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PubMed2006

Allometry, antilog transformations, and the perils of prediction on the original scale.

Biologists often use allometric equations that take the form of power functions (e.g., Y = aM(b), where M stands for mass and a and b are empirically fitted constants). Typically, these allometric equations are fitted by taking the antilog of log-log regressions. Predictions from these allometric equations are biased, and the bias my be appreciable. Methods for making predictions that correct for the bias are available, but they have rarely, if ever, been used by ecological and evolutionary physiologists. Just as physiologists would not use an instrument that was not properly calibrated, they should not use allometric equations to make predictions unless they account for the bias of those predictions. We analyzed 20 interspecific and 10 intraspecific data sets. We compared predictions from standard allometric equations with those from several alternative methods. Our analyses suggest that the bias of predictions from interspecific data sets may be substantial. For the intraspecific data sets we analyzed, the bias was likely to be small. Biologists, including ecological and evolutionary physiologists, should exercise care when using allometric equations to make predictions, particularly given that methods to adjust for bias are easily implemented.

Animals↗
PubMed2005

Phenotypic plasticity of growth trajectory and ontogenic allometry in response to density for eucalyptus hybrid clones and families.

BACKGROUND: and Aims Response to density is a crucial aspect of the ecology of trees in forests and plantations. Few studies have investigated the genetics of plasticity in response to density for growth traits such as height and circumference through development. METHODS: Two experiments were carried out in the field, the first with full-sib families of Eucalyptus urophylla x E. grandis hybrids, and the second with clones of E. tereticornis x E. grandis hybrids planted across a range of densities (625, 1111 and 2500 trees ha-1). Height, circumference and stem taper were measured through development in both experiments. Variance components were estimated and a repeated measure approach for plasticity and three different methods were used to compare the variance-covariance matrix across densities. KEY RESULTS: Genetic variance was significantly different from zero but the density x genotype interaction was significant only for clone experiments at the adult stage. Significant plasticity for three traits in both experiments was found. In the clone experiments, a significant clone x time x density interaction was found, suggesting that plasticity for growth and stem form is under genetic control. In both experiments, density did not affect environmental correlation, which remained high throughout tree development. The impact of density on genetic correlation was marked in the clone experiment, with a reduced value at lower density, but was not observed in the family trial. The differences between clones and family are mainly explained by the distribution of genetic variation within and among genotypes. CONCLUSIONS: The results suggest that plasticity for growth traits and form of tropical Eucalyptus species is under genetic control and that the environment changes genetic co-variation through ontogeny. The findings confirm that a tree population with a narrow genetic basis (represented by clones) is sensitive to a changing environment, whereas a population with a broader genetic basis (full-sib family here) exhibits a more stable reaction.

Body Size↗
PubMed1990

Selection on wing allometry in Drosophila melanogaster.

Five bivariate distributions of wing dimensions of Drosophila melanogaster were measured, in flies 1) subjected to four defined environmental regimes during development, 2) taken directly from nature in seven U.S. states, 3) selected in ten populations for change in wing form, and 4) sampled from 21 long inbred wild-type lines. Environmental stresses during development altered both wing size and the ratios of wing dimensions, but regardless of treatment all wing dimensions fell near a common allometric baseline in each bivariate distribution. The wings of wild-caught flies from seven widely separated localities, and of their laboratory-reared offspring, also fell along the same baselines. However, when flies were selected divergently for lateral offset from these developmental baselines, response to selection was rapid in every case. The mean divergence in offset between oppositely selected lines was 14.68 SD of the base population offset, after only 15 generations of selection at 20%. Measurements of 21 isofemale lines, founded from wild-caught flies and maintained in small populations for at least 22 years, showed large reductions in phenotypic variance of offsets within lines, but a large increase in the variance among lines. The variance of means of isofemale lines within collection localities was ten times the variance of means among localities of newly established wild lines. These observations show that much additive genetic variance exists for individual dimensions within the wing, such that bivariate developmental patterns can be changed in any direction by selection or by drift. The relative invariance of the allometric baselines of wing morphology in nature is most easily explained as the result of continuous natural selection around a local optimum of functional design.

