Development of a mathematical method for classifying and comparing tree architecture using parameters from a topological model of a trifurcating botanical tree

This paper describes a model for the topological mapping of trifurcating botanical trees. The model was based on a system of modular units that represented the interconnectivity of shoot meristems (terminal segments) and internodes (internal segments) within whole plant canopies, organized with increasing centrifugal ordering. The model was capable of describing the dynamics of plant growth as expressed by changes in topological parameters over time. Preliminary calculations for experimental trees indicated that the model represents growth in a biologically sound manner. Methods are described for the calculation of the architecture parameters size, size-complexity, structural complexity, and tree asymmetry index (TAI). Parameter calculations were based on the mathematical principles developed for the classification of bifurcating dendrite trees, and were designed to both extract structural information, and to enable statistical comparison between trees of different size. Parameters were mathematically adjusted for trifurcation, and appeared to be able to represent quantitatively the architectural properties of tree structures. In addition to the calculation of the TAI for trifurcating trees, new methods were developed to enable comparisons to be made of the architectural complexity of trifurcating trees of differing size. These were based on the principle of the pair-wise comparison of the mean centrifugal order number (MCON) with respect to segments against highest order number. We argue and illustrate that this principle can be more informative than that of pair-wise comparison of the MCON against tree degree (topological size). Further improvements to this method were made by examining branching points (vertices) rather than segments (links) to calculate the MCON.     

Neural rate equations for bursting dynamics derived from conductance-based equations

A method of obtaining rate equations from conductance-based equations is developed and applied to fast-spiking and bursting neocortical neurons. It involves splitting systems of conductance-based equations into fast and slow subsystems, and averaging the effects of fast terms that drive the slowly varying quantities by showing that their average is closely proportional to the firing rate. The dependence of the firing rate on the injected current is then approximated in the analysis. The resulting behavior of the slow variables is then substituted back into the fast equations, with the further approximation of replacing the fast voltages in these terms by effective values. For bursting neurons the method yields two coupled limit-cycle oscillators: a self-exciting oscillator for the slow variables that commences limit-cycle oscillations at a critical current and modulates a fast spike-generating oscillator, thereby leading to slowly modulated bursts with a group of spikes in each burst. The dynamics of these coupled oscillators are then verified against those of the conductance-based equations. Finally, it is shown how to place the results in a form suitable for use in mean-field equations for neural population dynamics.     

Predicting root biomass from branching patterns of Douglas-fir root systems

There are many examples of branching networks in nature, such as tree crowns, river systems, arteries and lungs. These networks have often been described as being self-similar, or following scale-invariant branching rules, and this property has been used to derive several scaling laws. In this paper we model root systems of Douglas-fir ( Pseudotsuga menziesii var. glauca (Beissn.) Franco) as branching networks following several simple branching rules. Our objective is to establish a relationship between trunk diameter and root biomass. We explore the effect of the self-similar branching assumption on this relationship. Using data collected from a mature stand in British Columbia, we find that branching asymmetry and the rate of root taper change with root size, thereby violating the assumption of self-similarity. However, the data are in general agreement with Leonardo da Vinci's area-preserving branching hypothesis. We use the field data to parameterize two models, one assuming self-similar branching and a second incorporating the measured size dependencies of branching parameters. The two models differ by only a small amount (≈8%) in their predictions. For both models, the predicted relationship between trunk diameter and root biomass is in good concordance with previously published empirical data. We conclude that the assumption of self-similar branching, although violated by the data, nevertheless provides a useful tool for predicting the allometric relationship between trunk diameter and root biomass. Finally, we use our models to show that the geometric properties of individual bifurcations fundamentally change the root biomass cost of different root topologies.     

Allometric equations to predict the total aboveground biomass of tree species in a planted forest in Egypt

The aim of this study is to estimate the total above‐ground biomass (TAGB), stem height (H), diameter at breast height (dbh) and basal area of five tree species (ages 7‐8 years) irrigated by municipal sewage water in the Egyptian‐Chinese friendship forest, Sadat City, Egypt. From the biomass data that obtained through destructive sampling, models for predicting aboveground biomass were developed. The highest values for stem density and height were estimated for Eucalyptus citriodora, while the lowest value for density was obtained for Dalbergia sissoo and stem height for Khaya senegalensis. The highest values for basal area and dbh were obtained for Casuarina spp., while the lowest values were recorded for Dalbergia sissoo. Eucalyptus camaldulensis had the highest stand stem biomass and TAGB (55.5, 83.9 t DW ha^‐1, respectively). In addition, Casuarina spp. had the highest leafy branches biomass (32.5 t DW ha^‐1) while Dalbergia sissoo had the lowest values for all tree components. All the generated allometric equations had high correlation coefficients at high probability levels. Moreover, the results revealed that not only the dbh data can be used as independent variable for biomass determination, but also stem height and size index are recommended for biomass estimation (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A stochastic model of tree architecture and biomass partitioning: application to Mongolian Scots pines

Background and Aims

Mongolian Scots pine (Pinus sylvestris var. mongolica) is one of the principal species used for windbreak and sand stabilization in arid and semi-arid areas in northern China. A model-assisted analysis of its canopy architectural development and functions is valuable for better understanding its behaviour and roles in fragile ecosystems. However, due to the intrinsic complexity and variability of trees, the parametric identification of such models is currently a major obstacle to their evaluation and their validation with respect to real data. The aim of this paper was to present the mathematical framework of a stochastic functional–structural model (GL2) and its parameterization for Mongolian Scots pines, taking into account inter-plant variability in terms of topological development and biomass partitioning.

