Exponential mapping of quantitative trait loci governing allometric relationships in organisms

Allometric scaling relationships or quarter-power rules, as a universal biological law, can be viewed as having some genetic component, and the particular genes (or quantitative trait loci, QTL) underlying these allometric relationships can be mapped using molecular markers. We develop a mathematical and statistical model for mapping allometric QTL on the basis of nonlinear power functions using Taylors approximation theory. Simulation studies indicate that the QTL position and effect can be estimated using our model, but the estimation precision can be improved from the higher- over lower-order approximation when the sample size used and gene effects are small. The application of our approach in a real example from forest trees leads to successful detection of a QTL governing the allometric relationship between 3rd-year stem height and 3rd-year stem biomass. It is expected that our model will have broad implications for genetic, evolutionary, biomedical and breeding research.     

Minimizing Bias in Biomass Allometry: Model Selection and Log‐Transformation of Data

Nonlinear regression is increasingly used to develop allometric equations for forest biomass estimation (i.e., as opposed to the traditional approach of log‐transformation followed by linear regression). Most statistical software packages, however, assume additive errors by default, violating a key assumption of allometric theory and possibly producing spurious models. Here, we show that such models may bias stand‐level biomass estimates by up to 100 percent in young forests, and we present an alternative nonlinear fitting approach that conforms with allometric theory.     

Allometric scaling and Bayesian priors for annual survival of birds and mammals

Allometric theory predicts that instantaneous mortality rates scale with body mass with a negative quarter power. Such a relationship would mean that the survival rate of one species is partly predictable from the survival rate of other species. We develop allometric regression models for annual adult survival of birds and mammals, using data collected from the literature. These models conform to the predictions of the allometric theory; the value of negative one-quarter for the scaling parameter is within the 95% credible interval, which is [-0.31, -0.10] for birds and [-0.35, -0.15] for mammals. The predictions are very well supported when evaluated using an independent set of data. The regression models can be used to provide objective and informative Bayesian priors for annual adult survival rates of birds and mammals or to act as a point of comparison in new studies.     

Predicting trophic relations in ecological networks: A test of the Allometric Diet Breadth Model

Few food web theory hypotheses/predictions can be readily tested using likelihoods of reproducing the data. Simple probabilistic models for food web structure, however, are an exception as their likelihoods were recently derived. Here I test the performance of a more complex model for food web structure that is grounded in the allometric scaling of interactions with body size and the theory of optimal foraging (Allometric Diet Breadth Model—ADBM). This deterministic model has been evaluated by measuring the fraction of trophic relations it correctly predicts. I contrasted this value with that produced by simpler models based on body sizes and found that the quantitative information on allometric scaling and optimal foraging does not significantly increase model fit. Also, I present a method to compute the p-value for the fraction of trophic interactions correctly predicted by the ADBM, or any other model, with respect to three probabilistic models. I find that the ADBM predicts significantly more links than random graphs, but other models can outperform it. Although optimal foraging and allometric scaling may improve our understanding of food webs, the ADBM needs to be modified or replaced to find support in the data.     

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。     

An analysis of structure: biomass structure relationships for characteristic species of the western Kalahari,Botswana

Savannah ecosystems are important carbon stocks on the Earth, and their quantification is crucial for understanding the global impact of climate and land‐use changes in savannahs. The estimation of aboveground/belowground plant biomass requires tested allometric relationships that can be used to determine total plant biomass as a function of easy‐to‐measure morphological indicators. Despite recent advances in savannah ecology, research on allometric relations in savannahs remains confined to a few site‐specific studies where basal area is typically used as the main morphometric parameter with plant biomass. We investigate allometric relations at four sites along a 950‐km transect in the Kalahari across mean rainfall gradient 170 mm yr^?1–550 mm yr^?1. Using data from 342 harvested trees/shrubs, we relate basal area, height and crown diameter to aboveground biomass. These relationships are strongest in trees and weakest in small shrubs. Strong allometric relationships are also determined for morphologically similar groups of woody vegetation. We show that crown diameter can be used as an alternative to basal area in allometric relationships with plant biomass. This finding may enhance the ability to determine aboveground biomass over large areas using high‐resolution aerial or satellite imagery without requiring ground‐based measurements of basal area.     