Animals↗
PubMed1996

Leaf allometry of Salix viminalis during the first growing season.

We established linear and exponential relationships between leaf area (A) and leaf length (L), leaf width (W), W(2), L(2) and LW, in Salix viminalis L. Most relationships were significantly nonlinear, but good fits were obtained with both linear and exponential models. The nonlinear relationship between A and LW differed for leaves from sylleptic and proleptic shoots. Leaves from sylleptic and proleptic shoots also differed in specific leaf area (area/weight). Leaf shape (width/length ratio and position of maximum leaf width) changed with leaf size and differed for leaves from sylleptic and proleptic shoots. Leaf area could be modeled adequately using implicit shape descriptions. A good fit was obtained when the basal and distal parts of the leaf were described as a parabola and an ellipse, respectively. The average area of single leaves and specific leaf area increased both along vertical profiles within shoots and during the growing period. Our results (1) indicate that nonlinear models should be used to estimate leaf area from linear leaf dimensions for plant species with leaves that vary in shape with leaf size, and (2) demonstrate the dependence of leaf characteristics on both sampling date during the growing season and spatial position in the canopy.

Journal Article↗
PubMed2002

Universal scaling in tree and vascular plant allometry: toward a general quantitative theory linking plant form and function from cells to ecosystems.

A general theory of allometric scaling that predicts how the proportions of vascular plants and the characteristics of plant communities change or scale with plant size is outlined. The theory rests, in part, on the assumptions of (1) minimal energy dissipation in the transport of fluid through space-filling, fractal-like, branching vascular networks; and (2) the absence of scaling with plant size in the anatomical and physiological attributes of leaves and xylem. The theory shows how the scaling of metabolism with plant size is central to the scaling of whole-plant form and function. It is shown how allometric constraints influence plant populations and, potentially, processes in plant evolution. Rapidly accumulating evidence in support of the general allometric model is reviewed and new evidence is presented. Current work supports the notion that scaling of how plants utilize space and resources is central to the development of a general synthetic and quantitative theory of plant form, function, ecology and diversity.

Biomass↗
PubMed1991

Tree allometry, leaf size and adult tree size in old-growth forests of western Oregon.

Relationships between tree height and crown dimensions and trunk diameter were determined for shade-tolerant species of old-growth forests of western Oregon. The study included both understory and overstory species, deciduous and evergreen angiosperms and evergreen conifers. A comparison of adult understory species with sapling overstory species of similar height showed greater crown width and trunk diameter in the former, whether the comparison is made among conifers or deciduous trees. Conifer saplings had wider crowns than deciduous saplings, but the crown widths of the two groups converged with increase in tree height. Conifer saplings had thicker trunks than deciduous saplings of similar crown width, possibly because of selection for resistance to stem bending under snow loads. The results suggest that understory species have morphologies that increase light interception and persistence in the understory, whereas overstory species allocate their biomass for efficient height growth, thereby attaining the high-light environment of the canopy. The greater crown widths and the additional strength requirements imposed by snow loads on conifer saplings result in less height growth per biomass increment in conifer saplings than in deciduous saplings. However, the convergence in crown width of the two groups at heights greater than 20 m, and the proportionately smaller effect of snow loads on large trees, may result in older conifers equalling or surpassing deciduous trees in biomass allocation to height growth.

Journal Article↗
PubMed1991

Allometry of acetylene reduction and nodule growth of Robinia pseudoacacia families subjected to varied root zone nitrate concentrations.

