, metabolic rate. allometric scaling | brain | cellular repair | metabolic rate | sleep times

Evidence from comparative studies of gene expression and evolution suggest that human neocortical neurons may be characterized by unusually high levels of energy metabolism. The current study examined whether there is a disproportionate increase in glial cell density in the human frontal cortex in comparison with other anthropoid primate species (New World monkeys, Old World monkeys, and hominoids) to support greater metabolic demands. Among 18 species of anthropoids, humans displayed the greatest departure from allometric scaling expectations for the density of glia relative to neurons in layer II/III of dorsolateral prefrontal cortex (area 9L). However, the human glia--neuron ratio in this prefrontal region did not differ significantly from allometric predictions based on brain size. Further analyses of glia--neuron ratios across frontal areas 4, 9L, 32, and 44 in a sample of humans, chimpanzees, and macaque monkeys showed that regions involved in specialized human cognitive functions, such as 'theory of mind' (area 32) and language (area 44) have not evolved differentially higher requirements for metabolic support. Taken together, these findings suggest that greater metabolic consumption of human neocortical neurons relates to the energetic costs of maintaining expansive dendritic arbors and long-range projecting axons in the context of an enlarged brain. allometry | human evolution | prefrontal cortex | brain energy metabolism | language evolution

A key regulatory gene in metamorphosing (holometabolous) insect life histories is the transcription factor broad (br), which specifies pupal development. To determine the role of br in a direct-developing (hemimetabolous) insect that lacks a pupal stage, we cloned br from the milkweed bug, Oncopeltus fasciatus (Of'br). We find that, unlike metamorphosing insects, in which br expression is restricted to the larval-pupal transition, Of'br mRNA is expressed during embryonic development and is maintained at each nymphal molt but then disappears at the molt to the adult. Induction of a supernumerary nymphal stage with a juvenile hormone (JH) mimic prevented the disappearance of br mRNA. In contrast, induction of a precocious adult molt by application of precocene II to third-stage nymphs caused a loss of br mRNA at the precocious adult molt. Thus, JH is necessary to maintain br expression during the nymphal stages. Injection of Of'br dsRNA into either early third- or fourth-stage nymphs caused a repetition of stage-specific pigmentation patterns and prevented the normal anisometric growth of the wing pads without affecting isometric growth or molting. Therefore, br is necessary for the mutable (heteromorphic) changes that occur during hemimetabolous development. Our results suggest that metamorphosis in insects arose as expression of br, which conveys competence for change, became restricted to one postembryonic instar. After this shift in br expression, the progressive changes that occur within the nymphal series in basal insects became compressed to the one short period of morphogenesis seen in the larva-to-pupa transition of holometabolous insects. evolution of metamorphosis | heteromorphosis | Oncopeltus | juvenile hormone | allometry

From a functional perspective, changes in abundance, and ultimately species replacement, during succession are a consequence of integrated suites of traits conferring different relative ecological advantages as the environment changes over time. Here we use structural equations to model the interspecific relationships between these integrated functional traits using 34 herbaceous species from a Mediterranean old-field succession and thus quantify the notion of a plant strategy. We measured plant traits related to plant vegetative and reproductive size, leaf functioning, reproductive phenology, seed mass, and production on 15 individuals per species monitored during one growing season. The resulting structural equation model successfully accounts for the pattern of trait covariation during the first 45 years post-abandonment using just two forcing variables: time since site abandonment and seed mass; no association between time since field abandonment and seed mass was observed over these herbaceous stages of secondary succession. All other predicted traits values are determined by these two variables and the cause--effect linkage between them. Adding pre-reproductive vegetative mass as a third forcing variable noticeably increased the predictive power of the model. Increasing the time after abandonment favors species with increasing life span and pre-reproductive biomass and decreasing specific leaf area. Allometric coefficients relating vegetative and reproductive components of plant size were in accordance with allometry theory. The model confirmed the trade-off between seed mass and seed number. Maximum plant height and seed mass were major determinants of reproductive phenology. Our results show that beyond verbal conceptualization, plant ecological strategies can be quantified and modeled. Key words: allometry; path analysis; phenology; plant size; reproductive allocation; secondary succession; seed mass; seed production; structural equation modeling.

The branching pattern and vascular geometry of biological tree structure are complex. Here we show that the design of all vascular trees for which there exist morphometric data in the literature (e.g., coronary, pulmonary; vessels of various skeletal muscles, mesentery, omentum, and conjunctiva) obeys a set of scaring laws that are based on the hypothesis that the cost of construction of the tree structure and operation of fluid conduction is minimized. The laws consist of scaling relationships between 1) length and vascular volume of the tree, 2) lumen diameter and blood flow rate in each branch, and 3) diameter and length of vessel branches. The exponent of the diameter-flow rate relation is not necessarily equal to 3.0 as required by Murray's law but depends on the ratio of metabolic to viscous power dissipation of the tree of interest. The major significance of the present analysis is to show that the design of various vascular trees of different organs and species can be deduced on the basis of the minimum energy hypothesis and conservation of energy under steadystate conditions. The present study reveals the similarity of nature's scaling laws that dictate the design of various vascular trees and the underlying physical and physiological principles. design; morphometry; minimum energy; shear stress; Murray's law

