Correlation between trunk and branch age in trees as a new parameter in the analysis of tree architecture

A method for characterizing tree form is developed by linear regression of the age of the trunk on the average branch age at different heights. This relationship holds for a wide variety of situations, including both theoretical models and observed tree samples. The intercept of the regression, a, the ‘index of trunk distinctness’, reflects the branching pattern inherent to the species and indicates whether the trunk is erect or not. The slope, b, is termed the ‘crown thickness coefficient’, because it indicates a branching pattern. Tree forms can be classified into nine theoretical groups; three of these are physically impossible. The method was applied to real trees and a and b are shown to be useful tree form characteristics. Possible applications of the method are briefly discussed.     

Precision of allometric scaling equations for trees can be improved by including the effect of ecological interactions

Allometric scaling relationships of the form Y = aX ^b are widely utilized in many types of models and analyses of tree structure. They are often viewed as static relationships where both the scaling exponent (b) and the normalization constant (a) obtain empirical values that are fixed within a single set of data. Among different sets of data, their values can show environmental variability. However, there have been only few attempts to give a mechanistic interpretation for this variability. We used field data to demonstrate how the scaling relationships in trees can be modified by ecological interactions. Moreover, we show how such processes can be incorporated into the scaling models to improve the fit and the information content of the scaling equations. When fixed theoretical scaling exponents were used instead of empirical exponents and when the effect of competitive interactions between trees was described by separate submodels that predicted the value of the normalisation constant in the scaling equations, it was possible to obtain 4–10% improvement in the model fit of three different structural scaling relationships. Our results suggest that unexplained variation in the values of the scaling parameters can be substituted by an identified effect of ecological factors on the value of the normalisation constant. This agrees with recent theoretical suggestions stating that ecological factors can directly influence the value of normalisation constants.     

Correcting for finite spatial scales of self-similarity when calculating fractal dimensions of real-world structures

Fractal geometry is a potentially valuable tool for quantitatively characterizing complex structures. The fractal dimension (D) can be used as a simple, single index for summarizing properties of real and abstract structures in space and time. Applications in the fields of biology and ecology range from neurobiology to plant architecture, landscape structure, taxonomy and species diversity. However, methods to estimate the D have often been applied in an uncritical manner, violating assumptions about the nature of fractal structures. The most common error involves ignoring the fact that ideal, i.e. infinitely nested, fractal structures exhibit self-similarity over any range of scales. Unlike ideal fractals, real-world structures exhibit self-similarity only over a finite range of scales.Here we present a new technique for quantitatively determining the scales over which real-world structures show statistical self-similarity. The new technique uses a combination of curve-fitting and tests of curvilinearity of residuals to identify the largest range of contiguous scales that exhibit statistical self-similarity. Consequently, we estimate D only over the statistically identified region of self-similarity and introduce the finite scale- corrected dimension (FSCD). We demonstrate the use of this method in two steps. First, using mathematical fractal curves with known but variable spatial scales of self-similarity (achieved by varying the iteration level used for creating the curves), we demonstrate that our method can reliably quantify the spatial scales of self-similarity. This technique therefore allows accurate empirical quantification of theoretical Ds. Secondly, we apply the technique to digital images of the rhizome systems of goldenrod (Solidago altissima). The technique significantly reduced variations in estimated fractal dimensions arising from variations in the method of preparing digital images. Overall, the revised method has the potential to significantly improve repeatability and reliability for deriving fractal dimensions of real-world branching structures.     

Plant form based on the pipe model theory II. Quantitative analysis of ramification in morphology

Ramification in tree structure was investigated by the main axis cutting method, which differs from the ordinary stratified clipping method. An axis running from the arbitrary terminal leader of the shoot to the stem base was termed the “main axis”. Cutting the main axis into pieces of constant length gives the “segment layer”, which consists of segments of the main axis and all branches and leaves diverging from the respective segments. There was a linear relationship between the weight of a main axis segment (in the range where leaves exist) of constant length and that of all the parts above the segment. Since plant form is determined by branches diverging regularly from the mother branch or stem, this linear relationship is considered to support the concept of the pipe model theory. It is also suggested that the proportionality constant of the linear relationship may specify the branching structure or ramifications of plant form.     

Growing trees: risks and rewards for society

Forests provide 1.75 billion cubic meters of timber each year and a similar amount of fuel wood. Our understanding of forest ecosystems is far from complete. Biotechnology can provide means to speed up adaptation by forest species in response to pathogen introduction, climate change, or other perturbations. Consensus building on forest issues is always likely to be difficult, as diversity in the nature of forests and their cultural and historical significance must be recognized. The potential risks and possible benefits of deploying or choosing not to deploy forest biotechnology products must be considered on a case-by-case, product- rather than process-driven basis for rational, evidence-based decisions to be reached. Aspects of ecologically neutral field trials, ecological and social perceptions of risk, and steady state and dynamic paradigms of nature are discussed alongside challenges facing biotechnology in adequately avoiding or limiting risks to allow deployment in forests. Communicated by Ronald Sederoff     

