Zero-sum allocational strategies determine the allometry of specific leaf area

? Premise of the study: Specific leaf area (SLA) is a critical component of the leaf economics spectrum, and many functional leaf traits have been empirically demonstrated to covary with SLA. However, a complete understanding of how change in leaf size influences SLA has not yet emerged. ? Methods: To help develop a more complete understanding of the determinants of variability in SLA, we present a covariation model of leaf allometry that predicts a zero-sum interdependence of leaf thickness, density, and surface area on leaf mass. We test the model's predictions on measurements of 900 leaves from 44 angiosperm species. ? Key results: We observe that "diminishing returns," the negative allometry (slope < 1) of surface area versus mass, does not hold universally across species. Rather, the scaling of SLA is linked to the relative allocation to thickness and density. Specifically, diminishing returns are observed when leaves grow thicker, more than their density decreases, with increasing mass. Finally, we confirm model predictions that the allometric dependence of area, thickness, and density on mass can be well approximated by a zero-sum allocational process. ? Conclusions: Our work adds to the growing body of evidence that allometric covariation is a hallmark of the scaling behavior of complex plant and leaf traits. Moreover, because our model makes predictions based on allocational constraints, it provides a foundation to understand how deviations from zero-sum tradeoffs in allocation to leaf thickness, density, or area determine the allometry of SLA and, ultimately, underlie adaptive strategies within and across plant species.     

Evaluating scaling models in biology using hierarchical Bayesian approaches

Theoretical models for allometric relationships between organismal form and function are typically tested by comparing a single predicted relationship with empirical data. Several prominent models, however, predict more than one allometric relationship, and comparisons among alternative models have not taken this into account. Here we evaluate several different scaling models of plant morphology within a hierarchical Bayesian framework that simultaneously fits multiple scaling relationships to three large allometric datasets. The scaling models include: inflexible universal models derived from biophysical assumptions (e.g. elastic similarity or fractal networks), a flexible variation of a fractal network model, and a highly flexible model constrained only by basic algebraic relationships. We demonstrate that variation in intraspecific allometric scaling exponents is inconsistent with the universal models, and that more flexible approaches that allow for biological variability at the species level outperform universal models, even when accounting for relative increases in model complexity.     

Plant allometry, leaf nitrogen and phosphorus stoichiometry, and interspecific trends in annual growth rates

• Background Life forms as diverse as unicellular algae,zooplankton, vascular plants, and mammals appear to obey quarter-powerscaling rules. Among the most famous of these rules is Kleiber's(i.e. basal metabolic rates scale as the three-quarters powerof body mass), which has a botanical analogue (i.e. annual plantgrowth rates scale as the three-quarters power of total bodymass). Numerous theories have tried to explain why these rulesexist, but each has been heavily criticized either on conceptualor empirical grounds. • N,P-Stoichiometry Recent models predicting growth rateson the basis of how total cell, tissue, or organism nitrogenand phosphorus are allocated, respectively, to protein and rRNAcontents may provide the answer, particularly in light of theobservation that annual plant growth rates scale linearly withrespect to standing leaf mass and that total leaf mass scalesisometrically with respect to nitrogen but as the three-quarterspower of leaf phosphorus. For example, when these relationshipsare juxtaposed with other allometric trends, a simple N,P-stoichiometricmodel successfully predicts the relative growth rates of 131diverse C₃ and C₄ species. • Conclusions The melding of allometric and N,P-stoichiometrictheoretical insights provides a robust modelling approach thatconceptually links the subcellular ‘machinery’ ofprotein/ribosomal metabolism to observed growth rates of uni-and multicellular organisms. Because the operation of this ‘machinery’is basic to the biology of all life forms, its allometry mayprovide a mechanistic explanation for the apparent ubiquityof quarter-power scaling rules.     

On the vegetative biomass partitioning of seed plant leaves, stems, and roots

A central goal of comparative life-history theory is to derive the general rules governing growth, metabolic allocation, and biomass partitioning. Here, we use allometric theory to predict the relationships among annual leaf, stem, and root growth rates (GL, GS, and GR, respectively) across a broad spectrum of seed plant species. Our model predicts isometric scaling relationships among all three organ growth rates: GL is proportional to GS is proportional to GR. It also provides a conceptual basis for understanding the differences in the absolute amounts of biomass allocated to construct the three organ types. Analyses of a large compendium of biomass production rates across diverse seed plant species provide strong statistical support for the predictions of the theory and indicate that reproductive investments may scale isometrically with respect to vegetative organ growth rates. The general rules governing biomass allocation as indexed by the scaling exponents for organ growth rates are remarkably indifferent to plant size and taxonomic affiliation. However, the allometric "constants" for these relationships differ numerically as a function of phenotypic features and local environmental conditions. Nonetheless, at the level of both inter- and intraspecific comparisons, the same proportional biomass allocation pattern holds across extant seed plant species.     