We examined the allometric relationship between resting metabolic rate (RMR; kJ [day.sup.-1]) and body mass (kg) in wild waterfowl (Anatidae) by regressing RMR on body mass using species means from data obtained from published literature (18 sources, 54 measurements, 24 species; all data from captive birds). There was no significant difference among measurements from the rest (night; n = 37), active (day; n = 14), and unspecified (n = 3) phases of the daily cycle (P > 0.10), and we pooled these measurements for analysis. The resulting power function (a[Mass.sup.b]) for all waterfowl (swans, geese, and ducks) had an exponent (b; slope of the regression) of 0.74, indistinguishable from that determined with commonly used general equations for nonpasserine birds (0.72-0.73). In contrast, the mass proportionality coefficient (b; y-intercept at mass = 1 kg) of 422 exceeded that obtained from the nonpasserine equations by 29%-37%. Analyses using independent contrasts correcting for phylogeny did not substantially alter the equation. Our results suggest the waterfowl equation provides a more appropriate estimate of RMR for bioenergetics analyses of waterfowl than do the general nonpasserine equations. When adjusted with a multiple to account for energy costs of free living, the waterfowl equation better estimates daily energy expenditure. Using this equation, we estimated that the extent of wetland habitat required to support wintering waterfowl populations could be 37%-50% higher than previously predicted using general nonpasserine equations. Key words: allometry, Anatidae. bioenergetics models, body mass, habitat requirements. resting metabolism, waterfowl. Resumen. Examinamos la relacion alomotrica entre la tasa metabolica en reposo (TMR; kJ [dia.sup.-1]) y la masa corporal (kg) en aves acuaticas silvestres (Anatidae) mediante la regresion de la TMR con la masa corporal usando valores promedio para las especies obtenidos a partir de datos publicados en la literatura (18 fuentes, 54 medidas, 24 especies; todos los datos son de aves en cautiverio). No hubo una diferencia significativa entre las medidas de las rases en reposo (noche; n = 37), activa (dia; n = 14) y no especificada (n = 3) del ciclo diario (P > 0.10), por lo que juntamos estos datos para el analisis. La funcion de poder resultante (a[Masa.sup.b]) para todas las aves (cisnes, gansos y patos) tuvo un exponente (b; pendiente de la regresion) de 0.74, que fue indistinguible de aquel determinado con ecuaciones generales comunmente usadas para ayes no paserinas (0.72-0.73). En contraste, el coeficiente de proporcionalidad de masa (b; y-intercepto de masa = 1 kg) de 422 excedio al obtenido a partir de ecuaciones para aves no paserinas por un 29% a 37%. Los analisis que usaron contrastes independientes corregidos por filogenia no alteraron sustancialmente la ecuacion. Nuestros resultados sugieren que la ecuacion para las aves acuaticas brinda una estimacion mas apropiada de la TMR para los analisis bioenergeticos de los anatidos que las ecuaciones generales para aves no paserinas. Cuando las ecuaciones de los anatidos fueron ajustadas con un multiplo para incorporar los costos energeticos de la vida en libertad, la ecuacion de los anatidos brindo mejores estimados del gasto diario de energia. Usando esta ecuacion, estimamos que la extension de humedales requerida para albergar a las poblaciones invernales de anatidos podria ser un 37% a 50% mayor que la predicha previamente usando las ecuaciones generales para aves no paserinas.

To better utilize limited resources for their survival and reproduction, all organisms undergo developmental changes in both body size and shape during ontogeny. The genetic analysis of size change with increasing age, i.e., growth, has received considerable attention in quantitative developmental genetic studies, but the genetic architecture of ontogenetic changes in body shape and its associated allometry have been poorly understood partly due to the lack of analytical tools. In this article, we attempt to construct a multivariate statistical framework for studying the genetic regulation of ontogenetic growth and shape. We have integrated biologically meaningful mathematical functions of growth curves and developmental allometry into the estimation process of genetic mapping aimed at identifying individual quantitative trait loci (QTL) for phenotypic variation. This model defined with high dimensions can characterize the ontogenetic patterns of genetic effects of QTL over the lifetime of an organism and assess the interplay between genetic actions/interactions and phenotypic integration. The closed forms for the residual covariance matrix and its determinant and inverse were derived to overcome the computational complexity typical of our high-dimensional model. We used a worked example to validate the utility of this model. The implications of this model for genetic research of evo-devo are discussed.