Allometric theory and the mechanical stability of large trees: proof and conjecture

Recent allometric theory has postulated that standing leaf mass will scale as the 3/4 power of stem mass and as the 3/4 power of root mass such that stem mass scales isometrically with respect to root mass across very large vascular plant species with self-supporting stems. We show that the isometric scaling of stem mass with respect to root mass (i.e., M(S) ∝ M(R)) can be derived directly from mechanical theory, specifically from the requirement that wind-induced bending moments acting at the base of stems must be balanced by a counter-resisting moment provided by the root system to prevent uprooting. This derivation provides indirect verification of the allometric theory. It also draws attention to the fact that leaf, stem, and root biomass partitioning patterns must accommodate the simultaneous performance of manifold functional obligations.     

甘肃南部7种高寒杜鹃生物量分配的异速生长关系

生物量分配模式影响着植物个体生长和繁殖到整个群落的质量和能量流动等所有层次的功能, 揭示高寒灌丛的生物量分配模式不仅可以掌握植物的生活史策略, 而且对理解灌丛碳汇不确定性具有重要意义。该研究以甘肃南部高山-亚高山区的常绿灌丛——杜鹃(Rhododendron spp.)灌丛的7个典型种为对象, 采用全株收获法研究了不同物种个体水平上各器官生物量的分配比例和异速生长关系。结果表明: 7种高寒杜鹃根、茎、叶生物量的分配平均比例为35.57%、45.61%和18.83%, 各器官生物量分配比例的物种差异显著; 7种高寒杜鹃的叶与茎、叶与根、茎与根以及地上生物量与地下生物量之间既有异速生长关系, 也有等速生长关系, 异速生长指数不完全支持生态代谢理论和小个体等速生长理论的参考值; 各器官异速生长关系的物种差异显著。结合最优分配理论和异速生长理论能更好地解释陇南山地7种高寒杜鹃生物量的变异及适应机制。     

The Energetic Determination, Spatial Dispersion and Density Dependence of Myrmeleon Ant Lion Pits in Las Cruces, Costa Rica

The amount of space used by an organism is energetically determined. We utilized a population of ant lion larvae in Costa Rica to test allometric theories concerning the use of space by organisms and how different densities of individuals affect the use of space. The area of ant lion trapping pits scaled with mass to the three-quarters power, supporting allometric theory for sessile organisms. Our analyses also show that larger ant lion larvae show spatial repulsion and facultative density dependent pit-building strategies.     

The scaling and selection of sexually dimorphic characters: an example using the Marbled Teal

Current theory and empirical evidence suggests that, if a character is sexually dimorphic as a result of sexual selection, it should be positively allometric (i.e. relatively larger in larger individuals), whereas if the dimorphism is the result of natural selection (e.g. niche divergence), it should be isometric. I show how this can be used to study the selective forces responsible for dimorphic morphological characters, using the monochromatic Marbled Teal Marmaronetta angustirostris as an example. In absolute terms, first-year male teals have a higher body mass, wing length, head length and bill length than females. In relative terms (controlling for body size), males still have longer wings, heads and bills. The scaling in Marbled Teal suggests that bill and head dimorphisms are due to sexual selection, whereas wing dimorphism is due to natural selection. Tail length is sexually monomorphic but positively allometric, possibly because of a display function. Such scaling studies are easy to carry out, and provide a useful complement to direct investigation of the influence of variation in the size of dimorphic characters on mating success, foraging efficiency etc.     