The effects of nitrate (NO(3) (-)) on acetylene reduction and growth were examined in nodulated seedlings from three open-pollinated families of black locust (Robinia pseudoacacia L.) grown in sand culture. In the first study, nine-week-old seedlings were supplied with 0.0, 0.5, 1.0, 5.0 or 15.0 mM NO(3) (-), for two weeks during which acetylene reduction and biomass were measured five times. In the second study, eight-week-old seedlings were supplied with 0.0, 1.0 or 5.0 mM NO(3) (-) for 51 days during which acetylene reduction and biomass were measured six times. Results were analyzed with and without adjustments for seedling size. In the first study, 15.0 mM NO(3) (-) significantly decreased total acetylene reduction but lower concentrations did not. In seedlings given 15.0 mM NO(3) (-), both nitrogenase activity and nodule biomass were reduced. Inhibition of nitrogenase activity by NO(3) (-) was reversible. In the second study, both the 1.0 and 5.0 mM NO(3) (-) treatments increased plant growth compared to the control (0.0 mM). At the end of the 51-day treatment period, total acetylene reduction and nodule biomass were greatest in the 1.0 mM NO(3) (-) treatment and least in the 5.0 mM NO(3) (-) treatment. However, when adjusted for seedling size, total acetylene reduction and nodule biomass were similar in the 0.0 and 1.0 mM NO(3) (-) treatments. The greater total acetylene reduction and nodule biomass of seedlings grown with 1.0 mM NO(3) (-) resulted from increased seedling size due to fertilization. After adjustment for plant size, total acetylene reduction, nodule biomass and nitrogenase activity were significantly lower in the 5.0 mM NO(3) (-) treatment compared with the control or 1.0 mM NO(3) (-) treatment. Adjustment for seedling size, by means of allometric principles, appears necessary to interpret treatment effects on total acetylene reduction and its components, nodule biomass and nitrogenase activity correctly.

Journal Article↗
PubMed2004

Tyrannosaurus en pointe: allometry minimized rotational inertia of large carnivorous dinosaurs.

Theropod dinosaurs attained the largest body sizes among terrestrial predators, and were also unique in being exclusively bipedal. With only two limbs for propulsion and balance, theropods would have been greatly constrained in their locomotor performance at large body size. Using three-dimensional restorations of the axial bodies and limbs of 12 theropod dinosaurs, and determining their rotational inertias (RIs) about a vertical axis, we show that these animals expressed a pattern of phyletic size increase that minimized the increase in RI associated with increases in body size. By contrast, the RI of six quadrupedal, carnivorous archosaurs exhibited changes in body proportions that were closer to those predicted by isometry. Correlations of low RI with high agility in lizards suggest that large theropods, with low relative RI, could engage in activities requiring higher agility than would be possible with isometric scaling.

Animals↗
PubMed2000

The allometry of patch selection in ruminants.

An axiomatic feature of food consumption by animals is that intake rate and prey abundance are positively related. While this has been demonstrated rigorously for large herbivores, it is apparent from patch selection trials that grazers paradoxically tend to prefer short, sparse swards to tall, dense swards. Indeed, migratory herbivores often shift from areas of high to low sward biomass during the growing season. As nutritional quality is an inverse function of grass abundance, herbivores appear to sacrifice short-term intake for nutritional gains obtainable by eating sparse forage of higher quality. Explicit models of this trade-off suggest that individual ruminants maximize daily rates of energy gain by choosing immature swards of intermediate biomass. As body mass is related positively to both ruminant cropping rates and digestibility, there should be an allometric link between grass abundance and energy maximization, providing a tool for predicting patterns of herbivore habitat selection. We used previously published studies to develop a synthetic model of trade-offs between forage abundance and quality predicting that optimal sward biomass should scale allometrically with body size. The model predicts size-related variation in habitat selection observed in a guild of grazing ungulates in the Serengeti ecosystem.

Animals↗
PubMed2005

Experimental allometry: effect of size manipulation on metabolic rate of colonial ascidians.