A simulation model of tree architecture development based on growth response to local light environment

A new model of three-dimensional tree architecture development was made, in which the growth of branches depends on their local light environment. The unit of the tree architecture is a linear stem called the branch unit (BU). Current-year BU's have leaves at their distal end. The local light environment is calculated considering mutual shading among leaved BU's. During the growth of a model tree, the number of leaved BU's increases and mutual shading becomes severe. The shadling leads to production of fewer new BU's and the death of some BU's, both of which restrain the overcrowding of BU's. The shape of the crowns of trees grown in a model forest stand varies with their position in the stand in a similar way as observed in real forests. This also results from the growth response of BU's to their local light environment. A model tree in which the photoassimillates were shared equally among the BU's was much disadvantaged in competition with the original model trees.     

Sampling-through-time in birth-death trees

I consider the constant rate birth-death process with incomplete sampling. I calculate the density of a given tree with sampled extant and extinct individuals.This density is essential for analyzing datasets which are sampled through time. Such datasets are common in virus epidemiology as viruses in infected individuals are sampled through time. Further, such datasets appear in phylogenetics when extant and extinct species data is available.I show how the derived tree density can be used (i) as a tree prior in a Bayesian method to reconstruct the evolutionary past of the sequence data on a calender-timescale, (ii) to infer the birth- and death-rates for a reconstructed evolutionary tree, and (iii) for simulating trees with a given number of sampled extant and extinct individuals which is essential for testing evolutionary hypotheses for the considered datasets.     

Intrinsic units of growth for teak trees

Attempts were made to evaluate intrinsic biological units of growth of teak trees, which were identified as age and size at inflection point of diameter at breast height. The observations were further utilized in estimating fractal dimension of the tree crown, which is an important eco-physiological characteristic of the species. A total of 38 teak plantations belonging to different age groups and site quality classes were selected for estimating the intrinsic units. Altogether, 57 stumps were identified for gathering information on age and size at inflection point at stump level (10 cm above ground) from the selected plantations. Photographs of the upper surface of the selected stumps were taken using a digital camera. Counting of annual rings/ring age and recording the radial distance from pith to each of the annual rings were done directly (visually) by using Photoshop and CorelDRAW software in a computer. Thus the age and size at inflection point at stump level were estimated. The values of intrinsic units at breast height level were estimated using allometric relations. The present study revealed that these units viz., (namely) age and size (diameter) at inflection point were 6 years and 6 cm at stump level, respectively. The corresponding values at breast-height level were estimated as 8 years and 10.6 cm including the bark. Fractal dimension was calculated based on the growth parameters, which were estimated through stump analysis. The fractal dimension worked out to 2.13 for the species. The value of fractal dimension obtained was biologically justifiable considering the light demanding nature of the species.     

An equivalent cable model for neuronal trees with active membrane

A non-uniform equivalent cable model of membrane voltage changes in branching neuronal trees with active ion channels has been developed. A general branching condition is formulated, extending Rall's 3/2 power rule for passive dendritic trees so that non-uniform cable segments can be treated. The theoretical results support the use of the dendritic profile model of Clements and Redman. The theory is then applied to dendrites of different morphological type yielding qualitative different response behaviour. Received: 25 September 1997 / Accepted: 13 November 1997     

Majority-rule (+) consensus trees

The construction of a consensus tree to summarize the information of a given set of phylogenetic trees is now routinely a part of many studies in systematic biology. One popular method is the majority-rule consensus tree. In this paper we introduce and characterize a new consensus method that refines the majority-rule tree by adding certain compatible clusters satisfying a simple criterion.     

Nodulation of legume trees from South East Brazil

Summary An extended survey of nodulation of legume trees from South-East Brazilian forests was conducted. Six new species from the Caesalpinioideae, 23 from the Mimosoideae and 27 from the Papilionoideae are reported to have nodules. Nitrogenase activity (acetylene reduction) was tested for all nodules and rhizobia were isolated from the most active.     

Gaussian approximations for phylogenetic branch length statistics under stochastic models of biodiversity

Stein's method for Gaussian approximations and derived results are used to study the distribution of two phylogenetic branch length statistics: the total height of cherries and the sum of external branch lengths. The Gaussian approximations are obtained under a particular model of phylogenetic tree recently introduced by Popovic. Under an appropriate normalization the model is shown to behave similarly as the coalescent, and the approximations given here are also valid in this context.     