林龄和竞争对日本落叶松各组分生物量异速关系的影响

基于7-、17-、30-和40年生日本落叶松生物量测定数据,应用方差分析和多重比较分析了林龄和林分内树木竞争类型(优势木、平均木和被压木)对各组分生物量分配比例和异速关系的影响,构建了含林龄和树木竞争类型作为哑变量的生物量异速方程,为准确估算日本落叶松人工林生物量和碳储量提供依据。结果表明:(1)林龄显著影响生物量分配比例的异速关系。随林龄增加干生物量比例增大,枝叶生物量比例减小,根生物量逐渐稳定。加入林龄的干、枝和叶生物量方程显著改善。年龄效应在幼龄林阶段作用最显著,需单独构建生物量模型。(2)树木竞争类型对生物量分配的影响小于林龄。立地条件一致下,虽然相同胸径的优势木比劣势木积累更多的枝叶生物量和少的干生物量,但它们分配生物量到不同器官的比例和方式是基本相同的,林内竞争不会导致生物量分配规律由"异速关系理论"向"环境优先理论"转化。因此,常规采用平均木法估算各组分生物量是可行的。(3)在近成熟林分中不同竞争类型树木的根生物量分配比例均较为稳定,采用根茎比比值来估算根生物量是可行的。     

Pitfalls and challenges of estimating population growth rate from empirical data: consequences for allometric scaling relations

The intrinsic rate of increase is a fundamental concept in population ecology, and a variety of problems require that estimates of population growth rate be obtained from empirical data. However, depending on the extent and type of data available (e.g. time series, life tables, life history traits), several alternative empirical estimators of population growth rate are possible. Because these estimators make different assumptions about the nature of age‐dependent mortality and density‐dependence of population dynamics, among other factors, these quantities capture fundamentally different aspects of population growth and are not interchangeable. Nevertheless, they have been routinely commingled in recent ecoinformatic analyses relating to allometry and conservation biology. Here we clarify some of the confusion regarding the empirical estimation of population growth rate and present separate analyses of the frequency distributions and allometric scaling of three alternative, non‐interchangeable measures of population growth. Studies of allometric scaling of population growth rate with body size are additionally sensitive to the statistical line fitting approach used, and we find that different approaches yield different allometric scaling slopes. Across the mix of population growth estimators and line fitting techniques, we find scattered and limited support for the key allometric prediction from the metabolic theory of ecology, namely that log₁₀(population growth rate) should scale as ?0.25 power of log₁₀(body mass). More importantly, we conclude that the question of allometric scaling of population growth rate with body size is highly sensitive to previously unexamined assumptions regarding both the appropriate population growth parameter to be compared and the line fitting approach used to examine the data. Finally, we suggest that the ultimate test of allometric scaling of maximum population growth rates with body size has not been done and, moreover, may require data that are not currently available.     

The effect of allometric partitioning on herbivory tolerance in four species in South China

Herbivory tolerance can offset the negative effects of herbivory on plants and plays an important role in both immigration and population establishment. Biomass reallocation is an important potential mechanism of herbivory tolerance. To understand how biomass allocation affects plant herbivory tolerance, it is necessary to distinguish the biomass allocations resulting from environmental gradients or plant growth. There is generally a tight balance between the amounts of biomass invested in different organs, which must be analyzed by means of an allometric model. The allometric exponent is not affected by individual growth and can reflect the changes in biomass allocation patterns of different parts. Therefore, the allometric exponent was chosen to study the relationship between biomass allocation pattern and herbivory tolerance. We selected four species (Wedelia chinensis, Wedelia trilobata, Merremia hederacea, and Mikania micrantha), two of which are invasive species and two of which are accompanying native species, and established three herbivory levels (0%, 25% and 50%) to compare differences in allometry. The biomass allocation in stems was negatively correlated with herbivory tolerance, while that in leaves was positively correlated with herbivory tolerance. Furthermore, the stability of the allometric exponent was related to tolerance, indicating that plants with the ability to maintain their biomass allocation patterns are more tolerant than those without this ability, and the tendency to allocate biomass to leaves rather than to stems or roots helps increase this tolerance. The allometric exponent was used to remove the effects of individual development on allocation pattern, allowing the relationship between biomass allocation and herbivory tolerance to be more accurately explored. This research used an allometric model to fit the nonlinear process of biomass partitioning during the growth and development of plants and provides a new understanding of the relationship between biomass allocation and herbivory tolerance.     