Modelling below- and above-ground biomass for non-woody and woody plants

BACKGROUND AND AIMS: Intraspecific relationships between below- and above-ground biomass (MB and MA, respectively) have been studied extensively to evaluate environmental effects on growth and development at the level of the individual plant. However, no current theoretical model for this relationship exists for broad interspecific trends. The aims of this paper are to provide a model and to test its predictions using a recently assembled, large database (1406 data entries for 257 species). METHODS: An allometric model was derived to predict the relationship between MB and MA for non-woody and woody plants based on previously developed scaling relationships for leaf, stem and root standing biomass and annual growth rates. The predictions of this model were tested by comparing the numerical values of predicted scaling exponents (the slopes of log-log regression curves) with those observed for the database. KEY RESULTS AND CONCLUSIONS: For non-woody plants and the juveniles of woody species, the model predicts an isometric scaling relationship (i.e. MB proportional, variant MA). For woody plants, a complex scaling function is predicted. But, for a particular set of biologically reasonable conditions, the model predicts MB proportional, variant MA across woody plants. These predictions accord reasonably well with observed statistical trends when non-woody and woody plants are studied separately (n=1061 and 345 data entries, respectively). Although the reliability of regression formulas to estimate MB based on MA measurements increased with increasing plant size, estimates of MB can be as much as two orders of magnitude off, even when using regression formulas with r2 >0.90 and F >53,000.     

Lack of Evidence for 3/4 Scaling of Metabolism in Terrestrial Plants

Scaling, as the translation of information across spatial, temporal, and organizational scales, is essential to predictions and understanding in all sciences and has become a central issue in ecology. A large body of theoretical and empirical evidence concerning allometric scaling in terrestrial individual plants and plant communities has been constructed around the fractal volume-filling theory of West, Brown, and Enquist （the WBE model）. One of the most thought-provoking findings has been that the metabolic rates of plants, like those of animals, scale with their size as a 3/4 power law. The earliest, single most-important study cited in support of the application of the WBE model to terrestrial plants claims that whole-plant resource use in terrestrial plants scales as the 3/4 power of total mass, as predicted by the WBE model. However, in the present study we show that empirical data actually do not support such a claim. More recent studies cited as evidence for 3/4 scaling also suffer from several statistical and data-related problems. Using a forest biomass dataset including 1 266 plots of 17 main forest types across China, we explored the scaling exponents between tree productivity and tree mass and found no universal value across forest stands. We conclude that there is not sufficient evidence to support the existence of a single constant scaling exponent for the metabolism-biomass relationship for terrestrial plants.     

Lack of Evidence for 3/4 Scaling of Metabolism in Terrestrial Plants

Scaling, as the translation of information across spatial, temporal, and organizational scales, is essential to predictions and understanding in all sciences and has become a central issue in ecology. A large body of theoretical and empirical evidence concerning allometric scaling in terrestrial individual plants and plant communities has been constructed around the fractal volume-filling theory of West, Brown, and Enquist (the WBE model). One of the most thought-provoking findings has been that the metabolic rates of plants, like those of animals, scale with their size as a 3/4 power law. The earliest, single most-important study cited in support of the application of the WBE model to terrestrial plants claims that whole-plant resource use in terrestrial plants scales as the 3/4 power of total mass, as predicted by the WBE model.However, in the present study we show that empirical data actually do not support such a claim. More recent studies cited as evidence for 3/4 scaling also suffer from several statistical and data-related problems. Using a forest biomass dataset including 1 266 plots of 17 main forest types across China, we explored the scaling exponents between tree productivity and tree mass and found no universal value across forest stands. We conclude that there is not sufficient evidence to support the existence of a single constant scaling exponent for the metabolism-biomass relationship for terrestrial plants.     