The aims of this study were to assess 1) whether the stature-adjusted body mass index (BMI) is a valid proxy for adiposity across both athletic and nonathletic populations, and 2) whether skinfold measurements increase in proportion to body size, thus obeying the principle of geometric similarity. The research design was cross-sectional, allowing the relationship between skinfold calliper readings (at eight sites and between specific athletic and nonathletic groups, n = 478) and body size (either mass, stature, or both) to be explored both collectively, using proportional allometric MANCOVA, and individually (for each site) with follow-up ANCOVAs. Skinfolds increase at a much greater rate relative to body mass than that assumed by geometric similarity, but taller subjects had less rather than more adiposity, calling into question the use of the traditional skinfold-stature adjustment, 170.18/stature. The best body-size index reflective of skinfold measurements was a stature-adjusted body mass index similar to the BMI. However, sporting differences in skinfold thickness persisted, having controlled for differences in body size (approximate BMI) and age, with male strength- and speed-trained athletes having significantly lower skinfolds (32% and 23%, respectively) compared with controls. Similarly, female strength athletes had 29% lower skinfold measurements compared to controls, having controlled for body size and age. These results cast serious doubts on the validity of BMI to represent adiposity accurately and its ability to differentiate between populations. These findings suggest a more valid (less biased) assessment of fatness will be obtained using surface anthropometry such as skinfolds taken by experienced practitioners following established procedures. KEY WORDS anthropometry; skinfold; proportional allometric; MANCOVA; ANCOVA

Study is conducted to review that '3/4-power scaling law' of metabolic rate is not universal, either within or among animal species. Significant variation in the scaling of metabolic rate with body mass is described for animals, unicells and plants.

A series of experiments was conducted to examine the effects of competition on allometry and defense using tomato plants (Lycopersicon esculentum). No mortality occurred over the 4-wk test period, even with a plant density of 30 plants per 10-[cm.sup.2]. However, allometric patterns for log canopy diameter vs. log height indicated that competition occurred as early as 8 d after transplant and for pots with as few as two young plants (density of about 2 plants per 10-cm2). There was a change towards less root mass for greater height as competition increased. Leaf concentration of the allelochemicals chlorogenic acid, rutin and tomatine increased with decreasing competition, with the sum of these exhibiting a sigmoid-like pattern for allelochemical concentration. But competition did not affect leaf proteinase inhibitor activity, or petiole glandular trichomes or total trichomes. While the results are compatible with the growth-differentiation balance (GDB) hypothesis, they also indicate some of the difficulties that will be encountered in testing the GDB hypothesis rigorously.

Survival rates during the first winter of life are strongly size dependent and variable in many temperate fish populations. Starvation is often implicated as the cause of size-dependent first-winter mortality, and interannual variation in energy accumulation and the allocation between growth and storage is a likely source of variability. We examined these processes in young-of-the-year Hudson River striped bass Morone saxatilis, which are known to experience size-selective winter mortality and a winter energy deficit. Neutral-lipid and lean-tissue masses were determined for fish of five consecutive year classes collected through the first year of life. Differences in scaling relationships between body length and neutral-lipid and lean-tissue mass were used to infer patterns of resource allocation. Lipid reserves scaled isometrically with body length in summer but increased at a greater rate than did body length in autumn and winter. Lean-tissue allometries were less variable but followed a similar seasonal cycle. Allometric slopes were homogeneous across years, but significant interannual variation in length-specific lipid content and lean-tissue mass in the later half of the growing season indicated variable allocation patterns. During winter, up to 21% of total energy content and 50% of neutral-lipid stores were depleted. The results indicate that energy allocation patterns result from interactions among season, ontogenetic stage, and body size. The variation in growth, allocation, and severity of the winter energy deficit likely interact to determine first-winter survival. Key words: allometry: energy allocation; Hudson River, USA; lipid reserves; Morone saxatilis; seasonality; striped bass, juvenile.

Accumulation of noncoding DNA and therefore genome size (C-value) may be under strong selection toward increase of body size accompanied by low metabolic costs. C-value directly affects cell size and specific metabolic rate indirectly. Body size can enlarge through increase of cell size and/or cell number, with small cells having higher metabolic rates. We argue that scaling exponents of interspecific allometries of metabolic rates are by-products of evolutionary diversification of C-values within narrow taxonomic groups, which underlines the participation of cell size and cell number in body size optimization. This optimization leads to an inverse relation between slopes of interspecific allometries of metabolic rates and C-value. To test this prediction we extracted literature data on basal metabolic rate (BMR), body mass, and C-value of mammals and birds representing six and eight orders, respectively. Analysis of covariance revealed significant heterogeneity of the allometric slopes of BMR and C-value in both mammals and birds. As we predicted, the correlation between allometric exponents of BMR and C-value was negative and statistically significant among mammalian and avian orders. allometry | genome size | body size optimization | cell number

The fundamentals of mechanics provide a strong basis for the hypothesis that allometry could be an important constraint on evolutionary changes in shape. Empirical evidence that allometry accounts for sufficient shape variation to be an effective constraint is much weaker. Numerous studies claim to show that most shape variation is correlated with size, but nearly all these studies use morphometric methods that confound size and shape. Consequently, the proportion of the shape variation correlated with size remains unknown. To address this issue, I examined ontogenetic change and adult variation in lower jaws of the fox squirrel, Sciurus niger. Jaw morphologies were quantified using traditional distance measurements and geometric shape variables computed from landmark coordinates. The same analyses were performed on each data set. As expected, analyses of the distance measurements found that allometry accounted for nearly all ontogenetic variation. The same analysis on the coordinate data found that allometry accounts for 50% of the variation in distance measurements but Key words: allometry, evolutionary constraints, morphometrics, Sciurus niger, shape