Methods

In GL2, plant organogenesis is determined by the realization of random variables representing the behaviour of axillary or apical buds. The associated probabilities are calibrated for Mongolian Scots pines using experimental data including means and variances of the numbers of organs per plant in each order-based class. The functional part of the model relies on the principles of source–sink regulation and is parameterized by direct observations of living trees and the inversion method using measured data for organ mass and dimensions.

Key Results

The final calibration accuracy satisfies both organogenetic and morphogenetic processes. Our hypothesis for the number of organs following a binomial distribution is found to be consistent with the real data. Based on the calibrated parameters, stochastic simulations of the growth of Mongolian Scots pines in plantations are generated by the Monte Carlo method, allowing analysis of the inter-individual variability of the number of organs and biomass partitioning. Three-dimensional (3D) architectures of young Mongolian Scots pines were simulated for 4-, 6- and 8-year-old trees.

Conclusions

This work provides a new method for characterizing tree structures and biomass allocation that can be used to build a 3D virtual Mongolian Scots pine forest. The work paves the way for bridging the gap between a single-plant model and a stand model.     

Polymers derived from hemicellulosic parts of lignocellulosic biomass

Furfural, which is directly derived from the hemicellulosic parts of lignocellulosic biomass, is considered as one of the most promising platform chemicals to manufacture commodity chemical products such as polymers and their monomers. Its production has already been commercialized. In this review, potentially relevant methods for producing important chemicals from furfural, which are used as monomers for different polymers, and for the polymerization of furfural and its derivatives (e.g., furfuryl alcohol), have been discussed. First, the production of furfural from different lignocellulosic biomasses is presented. Next, the synthesis of various monomers and their highest available yields from furfural are discussed. The polymers that can be directly produced from furfural and its derivatives are explored. Finally, the challenges of producing furfural-based products have been highlighted.

     

A new method for non-destructive measurement of biomass, growth rates, vertical biomass distribution and dry matter content based on digital image analysis

BACKGROUND AND AIMS: Biomass is an important trait in functional ecology and growth analysis. The typical methods for measuring biomass are destructive. Thus, they do not allow the development of individual plants to be followed and they require many individuals to be cultivated for repeated measurements. Non-destructive methods do not have these limitations. Here, a non-destructive method based on digital image analysis is presented, addressing not only above-ground fresh biomass (FBM) and oven-dried biomass (DBM), but also vertical biomass distribution as well as dry matter content (DMC) and growth rates. METHODS: Scaled digital images of the plants silhouettes were taken for 582 individuals of 27 grass species (Poaceae). Above-ground biomass and DMC were measured using destructive methods. With image analysis software Zeiss KS 300, the projected area and the proportion of greenish pixels were calculated, and generalized linear models (GLMs) were developed with destructively measured parameters as dependent variables and parameters derived from image analysis as independent variables. A bootstrap analysis was performed to assess the number of individuals required for re-calibration of the models. KEY RESULTS: The results of the developed models showed no systematic errors compared with traditionally measured values and explained most of their variance (R(2) > or = 0.85 for all models). The presented models can be directly applied to herbaceous grasses without further calibration. Applying the models to other growth forms might require a re-calibration which can be based on only 10-20 individuals for FBM or DMC and on 40-50 individuals for DBM. CONCLUSIONS: The methods presented are time and cost effective compared with traditional methods, especially if development or growth rates are to be measured repeatedly. Hence, they offer an alternative way of determining biomass, especially as they are non-destructive and address not only FBM and DBM, but also vertical biomass distribution and DMC.     

Predicting tree diameter and height from above-ground biomass for four eucalypt species

Summary Previous work has suggested that tree stems are structured dimensionally to resist the forces to which they are subjected by the weight of the crown and the action of wind, snow and other loads on the crown. This proposition has been used to develop allometric relationships relating diameter at breast height or height of individual trees growing in even-aged monoculture to their above-ground fresh biomass. These models have practical application as estimators of tree diameters or heights from tree biomass as extensions of mechanistically based models of forest tree growth which predict tree biomasses. The present work applied these models to Eucalyptus regnans F. Muell, E. delegatensis R. Baker, E. nitens (Deane: Maiden) Maiden and E. grandis Hill ex Maiden trees, growing in plantation or regrowth stands, aged between 1.5 and 20 years, at eight geographically diverse sites extending from temperate to sub-tropical regions of Australia. While the models held for the various species at the various sites, their parameter values differed significantly between sites and/or species. This suggested there may be some inadequacy in the models. However, the differences were small and it was found reasonable to fit single models across all species and sites for practical use in estimating diameter or height. The errors about predicted values of height and diameter from these models were quantified. The models were also found to estimate diameter or height with little loss of precision when dry biomass was used in place of fresh biomass.     