植物的表型可塑性、异速生长及其入侵能力

表型可塑性是指同一个基因型对不同环境响应产生不同表型的特性,特定性状的可塑性本身可以遗传,也可以接受选择而发生进化。植物个体的异速生长是指生物体某一特征的相对生长速率不等于第二种特征的相对生长速率的特性,该特性是由物种的遗传性决定的一种固定特征,植物往往朝着最佳的异速生长曲线进化。植物特定基因型在不同环境下,诸如生物量分配和种群几何学上的一些表型差异,既可由异速生长造成,也可由表型可塑性造成。植物本身的异速生长是一种"外观可塑性",而异速生长曲线的改变才是真正的可塑性。植物的表型可塑性、异速生长对于入侵植物的适应具有重要意义。干扰等异质性生境下表型可塑性成为物种生存扩散的有利性状,表型可塑性强的物种更有可能成为广布种。植物本身的异速生长特性或其异速生长曲线的改变都能影响其入侵能力。     

Genetic mapping of allometric scaling laws

Many biological processes, from cellular metabolism to population dynamics, are characterized by particular allometric scaling relationships between rate and size (power laws). A statistical model for mapping specific quantitative trait loci (QTLs) that are responsible for allometric scaling laws has been developed. We present an improved model for allometric mapping of QTLs based on a more general allometry equation. This improved model includes two steps: (1) use model II regression analysis to estimate the parameters underlying universal allometric scaling laws, and (2) substitute the estimated allometric parameters in the mixture-based mapping model to obtain the estimation of QTL position and effects. This model has been validated by a real example for a mouse F2 progeny, in which two QTLs were detected on different chromosomes that determine the allometric relationship between growth rate and body weight.     

A statistical model for the genetic origin of allometric scaling laws in biology

Many biological processes, from cellular metabolism to population dynamics, are characterized by particular allometric scaling (power-law) relationships between size and rate. Although such allometric relationships may be under genetic determination, their precise genetic mechanisms have not been clearly understood due to a lack of a statistical analytical method. In this paper, we present a basic statistical framework for mapping quantitative genes (or quantitative trait loci, QTL) responsible for universal quarter-power scaling laws of organic structure and function with the entire body size. Our model framework allows the testing of whether a single QTL affects the allometric relationship of two traits or whether more than one linked QTL is segregating. Like traditional multi-trait mapping, this new model can increase the power to detect the underlying QTL and the precision of its localization on the genome. Beyond the traditional method, this model is integrated with pervasive scaling laws to take advantage of the mechanistic relationships of biological structures and processes. Simulation studies indicate that the estimation precision of the QTL position and effect can be improved when the scaling relationship of the two traits is considered. The application of our model in a real example from forest trees leads to successful detection of a QTL governing the allometric relationship of third-year stem height with third-year stem biomass. The model proposed here has implications for genetic, evolutionary, biomedicinal and breeding research.     

Interpreting reproductive allometry: Individual strategies of allocation explain size-dependent reproduction in plant populations

Size-dependent or allometric relationships between reproductive and vegetative size are extremely common in plant populations. Reproductive allometry where plant size differences are due to environmental variability has been interpreted both as an adaptive strategy of plant growth and allocation, and as the product of fixed developmental constraints. Patterns of development are crucial in defining reproductive allometry but development is not fixed across individuals. For example, environmental adversity (e.g. resource impoverishment) tends to favor reproduction at relatively small sizes – an adaptive response to environmental adversity. While small individuals may have lower reproductive output than large individuals, all plants should maximize their reproductive output and relative allocation to reproduction may be constant across sizes. Thus, where individual plants within a population initiate reproduction at different sizes, no significant reproductive allometry is an appropriate null expectation. Reproductive allometry occurs in plant populations where initiating reproduction at small sizes yields relatively high or low reproductive size at final development. Both of these outcomes are common in plant populations. Our interpretation of reproductive allometry combines previous adaptive and developmental constraint interpretations, and is the first to successfully explain the range of relationships in plant populations where relative allocation has been observed to increase, decrease or remain constant will increasing plant size.     

Species richness, endemism, and abundance patterns: tests of two fractal models in a serpentine grassland

Although scaling relationships that characterize fractal species distributions offer an exciting potential for unification in biogeography, empirical support for fractal theory remains the subject of debate. We synthesize and test multiple predictions of two interrelated fractal models and a null model of random placement using Californian serpentine grassland data describing the spatial location of over 37 000 individually identified plants. The endemics–area relationship and species‐abundance distribution recently derived from a community‐level fractal property performed poorly because of an inaccurate assumption of homogeneity among species. In contrast, a species‐level fractal model that incorporates species‐level differences predicted abundances well, but systematically overestimated endemism and predicted a species–area relationship that violated the observed power law. These findings indicate that in order to make predictions based on the existence of a power‐law species–area relationship, ecologists need a unifying theory of how the community‐level fractal property arises in the presence of species‐level distributional differences.     