We examined morphological variability and evolution of the baculum (os penis) across the Mustelidae through allometric analyses and character mapping. Fifty-four species and 26 genera (including 2 fossil forms) were examined with numerous caniform out-group species. Allometric analyses showed that bacular length is relatively constant across mustelids and caniforms; only a tendency to a slightly shortened baculum in mephitines was observed. Character mapping revealed the ancestral mustelid baculum to be an elongated rod-shaped bone that lacks a urethral groove and possesses a simple, nondistinct distal tip. This form is largely retained in mephitines and, to a lesser degree, in lutrines. From the ancestral condition, it is possible to derive forms with a more complicated head that has projections and openings (e.g., melines, Eira barbara, Galictis, Gulo gulo, Martes) or spoon-shaped and cup-shaped processes (e.g., Ictonyx, Mellivora capensis). Another evolutionary trajectory involves the distal tip of the baculum becoming hook-shaped and the urethral groove well developed (e.g., Mustela, Vormela peregusna). Although the structure of the baculum distinguishes closely related species, many features are derived independently in more distantly related forms. Therefore, bacular structure provides restricted phylogenetic information and should be analyzed in concert with other data sources (e.g., morphology of the basicranial region). Key words: allometry, baculum, independent contrasts, morphology, Mustelidae, phylogeny

We examined the relationship between meristem allocation and plant size for four annual plant species: Arabidopsis thaliana, Arenaria serphyllifolia, Brassica rapa, and Chaenorrhinum minus. Gradients of light and nutrient availability were used to obtain a range of plant sizes for each of these species. Relative allocation to reproductive, inactive, and growth meristems were used to measure reproductive effort, apical dominance, and branching intensity, respectively. We measured allocation to each of these three meristem fates at weekly intervals throughout development and at final developmental stage. At all developmental stages reproductive effort and branching intensity tended to increase with increasing plant size (i.e., due to increasing resource availability) and apical dominance tended to decrease with increasing plant size. We interpret these responses as a strategy for plants to maximize fitness across a range of environments. In addition, significant differences in meristem response among species may be important in defining the range of habitats in which a species can exist and may help explain patterns of species competition and coexistence in habitats with variable resource availability. Key words: allometry; development; functional response; light gradient; meristem allocation; nutrient gradient.

The slope of the preload recruitable stroke work relationship ([M.sub.w]) is a highly linear, load-insensitive contractile index. To investigate whether [M.sub.w] can be determined from a single steadystate beat, 45 patients were studied during cardiac catheterization. Single-beat [M.sub.w] (SB[M.sub.w]) was calculated directly from the baseline stroke work and baseline left ventricular (LV) end-diastolic volume (ED[V.sub.B]), and the volume-axis intercept ([V.sub.w]) was estimated as k x ED[V.sub.B] + (k - 1) x L[V.sub.wall], where k is the ratio of the epicardial shell volumes corresponding to [V.sub.w] and ED[V.sub.B] and L[V.sub.wall] is the wall volume. The mean of individual k values was 0.72 [+ or -] 0.04, which correlated with LV mass significantly (r = 0.60, P < 0.001). SB[M.sub.w] calculated from a constant k of 0.7 predicted [M.sub.w] well (r = 0.88, P < 0.0001), and the prediction improved slightly when k was estimated from individual LV mass (r = 0.93, P < 0.0001). Subgroup analyses revealed that the single-beat technique also worked in patients with small or large LV mass or volume or with regional wall motion abnormalities. The absolute change in SB[M.sub.w] after dobutamine infusion also correlated with that in [M.sub.w]. In conclusion, [M.sub.w] can be estimated from a steady-state beat without alteration of preload. hemodynamics; contractility; allometry

We measured water-influx rate during the hot summer in free-ranging adult Arabian oryxes (Oryx leucoryx) in Mahazat as-Sayd, a 2,244-[km.sup.2] protected area in west-central Saudi Arabia. Oryxes obtained 2,294 ml/day of water in their food and from oxidative water, the latter amounting to 14.2% of total water influx. For ungulates living in hot environments, we constructed an allometric curve: log(water-influx rate [liters/day]) = -0.885 + 0.922*log(body mass [kg]), ([r.sup.2] = 0.77, F = 26.8, P < 0.001, n = 10). The Arabian oryx had the lowest mass-specific water-influx rate (31.5 ml [kg.sup.-0.922] [day.sup.-1]), only 32% that of the camel (99.3 ml [kg.sup.-0.922] [day.sup.-1]), emphasizing the degree of evolutionary specialization in oryx. Between June and September, oryxes grazed primarily on 3 grasses, Panicum turgidum, Lasiurus scindicus, and Stipagrostis. P. turgidum, taken in largest quantity, had the highest moisture content, 35-45% per g of wet matter. Dry matter intake averaged about 3.1 kg during the summer months; plant intake varied inversely with moisture content. Key words: allometry, antelope, Arabian oryx, Artiodactyla, desert, Oryx leucoryx, water influx