兴安落叶松分枝格局的分形特征

对于树木分枝格局分形特征的定量描述,可以加深对树木生长过程的理解。本文采用分形几何学对兴安落叶松(Larix gmelini)的分枝格局进行研究,结果表明1)兴安落叶松分枝格局是一种分形结构,存在自相似性。2)兴安落叶松分枝格局的分形维数介于1.4~1.7之间,揭示了它的结构复杂性程度和占据生态空间、利用生态空间的能力。分形维数在树木光合作用及生长发育研究中是一个有用的参数。     

An ANN model for treatment prediction in HBV patients

Two types of antiviral treatments, namely, interferon and nucleoside/nucleotide analogues are available for hepatitis infections. The selection of drug and dose determined using known pharmacokinetics and pharmacodynamics data is important. The lack of sufficient information for pharmacokinetics of a drug may not produce the desired results. Artificial neural network (ANN) provides a novel model-independent approach to pharmacokinetics and pharmacodynamics data. ANN model is created by supervised learning of 90 patients sample to predict the treatment strategy (lamivudine only and Lamivudine + Interferon) on the basis of viral load, liver function test, visit number, treatment duration, ethnic area, sex, and age. The model was trained with 68 (77.3%) samples and tested with 20 (22.7%) samples. The model produced 92% accuracy with 92.8% sensitivity and 83.3% specificity.     

Shear effects on failure of hollow trees

It is shown that bending stresses in a non-cracked hollow trunk can never explain failure. Consequently, stem breakage due to bending stress cannot be primary failure. It is shown by field studies and simple theoretical assessments that the initiation of a longitudinal shear crack is primarily responsible for failure. Due to cracking, the bending stresses increase and failure by bending happens as secondary failure. As a result, bending theory of a non-cracked closed circular pipe is inappropriate to describe failure of hollow trees. In the appendix is shown the reason for high shear stresses at the tree base and why the shear stresses increase more due to hollowness than to bending stresses.     

An allometric analysis of the giraffe cardiovascular system

There has been co-evolution of a long neck and high blood pressure in giraffes. How the cardiovascular system (CVS) has adapted to produce a high blood pressure, and how it compares with other similar sized mammals largely is unknown. We have measured body mass and heart structure in 56 giraffes of both genders ranging in body mass from 18 kg to 1500 kg, and developed allometric equations that relate changes in heart dimensions to growth and to cardiovascular function. Predictions made from these equations match measurements made in giraffes. We have found that heart mass increases as body mass increases but it has a relative mass of 0.51 ± 0.7% of body mass which is the same as that in other mammals. The left ventricular and interventricular walls are hypertrophied and their thicknesses are linearly related to neck length. Systemic blood pressure increases as body mass and neck length increase and is twice that of mammals of the same body mass. Cardiac output is the same as, but peripheral resistance double that predicted for similar sized mammals. We have concluded that increasing hydrostatic pressure of the column of blood during neck elongation results in cardiac hypertrophy and concurrent hypertrophy of arteriole walls raising peripheral resistance, with an increase in blood pressure following.     

Iterative character weighting based on mutation frequency: A new method for constructing phyletic trees

Summary In this paper we present an iterative character weighting method for the construction of phyletic trees. An initial tree is used to calculate the character weights, which are the number of mutations normalized so that the possible range is corrected for. The weights obtained are used to adjust the tree; this process is iterated until a stable tree is found. Using data generated according to a model tree, we show that the trees constructed by the iterative character weighting method converge to the true underlying tree. Using biological data, the trees become closer to the systematic classification of the species concerned, and patterns conflicting with the phylogenetic pattern can be singled out. The method involves a combination of minimal length methods and similarity methods, whereby the strict parsimony criterion is relaxed.     

Interspecific patterns underlying variations in allometric relationship of sympatric Sterculiaceae species in a Bornean rainforest

We compared aboveground tree forms among closely related species in two genera of the Sterculiaceae (Scaphium and Heritiera) in a Bornean mixed dipterocarp forest. Two significant allometric patterns were detected: a negative correlation between the height at the onset of branching and the slope of the species-specific Cr (crown width)-D (stem diameter) allometric relationship for juveniles (D<10 cm), and a negative correlation between H _max (observed maximum height) and the Cr-D slope. The slope of the Cr-D allometric relationship of branched trees was significantly steeper than that of monoaxial (unbranched) trees in most species. These results suggest that the branching growth habit is better adapted than the monoaxial growth habit to crown expansion, and that the morphology of short species is better adapted to crown expansion than that of tall species. We did not detected significant correlations between the height at the onset of branching and the slope of the H (height)-D allometric relationship for juvenile trees, and between H _max and the H-D slope. In addition, the monoaxial and branched juvenile of most species did not differ significantly in the allometric slopes of the H-D relationship. Therefore, the study does not support the hypotheses that a monoaxial growth habit favors rapid height growth and that tall species have allometries better adapted to height growth.     

Effect of selection on the topology of genealogical trees

Selection is one of the factors that most influence the shape of genealogical trees. Here we report results of simulations of the infinite-sites version of Moran's model of population genetics aiming at quantifying how the presence of selection affects the branching pattern (topology) of binary genealogical trees. In particular, we consider a scenario of purifying or negative selection in which all mutations are deleterious and each new mutation reduces the fitness of the individual by the same fraction. Analysis of five statistical measures of tree balance or symmetry borrowed from taxonomy indicates that the genealogical trees of samples of populations in which selection is actuating are in the average more asymmetric than neutral trees and that this effect is enhanced by increasing the sample size. However, a quantitative evaluation of the power of these balance measures to detect a tree topology significantly distinct from the neutral one indicates that they are not useful as tests of neutrality of mutations.