Scaling relations for a functionally two-dimensional plant: Chamaesyce setiloba (Euphorbiaceae)

Many characteristics of plants and animals scale with body size as described by allometric equations of the form Y = βM(α), where Y is an attribute of the organism, β is a coefficient that varies with attribute, M is a measure of organism size, and α is another constant, the scaling exponent. In current models, the frequently observed quarter-power scaling exponents are hypothesized to be due to fractal-like structures. However, not all plants or animals conform to the assumptions of these models. Therefore, they might be expected to have different scaling relations. We studied one such plant, Chamaesyce setiloba, a prostrate annual herb that grows to functionally fill a two-dimensional space. Number of leaves scaled slightly less than isometrically with total aboveground plant mass (α ≈ 0.9) and substantially less than isometrically with dry total stem mass (α = 0.82), showing reduced allocation to leaf as opposed to stem tissue with increasing plant size. Additionally, scalings of the lengths and radii of parent and daughter branches differed from those predicted for three-dimensional trees and shrubs. Unlike plants with typical three-dimensional architectures, C. setiloba has distinctive scaling relations associated with its particular prostrate herbaceous growth form.     

Analysing the allometry of multiple interacting traits

Since form and function are tightly integrated in plants, and since plant attributes often scale allometrically, it follows that plant allometry is inherently multivariate. Unfortunately, traditional statistical methods for studying allometric relationships are very restrictive and do not allow one to model multivariate allometric patterns that follow realistic biological hypotheses. In this paper I describe a new statistical test (‘d-sep test’) that allows one to test, and potentially falsify, alternative multivariate orderings of cause-and-effect in the context of allometry.     

Allometry of cetacean forelimb bones

This study examines the allometric scaling relationships of the cetacean humerus, radius, and ulna. Bone lengths and diameters were measured for 20 species of odontocete and three species of mysticete cetaceans, representing eight of the nine extant cetacean families. The scaling of individual bone proportions (bone length vs. cranio-caudal diameter, bone length vs. dorso-ventral diameter), and of individual bone dimensions against estimated body mass, are compared to models of geometric and elastic similarity. The geometric similarity model describes the scaling relationship of bone length vs. cranio-caudal diameter and body mass vs. cranio-caudal diameter for the humerus only; geometric similarity also describes the scaling relationship of body mass vs. bone length for all three bones. None of the scaling relationships fits the elastic similarity model. The scaling relationships of bone length vs. dorso-ventral diameter for all three bones, and bone length vs. cranio-caudal diameter for the radius and ulna, exhibit negative allometry, indicating that large bones are less robust than small bones. Negative allometry of structural support elements has not been previously described for terrestrial mammals or plants. The high relative swimming speeds of small delphinids may generate sufficient stresses to require more robust bones relative to those of larger whales. © 1994 Wiley-Liss, Inc.     

Competition and Allometry in Kochia scoparia

Comparisons between crowded and uncrowded Kochia scoparia individualsdemonstrate pronounced effects of competition on plant allometryas well as on the distributions of different aspects of size.Non-destructive measurements of height and stem diameter and,for a subset of the populations, the number and length of leavesand branches, were taken at three times, and the plants wereharvested after the third measurement. The sequential measurementsafforded the opportunity to obtain information of the effectsof competition on allometric growth trajectories of individuals,as well as on static inter-individual allometric relationships. The distributions of most size measures appeared to be normalfor the uncrowded population. Crowded populations developeda negatively-skewed height distribution and a high-inequalitymass distribution, whereas the diameter distributions remainednormal. Plants grown without neighbours showed simple allometricrelationships between height, diameter and weight. For isolatedplants, the 'static' allometric relationship between plantsof different sizes and the allometric growth trajectory of individualswere similar. Crowded populations showed complex allometry;the static inter-individual relationships between height, diameterand weight were curvilinear (on log-log scale). There were largedifferences in the allometric growth slopes of uncrowded vs.crowded plants. Allometric relationships between stem diameterand plant mass, and between total length of leaves and totallength of branches, did not seem to be altered by competition. The data suggest that height was the most important aspect ofsize influencing future growth of individuals in the crowdedpopulation. Only plants above a certain height were able tocontinue to grow from the second to third measurement in thecrowded population. This supports the hypothesis that asymmetriccompetition for light is the cause of the allometric changesand of the increase in size variability due to competition.Copyright1994, 1999 Academic Press Allometric growth, allometry, competition, growth, Kochia     

Reproductive allometry in Malaysian rain forest trees: Biomechanics versus optimal allocation