Gompertz curves,allometry and embryogenesis

A number of new properties of the Gompertz curve are derived. In particular, the curve is shown to be of particular importance in the theory of biological similitude, because of a direct relation to the allometric law. A discussion is included indicating some of the practical limitations of the theory.     

Joint multiple quantitative trait loci mapping for allometries of body compositions and metabolic traits to body weights in broiler

In order to map quantitative trait loci (QTLs) for allometries of body compositions and metabolic traits in chicken, we phenotypically characterize the allometric growths of multiple body components and metabolic traits relative to BWs using joint allometric scaling models and then establish random regression models (RRMs) to fit genetic effects of markers and minor polygenes derived from the pedigree on the allometric scalings. Prior to statistically inferring the QTLs for the allometric scalings by solving the RRMs, the LASSO technique is adopted to rapidly shrink most of marker genetic effects to zero. Computer simulation analysis confirms the reliability and adaptability of the so-called LASSO-RRM mapping method. In the F₂ population constructed by multiple families, we formulate two joint allometric scaling models of body compositions and metabolic traits, in which six of nine body compositions are tested as significant, while six of eight metabolic traits are as significant. For body compositions, a total of 14 QTLs, of which 9 dominant, were detected to be associated with the allometric scalings of drumstick, fat, heart, shank, liver and spleen to BWs; while for metabolic traits, a total of 19 QTLs also including 9 dominant be responsible for the allometries of T4, IGFI, IGFII, GLC, INS, IGR to BWs. The detectable QTLs or highly linked markers can be used to regulate relative growths of the body components and metabolic traits to BWs in marker-assisted breeding of chickens.     

Using the Past to Predict the Present: Confidence Intervals for Regression Equations in Phylogenetic Comparative Methods

Two phylogenetic comparative methods, independent contrasts and generalized least squares models, can be used to determine the statistical relationship between two or more traits. We show that the two approaches are functionally identical and that either can be used to make statistical inferences about values at internal nodes of a phylogenetic tree (hypothetical ancestors), to estimate relationships between characters, and to predict values for unmeasured species. Regression equations derived from independent contrasts can be placed back onto the original data space, including computation of both confidence intervals and prediction intervals for new observations. Predictions for unmeasured species (including extinct forms) can be made increasingly accurate and precise as the specificity of their placement on a phylogenetic tree increases, which can greatly increase statistical power to detect, for example, deviation of a single species from an allometric prediction. We reexamine published data for basal metabolic rates (BMR) of birds and show that conventional and phylogenetic allometric equations differ significantly. In new results, we show that, as compared with nonpasserines, passerines exhibit a lower rate of evolution in both body mass and mass-corrected BMR; passerines also have significantly smaller body masses than their sister clade. These differences may justify separate, clade-specific allometric equations for prediction of avian basal metabolic rates.     

Diversity trends and their ontogenetic basis: an exploration of allometric disparity in rodents

It has been hypothesized that most morphological evolution occurs by allometric differentiation. Because rodents encapsulate a phenomenal amount of taxonomic diversity and, among several clades, contrasting levels of morphological diversity, they represent an excellent subject to address the question: how variable are allometric patterns during evolution? We investigated the influence of phylogenetic relations and ecological factors on the results of the first quantification of allometric disparity among rodents by exploring allometric space, a multivariate morphospace here derived from, and encapsulating all, the ontogenetic trajectories of 34 rodent species from two parallel phylogenetic radiations. Disparity was quantified using angles between ontogenetic trajectories for different species and clades. We found an overlapping occupation of allometric space by muroid and hystricognath species, revealing both clades possess similar abilities to evolve in different directions of phenotypic space, and anatomical diversity does not act to constrain the labile nature of allometric patterning. Morphological features to enable efficient processing of food serve to group rodents in allometric space, reflecting the importance of convergent morphology, rather than shared evolutionary history, in the generation of allometric patterns. Our results indicate that the conserved level of morphological integration found among primates cannot simply be extended to all mammals.