The relationship between allometry and sexual dimorphism in the human craniofacial complex was analyzed using geometric morphometric methods. Thin-plate splines (TPS) analysis has been applied to investigate the lateral profile of complete adult skulls of known sex. Twenty-nine three-dimensional (3D) craniofacial and mandibular landmark coordinates were recorded from a sample of 52 adult females and 52 adult males of known age and sex. No difference in the influence of size on shape was detected between sexes. Both size and sex had significant influences on shape. As expected, the influence of centroid size on shape (allometry) revealed a shift in the proportions of the neurocranium and the viscerocranium, with a marked allometric variation of the lower face. Adjusted for centroid size, males presented a relatively larger size of the nasopharyngeal space than females. A mean-male TPS transformation revealed a larger piriform aperture, achieved by an increase of the angulation of the nasal bones and a downward rotation of the anterior nasal floor. Male pharynx expansion was also reflected by larger choanae and a more posteriorly inclined basilar part of the occipital clivus. Male muscle attachment sites appeared more pronounced. In contrast, the mean-female TPS transformation was characterized by a relatively small nasal aperture. The occipital clivus inclined anteriorly, and muscle insertion areas became smoothed. Besides these variations, both maxillary and mandibular alveolar regions became prognathic. The sex-specific TPS deformation patterns are hypothesized to be associated with sexual differences in body composition and energetic requirements. Am J Phys Anthropol 117: 236-245, 2002. KEY WORDS geometric morphometrics; 2D landmarks; partial warp scores; neurocranial rotation; nasal cavity

Byline: Olaf Dreyer (1), Raymond Puzio (2) Keywords: Key words or phrases: Allometric scaling -- Metabolism -- Mass Abstract: In this paper we give a derivation for the allometric scaling relation between the metabolic rate and the mass of animals and plants. We show that the characteristic scaling exponent of 3/4 occurring in this relation is a result of the distribution of sources and sinks within the living organism. We further introduce a principle of least mass and discuss the kind of flows that arise from it. Author Affiliation: (1) Center for Gravitational Physics and Geometry, The Pennsylvania State University, 104 Davey Laboratory, University Park, PA 16802--6300, USA. e-mail: dreyer@phys.psu.edu, US (2) Department of Physics and Astronomy, University of Mississippi, 108 Lewis Hall, University, MS 38677, USA. e-mail: puzio@phy.olemiss.edu, US Article note: Received: 13 August 1999/Revised version: 21 November 2000/APPublished online: 17 July 2001

Byline: Atsushi Kume (1), Yoshio Ino (1) Keywords: Keywords: Allometry, Aucuba japonica, Critical size for flowering, Growth form, Pith, Shoot size Abstract: , an evergreen broad-leaved shrub. Aucuba Japonica var. borealis is widely distributed in heavy snowfall areas in Japan and is covered, shaded and physically pressured by snow for more than four months of the year. On the other hand, var. japonica is widely distributed in light snowfall areas. The sizes of new shoots and leaves were significantly different between the two varieties with different critical shoot sizes for flowering. The average new shoot dry mass of var. borealis was about one third of that of var. japonica. Despite the differences in growing conditions and shoot size, no significant differences were observed in the allometry of their shoot organs between the two varieties. Large new shoots had thicker and longer stems per biomass than small shoots because of their larger pith volume. The large shoots showed higher efficiency of stem growth per invested biomass and had a higher rate of annual height increase than small shoots. When the size of new shoot rapidly increased from year to year, i.e. the plants are growing well, initiation of flowering was postponed and vegetative growth continued. Small new shoots were tolerant of low productivity conditions but traded vertical growth for an increase in matter allocation to leaves. Author Affiliation: (1) Department of Biology, School of Education, Waseda University, Tokyo, 169--8050 Japan, JP Article note: Received 8 July 1999/ Accepted in revised form 1 September 2000

Bacula are relatively small in terrestrially mating species of pinnipeds (otariids and elephant seals, Mirounga), perhaps reflecting adaptive size reduction to minimize bacular fracture. Fur seals and sea lions (Otariidae) are a good group with which to investigate this question, because most species copulate solely on land and body size varies interspecifically. We studied bacular size and relative growth in the largest extant otariid, the Steller sea lion (Eumetopias jubatus). Bacula roughly tripled in length and increased 30-fold in mass between 1 and 8 years of age. Allometric relationships changed over development; bacular length and mass changed from being initially positively allometric to body length to negatively allometric and isometric, respectively; bacular mass and thickness were positively allometric to body length throughout life, and apical growth was isometric then was positively allometric to bacular length. In adults (>7 years of age), bacula averaged 18.1 cm length (6.2% of body length), 36.7 g mass, and 2.02 g/cm density (mass:length). The baculum of Eumetopias is about the same length relative to body length as in other adult male otariids but is about twice the density, presumably to increase strength. Information on small or aquatically mating species of otariid are needed to extend our findings and interpretations.