Summary Quantitative predictions of reproductive allometry in iteroparous plants may be derived from two bodies of theory: biomechanics and optimal allocation theory. Biomechanical theory predicts allometric scaling exponents between reproductive (R) and vegetative (V) biomass in the range of 0.44–1.33, while very general models of life history evolution predictR–V exponents > 1 in all cases. These predictions are examined in light of allometric patterns of flower and fruit production in 32 species of Malaysian rain forest trees. Among these species the mean estimatedR–V exponents are in the range 1.8–2.0 for staminate flower, pistillate flower and fruit production. This range of exponent values provides unambiguous support for some of the general predictions of optimal allocation models, but not for biomechanical theory. Optimal allocation models also predict a positive relationship between species size andR–V slope and a positive relationship between species size andR–V intercept parameters. The latter, but not the former prediction is supported by the data.R–V allometries in sexes of dioecious species were also found to differ in intercept, though not slope, reflecting smaller sizes at reproductive onset in staminate trees. Further critical examinations of reproductive allometry are encouraged as a relatively unexplored avenue for increasing the contact of theory and data in studies of life history evolution in long-lived organisms such as tropical trees.     

BODY AND LIMB SIZE DISSOCIATION AT THE ORIGIN OF BIRDS: UNCOUPLING ALLOMETRIC CONSTRAINTS ACROSS A MACROEVOLUTIONARY TRANSITION

The origin of birds and powered flight is a classic major evolutionary transition. Research on their origin often focuses on the evolution of the wing with trends of forelimb elongation traced back through many nonavian maniraptoran dinosaurs. We present evidence that the relative forelimb elongation within avian antecedents is primarily due to allometry and is instead driven by a reduction in body size. Once body size is factored out, there is no trend of increasing forelimb length until the origin of birds. We report that early birds and nonavian theropods have significantly different scaling relationships within the forelimb and hindlimb skeleton. Ancestral forelimb and hindlimb allometric scaling to body size is rapidly decoupled at the origin of birds, when wings significantly elongate, by evolving a positive allometric relationship with body size from an ancestrally negative allometric pattern and legs significantly shorten by keeping a similar, near isometric relationship but with a reduced intercept. These results have implications for the evolution of powered flight and early diversification of birds. They suggest that their limb lengths first had to be dissociated from general body size scaling before expanding to the wide range of fore and hindlimb shapes and sizes present in today's birds.     

Morphological variation in Puya (Bromeliaceae): an allometric study

A group of representative species of the genus Puya was studied to determine if there are allometric relationships between vegetative and floral parts, whether these relationships correlate with their pollination system and if plant size is correlated with elevation and latitude. Fifty-three species representing the morphological variation and distribution of the genus were studied. Total plant height, as well as leaf, inflorescence, petal and sepal length were measured and these data subjected to univariate and multivariate analyses. To test for correlation between plant size and altitudinal and latitudinal distribution, ANOVAs were performed. When the pollination system of a species is known, additional multivariate and univariate analyses were also performed. The results indicate that the characters studied are correlated with a size component, exhibiting positive allometry for sepal and petal length and negative allometry for leaf length. Inflorescence length is an isometric character. There was no significant correlation between plant size and altitudinal or latitudinal distribution. The ANOVAs show that the only character correlated to pollinator type was petal length. Small plants with small flowers are correlated to pollinators such as insects, while medium to large plants with medium to large-sized flowers are correlated with pollinators such as birds and bats. Large plants have small flowers, that are more evident and attract more pollinators.     

Scaling indicator and planning plane: An indicator and a visual tool for exploring the relationship between urban form,energy efficiency and carbon emissions

Ecosystems and other naturally resilient systems exhibit allometric scaling in the distribution of sizes of their elements. In this paper we define an allometry inspired scaling indicator for cities that is a first step toward quantifying the stability borne of a complex systems’ hierarchical structural composition. The scaling indicator is calculated using large census datasets and is analogous to fractal dimension in spatial analysis. Lack of numerical rigor and the resulting variation in scaling indicators – inherent in the use of box counting mechanism for fractal dimension calculation for cities – has been one of the hindrances in the adoption of fractal dimension as an urban indicator of note. The intra-urban indicator of scaling in population density distribution developed here is calculated for 58 US cities using a methodology that produces replicable results, employing large census-block wise population datasets from the 2010 US Census and the 2007 US Economic Census. We show that rising disparity – as measured by the proposed indicator of population density distribution in census blocks in Metropolitan Statistical Areas adversely affects energy consumption efficiency and carbon emissions in cities and leads to a higher urban carbon footprint. We then define a planning plane as a visual and analytic tool for incorporation of scaling indicator analysis into policy and decision-making.