The allometric scaling of metabolic rate of organisms, the three-quarters power rule, has led to a questioning of the basis for the relation. We attacked this problem experimentally for the first time by employing the modular organism, the ascidian that forms a single layered flat colony, as a model system. The metabolic rate and colony size followed the three-quarters power relation, which held even after the colony size was experimentally manipulated. Our results established that the three-quarters power relation is a real continuous function, not an imaginary statistical regression. The fact that all the hypotheses failed to explain why the two-dimensional organism adhered to the three-quarters power relation led us to propose a new hypothesis, in which the allometric relation derives from the self-organized criticality based on local interaction between modulus-comprising organisms.

Animals↗
PubMed2002

Allometry of male genitalia in a species of soldier beetle: support for the one-size-fits-all hypothesis.

Hypotheses about the functions of the male genitalia and the male scape in insects were tested by measuring the slopes of allometric relations in six populations of Chauliognathus scutellaris. All allometric relations used elytron length as the indicator of overall body size. Male genitalia have lower slopes than male pronota (a structure not involved in reproduction), male scapes (secondary sexual characters) have higher slopes than male pronota, and female scapes have slopes that are not different from the slopes of female pronota. These results support Eberhard's one-size-fits-all hypothesis regarding the size of male genitalia in insects, and they raise questions about the role of the male scape in reproductive activities.

Animals↗
PubMed2006

Wood mechanics, allometry, and life-history variation in a tropical rain forest tree community.

Wood density plays a central role in the life-history variation of trees, and has important consequences for mechanical properties of wood, stem and branches, and tree architecture. Wood density, modulus of rupture, modulus of elasticity, and safety factors for buckling and bending were determined for saplings of 30 Bolivian rain forest tree species, and related to two important life-history axes: juvenile light demand and maximum adult stature. Wood density was strongly positively related to wood strength and stiffness. Species safety factor for buckling was positively related to wood density and stiffness, but tree architecture (height : diameter ratio) was the strongest determinant of mechanical safety. Shade-tolerant species had dense and tough wood to enhance survival in the understorey, whereas pioneer species had low-density wood and low safety margins to enhance growth in gaps. Pioneer and shade-tolerant species showed opposite relationships between species traits and adult stature. Light demand and adult stature affect wood properties, tree architecture and plant performance in different ways, contributing to the coexistence of rain forest species.

Biometry↗
PubMed2006

A phyletic perspective on the allometry of plant biomass-partitioning patterns and functionally equivalent organ-categories.

Biomass-partitioning patterns influence the functioning of aquatic and terrestrial vegetation at all levels, ranging from individual growth and reproduction to the flow of mass and energy through entire communities. For this reason, leaf, stem and root dry biomass-partitioning patterns across taxonomically and ecologically diverse seed plants (spermatophytes) have been intensively investigated, both empirically and theoretically. By contrast, phyletically disparate plants (e.g. green and brown algal macrophytes, mosses and pteridophytes) have not been examined to determine whether the partitioning of their body parts into 'leaf', 'stem' and 'root' analogs accords with that of spermatophytes. In this review, the biomass-partitioning patterns of siphonous and brown algal macrophytes, mosses and pteridophytes were compared allometrically with those of spermatophytes and were shown to be largely in statistical accordance (thus lending support to the hypothesis that a single scaling relationship exists across eukaryotic photoautotrophs). This concordance is argued to support the hypothesis of functional equivalence across analogous, but developmentally different, body parts, a feature that permits the use of simpler biological model systems with which to derive analytical explanations for the biomass-partitioning patterns reported for more complex seed plants.

Biomass↗
PubMed2005

Allometry of alarm calls: black-capped chickadees encode information about predator size.

Many animals produce alarm signals when they detect a potential predator, but we still know little about the information contained in these signals. Using presentations of 15 species of live predators, we show that acoustic features of the mobbing calls of black-capped chickadees (Poecile atricapilla) vary with the size of the predator. Companion playback experiments revealed that chickadees detect this information and that the intensity of mobbing behavior is related to the size and threat of the potential predator. This study demonstrates an unsuspected level of complexity and sophistication in avian alarm calls.

Animals↗