The objective of this study was to determine whether the factor of safety for mechanical stability varied among stems differing in size and age within the superstructure of a large dicot tree. Two factors of safety were selected for study: the quotient of the critical buckling height and the actual length of stems, Hcrit/L, and the quotient of the modulus of rupture (the force per unit area required to break a stem) and the working stress (the force per unit area resulting from the biomass measured distal to a stem), [M.sub.R]/[[Sigma].sub.w]. These two dimensionless safety factors were determined for a total of 420 shoot segments comprising much of the aboveground biomass of a Robinia pseudoacacia (Fabaceae) tree measuring 18.7 m in height and 1347 kg in mass, and 0.46 m in diameter (40 yr old) at 1.2 m from the ground. An S-shaped trend was observed when each of the two factors of safety was plotted as a function of stem age. Each factor decreased from a local maximum for the most distal (peripheral) stems in the canopy to a local minimum value for stems [approximately]10 yr old; each factor increased again to another local maximum for stems 11-18 yr old, and then decreased steadily toward the base of the trunk. This trend was the result of the allometric relationships among stem diameter, length, biomass, and material properties (stiffness and strength) with respect to stem age. Although they were disproportionately more slender than their older counterparts, peripheral stems were sufficiently stiff and strong to sustain the stresses resulting from their weight and that of foliage without deflecting under these loads, yet they were sufficiently flexible to easily bend and thereby presumably provide a mechanism to reduce the drag forces acting on the entire tree. In contrast, the internally imposed mechanical forces acting on progressively older stems increased at a greater rate than the observed rate of increase in stem stiffness, strength, or diameter. The probability of mechanical failure, which must be considered from a demographic perspective (i.e., an age-dependent phenomenon), thus increased from older branches to the base of the trunk. Reports of similar allometric trends based on interspecific comparisons among diverse dicot species comply with the allometry observed for the R. pseudoacacia tree and suggest that the S-shaped trend for the factor of safety holds for stems differing in age drawn from individual trees and for the trunks of conspecifics differing in age drawn from a dense population. Key words: biomechanics; dicot trees; Fabaceae; factor of safety; plant allometry; Robinia pseudoacacia; stem stiffness and strength.

The allometry of axis length, diameter, and taper is described for the trunk, rachis, and rachilla of nonbranching ramets of Aralia spinosa. Significant log-linear relationships were found between length and diameter for all axis categories, and in all cases, scaling was negatively allometric. Linear models best described the relationship between length and diameter for the rachis and rachilla, while a quadratic model best described this relationship for the trunk. During the trunk-building stage, the safety factors for trunk height were size dependent, with larger trunks exceeding their predicted critical buckling height. Taper was described by a linear relationship between diameter and position along the axis for all axis categories. All rachises and rachillas sampled exhibited taper along the length of the axis, however, only 51% of the trunks showed continuous taper. The trunk was less tapered than the rachis, but no differences in taper were found between the trunk and the rachilla, or the rachis and the rachilla. In unbranched ramets the large bipinnately compound leaves occupy the space normally occupied by lateral branches. We suggest that the rachis and rachilla are functionally equivalent to branches, that is, acting as axes of exploration and exploitation of the environment. Key words: allometry; Aralia spinosa; Araliaceae; critical buckling height; pinnately compound leaf; taper.

We investigated quantitative relationships of bacular size to age, length of body, and testicular size in the harp seal (Pagophilus groenlandicus), based on collections made in the northwestern Atlantic from 1985 to 1992. Bacular growth was faster than growth in length of body except in old seals (>9 years of age), in which relative growth was isometric. A pubertal spurt in growth in bacular size occurred between 3 and 4 years of age when length increased by 48.3%, mass by 331%, and density by 185%. Concurrently, length of body showed a spurt in growth of 7.2%. Bacular length reached 90% of its asymptotic size of 17.4 cm at ca. 9 years of age, and bacular mass reached that point relative to its asymptote (49.6 g) later at ca. 20 years. In contrast, length of body reached 90% of asymptotic size (176 cm) at only 5-6 years of age. In old seals, bacular length was correlated positively with length of body and age independently. It averaged 9.9% of length of body in old seals. Bacular size was variable: CV = 8.3% for bacular length and 32.8% for bacular mass in old seals. Testicular size peaked in February and March. For young seals ([less than or equal to] 9 years old), growth in bacular length was isometric, and growth in bacular mass was positively allometric relative to testicular length and mass. In contrast, testicular length and mass of breeding old seals were not correlated significantly with bacular size, length of body, or age. In breeding old seals, testes averaged 10.1 cm in length (range = 7.4-13.2 cm, CV = 10.9%) and 128 g in mass (range = 60.6-204 g, CV = 24.9%), and testicular length averaged 5.7% of length of body. Variation in bacular and testicular size suggests that males have variable reproductive strategies. Comparative analyses on phocid species with known mating systems are needed to test this interpretation. Key words: Pagophilus groenlandicus, harp seal, baculum, allometry, sexual selection, growth

Much research has focused on the connection between development and evolution, with heterochrony being the key concept, defined as evolutionary changes in rates and timing of developmental processes. The methods of analysing heterochrony are examined, and ancestral and descendant ontogenies are compared. Allometry does not deal with time explicitly, unlike heterochrony, and two main approaches to the study of allometry are reviewed.

Size, allometry, and mechanical design were measured for trees of three canopy species in a tropical rain forest in French Guiana. Mechanical design was expressed as the safety factor, using the elastic-stability model, and the wind resistance factor, using the constant-stress model. Changes with ontogeny were described as regressions using stem diameter as the independent variable, and they were compared between species. Height, crown size, and the wind resistance factor increased with ontogeny. The safety factor decreased to a minimum and then increased continuously in thicker trees. The crown width/height ratio did not change with ontogeny. Interspecific differences in allometry and mechanical design were related to the adult stature of the species, and not to shade tolerance. The short stature species (Vouacapoua americana) was less slender (height:DBH [stem diameter at 1.3 m] ratio) and had a higher crown width/height ratio than the tall stature species (Goupia glabra and Dicorynia guianensis). Vouacapoua had a higher safety factor, but a similar wind resistance factor. The safety factors of our study species were lower than those of two temperate tree species because of a higher slenderness. Differences in safety factors between tropical and temperate trees may result from unrealistic assumptions of the elastic-stability model, and may also be related to lower light levels and/or wind rates in the tropics. Key words: allometry; buckling height; constant-stress model; elastic-stability model; French Guiana; mechanical design; safety factor; tree; wind resistance factor.

Irrespective of an organism's size, the proportional sizes of its parts remain constant. An experimental model reveals size-dependent adjustment of segment formation and gene-expression oscillations in vertebrates. See Letter p.101 [...]

1 We examined architectural and life-history traits of 14 abundant non-pioneer tree species at various size classes in a warm-temperate rain forest on Yakushima Island, southern Japan. The 14 species were categorized according to maximum attainable size (five canopy, seven subcanopy and two understorey species). 2 Within each maximum-size category, the relative frequency of trees of 2-8 cm d.b.h. (trunk diameter at breast height) in gaps compared with closed-canopy stands differed between species. In the closed-canopy stands, the positions of the crowns in the heterogeneous canopy differed between species within each of the canopy and subcanopy categories at 8-40 cm d.b.h. 3 We regressed the relationship between d.b.h. and crown architecture by a non-linear allometric equation for the 14 species. There was a continuum from wide-crown species to narrow-crown species within canopy and subcanopy categories at 2-16 cm d.b.h. The two understorey species were wide-crown species throughout their ontogeny. 4 Interspecific differences in both rate of increase of d.b.h. and mortality over 10 years (1983-93) were detected within the canopy and subcanopy categories. 5 Principal component analysis based on five architectural and life-history traits revealed species differentiation within the canopy and subcanopy categories, reflecting a trade-off between responsiveness to increasing light in narrow-crown species and shade tolerance in wide-crown species. Multiple regression analyses suggested that most of these traits could be predicted by the light environments experienced by species rather than by species' maximum sizes. We concluded that species differentiation in this community was primarily related to different regeneration behaviour in gaps by trees of 2-8 cm d.b.h., and to different space occupation in the heterogeneous canopy at 8-16cm d.b.h. Keywords: allometry, canopy heterogeneity, community structure, gap, growth, mortality

Traditionally, aquatic and terrestrial mammals have been believed to differ in the allometric relationship of surface area and body mass. Such differences commonly are assumed to be of adaptive significance. However, no previous analyses have explicitly compared these groups or accounted for bias resulting from phylogenetic relationships. I used Monte Carlo simulations to evaluate the relationship of surface area to body mass of 56 aquatic and terrestrial species of mammals. These procedures specifically incorporate the phylogenetic structure of the data. There was no support for the assumption of differing mass-specific surface areas of marine mammals and terrestrial mammals. Key words: Allometry, marine mammals, Monte Carlo simulations, phylogeny, semiaquatic mammals, surface area

Starting from macroscopic and microscopic facts of cerebellar histology, we propose a new functional interpretation that may elucidate the role of the cerebellum in movement control. The idea is that the cerebellum is a large collection of individual lines (Eccles's 'beams': Eccles et al. 1967a) that respond specifically to certain sequences of events in the input and in turn produce sequences of signals in the output. We believe that the sequence-in/sequence-out mode of operation is as typical for the cerebellar cortex as the transformation of sets into sets of active neurons is typical for the cerebral cortex, and that both the histological differences between the two and their reciprocal functional interactions become understandable in the light of this dichotomy. The response of Purkinje cells to sequences of stimuli in the mossy fiber system was shown experimentally, by Heck on surviving slices of rat and guinea pig cerebellum. Sequential activation of a row of eleven stimulating electrodes in the granular layer, imitating a 'movement' of the stimuli along the folium, produces a powerful volley in the parallel fibers that strongly excites Purkinje cells, as evidenced by intracellular recording. The volley, or 'tidal wave,' has maximal amplitude when the stimulus moves toward the recording site at the speed of conduction in parallel fibers, and much smaller amplitudes for lower or higher 'velocities.' The succession of stimuli has no effect when they 'move' in the opposite direction. Synchronous activation of the stimulus electrodes also had hardly any effect. We believe that the sequences of mossy fiber activation that normally produce this effect in the intact cerebellum are a combination of motor planning relayed to the cerebellum by the cerebral cortex, and information about ongoing movement, reaching the cerebellum from the spinal cord. The output elicited by the specific sequence to which a 'beam' is tuned may well be a succession of well timed inhibitory volleys 'sculpting' the motor sequences so as to adapt them to the complicated requirements of the physics of a multijointed system. Keywords: allometric relation; cerebellum; cerebrocerebellar interaction; motor control; parallel fibers; sequence addressable memory; spatiotemporal activity; synchronicity

Cross-sectional growth data were obtained from the skeletal remains of children from the Iron Age site of K2 near the Limpopo River. Standard measurements of the diaphyseal lengths of the long bones from both limbs were recorded and compared to published skeletal data. For this purpose, data on Eskimo and Aleut skeletons, Libben skeletons, and skeletons from Indian Knoll and Altenerding were used. An attempt to study growth allometrically was made. K2 children were growing as well as children from these other groups. Comparison of data for K2 children with those on living South African 'Cape Coloured' rural children, studied during the late 1980s, shows the similarity of growth of both groups. KEY WORDS Community health, Allometry, Mapungubwe, Long bone

We have analyzed the growth allometry of external body proportions in Efe pygmies from Zaire and combined these data with values from the literature for comparable dimensions in adult pygmies and nonpygmies. We sequentially tested the hypotheses that adult proportion differences between 1) male vs. female Efe, and 2) pygmies vs. nonpygmies result from ontogenetic scaling, or the differential extension of common patterns of growth allometry. Results indicate an almost complete concordance of allometric trajectories for male and female Efe. These preliminary analyses also strongly suggest that adult nonpygmy Africans generally differ from pygmies in their terminal size and correlated allometric consequences, rather than in more fundamental alterations of underlying patterns of growth. Biacromial diameter emerges as the measurement most likely to depart from this general pattern. These results provide further evidence that shifts in systemic growth hormones yielding differences in terminal overall body size may be accompanied by global and coordinated allometric transformations. Certain proportion differences previously interpreted by some as specific evidence of primitive retention in pygmies in fact reflect simple growth allometric correlates of the derived rapid size decrease in these groups. Selected divergent body proportions characterizing adult pygmies, previously interpreted by some as independent evidence of climatic adaptation, also reflect such allometric correlates of ontogenetic scaling. We critically assess arguments that the small overall body size of pygmies was specifically selected for reasons of thermoregulatory efficiency, and consider an alternative or complementary scenario, based on selection for small size in order to reduce caloric requirements. KEY WORDS Ontogenetic scaling, Anthropometrics, Growth physiology, Microevolutionary dwarfism, Tropical forest

The distribution of juvenile cephalopods and adaptive allometry of the brachial crown was studied in samples from two stations in the Scotia Sea. An undescribed Brachioteuthis sp. was the most common species. Galiteuthis glacialis and Alluroteuthis antarcticus were also present at both stations. Histioteuthis eltaninae, Bathyteuthis abyssicola and Psychroteuthis glacialis were found at Station 1, in the open ocean south of the Antarctic Polar Front, and Mastigoteuthis psychrophila and a Chiroteuthis sp. at Station 2, on the South Georgia northwestern slope. Positive allometric growth in the brachial crown may be related to peaks in biomass spectra.

Liver and kidney cortex slices from rat, mouse, rabbit, sheep and cattle of varying body mass are experimentally investigated to determine the allometric relationship between body mass and tissue metabolism. The study reveals that a 11-fold difference exists in the mass-specific basal metabolic rates. The metabolic rate difference indicates the level of energetic costs of sodium pump activity.

Size-dependent variations in the critical buckling height Hcrit and actual height H of plants were determined for a total of 111 species with self-supporting stems ranging in diameter between 0.03 cm [is less than or equal to] D [is less than or equal to] 3.0 m. For each species, experimentally determined values for the physical properties of stems (Young's elastic modulus and bulk tissue density) were used to compute Hcrit. For small species (D < 3 cm), empirically determined critical buckling loads were used to compute Hcrit by means of the Elastica equation and the more traditionally employed Greenhill formula; for larger species (D [is greater than or equal to] 3 cm), Greenhill's formula was used exclusively to estimate Hcrit. Within most of the size-range examined, the predicted values of Hcrit from the Elastica equation and Greenhill's formula were statistically indistinguishable. Regression analyses showed that the interspecific allometry of Hcrit parallels that of H such that the safety factor against the elastic mechanical failure of stems (i.e., Hcrit/H) under their own biomass was roughly constant. Since the safety factor against elastic buckling is independent of plant size, a general allometric 'rule,' Hcrit/H [is approximately equal to] 4, appears to govern the evolution of plant size.

Interspecific correlations between plant height and basal stem diameter (the allometry of height) and between stem length distal to where diameter is measured (the allometry of stem taper) were determined for a total of 265 species with self-supporting stems and for the shoots of five conifers and 15 angiosperm vine species. The allometric equations obtained for these data are proposed as a method to predict the heights of fossil plants for which basal stem diameters are either known or inferred, and to predict the missing lengths of fragmented stems based on the most proximal stem diameters observed.