A software tool for standardised non-destructive biomass estimation in short rotation forestry

Following an evaluation of the various methods available for non-destructive biomass estimation in short rotation forestry, a standardised procedure was defined and incorporated into a computer programme (BioEst). Special efforts were made to ensure that the system can be used by people who are unfamiliar with computers and mathematics. BioEst provides an interface between a calliper and a spreadsheet programme which was written in Microsoft Excel macro language. Therefore, it is simple to modify the programme and create personal protocols. BioEst can be run on a portable PC with Microsoft Excel for Windows. The computer continuously recalculates an estimate of the amount of biomass per hectare, as well as some summary statistics, when fed data on shoot diameter obtained by making row-section-wise measurements with a standard digital calliper. BioEst is available without cost from the author.     

An immunoglobulin preparation as a calibrating agent for the gel filtration method

The fractional composition of commercial immunoglobulin was studied by the method of gel filtration on ultragel AcA-34 and the possibility of its use for the calibration of a chromatographic column was shown. The fractionation of a specimen of IgG revealed the presence of 4 fractions. Their molecular weights corresponded to dimers, monomers, Fab fragments and low-molecular peptides. The qualitative fractional composition of the preparation was shown to be stable during 3 years of storage, as well as after keeping the preparation at 37 degrees C for 1 month. The attested characteristic of each IgG fraction, the distribution coefficient (Kav), was established. The use of a specimen of immunoglobulin obtained with the use of the modified Cohn's method--as calibrant will make it possible to calibrate the columns for a shorter period and to control the correctness of the analysis.     

Modification of tree architecture by a gall-forming aphid

Herbivory may substantially alter the architectural structure of plants. Among insects, gall-formers that substantially manipulate host traits may have a profound effect on the plants even at low densities. The aphid, Baizongia pistaciae induces banana-like large galls on the terminal buds of Pistacia palaestina. We hypothesized that these large galls are associated with the shape of the plant which may grow as a tree or a bush. In the natural Mediterranean forest, we monitored the effects of the galls on infested branches. In the year of gall formation, usually (~95%) there is neither elongation nor branching beyond the position of the gall. However, in the following years, galled branches produced more lateral branches (branching) than ungalled branches. This effect persists for at least 2 years. Consequently, galled branches carried more leaves and tended to gain more biomass than ungalled branches. Galling did not affect fruit yield. We suggest that repeated galling by B. pistaciae may promote bush-like architecture in P. palaestina.     

Branch architecture,light interception and crown development in saplings of a plagiotropically branching tropical tree,Polyalthia jenkinsii (Annonaceae)

To investigate crown development patterns, branch architecture, branch-level light interception, and leaf and branch dynamics were studied in saplings of a plagiotropically branching tree species, Polyalthia jenkinsii Hk. f. & Thoms. (Annonaceae) in a Malaysian rain forest. Lengths of branches and parts of the branches lacking leaves ('bare' branches) were smaller in upper branches than in lower branches within crowns, whereas lengths of 'leafy' parts and the number of leaves per branch were larger in intermediate than in upper and lower branches. Maximum diffuse light absorption (DLA) of individual leaves was not related to sapling height or branch position within crowns, whereas minimum DLA was lower in tall saplings. Accordingly, branch-level light interception was higher in intermediate than in upper and lower branches. The leaf production rate was higher and leaf loss rate was smaller in upper than in intermediate and lower branches. Moreover, the branch production rate of new first-order branches was larger in the upper crowns. Thus, leaf and branch dynamics do not correspond to branch-level light interception in the different canopy zones. As a result of architectural constraints, branches at different vertical positions experience predictable light microenvironments in plagiotropic species. Accordingly, this pattern of carbon allocation among branches might be particularly important for growth and crown development in plagiotropic species.     

Microbial and plant derived biomass for removal of heavy metals from wastewater

Discharge of heavy metals from metal processing industries is known to have adverse effects on the environment. Conventional treatment technologies for removal of heavy metals from aqueous solution are not economical and generate huge quantity of toxic chemical sludge. Biosorption of heavy metals by metabolically inactive non-living biomass of microbial or plant origin is an innovative and alternative technology for removal of these pollutants from aqueous solution. Due to unique chemical composition biomass sequesters metal ions by forming metal complexes from solution and obviates the necessity to maintain special growth-supporting conditions. Biomass of Aspergillus niger, Penicillium chrysogenum, Rhizopus nigricans, Ascophyllum nodosum, Sargassum natans, Chlorella fusca, Oscillatoria anguistissima, Bacillus firmus and Streptomyces sp. have highest metal adsorption capacities ranging from 5 to 641 mg g(-1) mainly for Pb, Zn, Cd, Cr, Cu and Ni. Biomass generated as a by-product of fermentative processes offers great potential for adopting an economical metal-recovery system. The purpose of this paper is to review the available information on various attributes of utilization of microbial and plant derived biomass and explores the possibility of exploiting them for heavy metal remediation.     

A new method to estimate branch biomass from terrestrial laser scanning data by bridging tree structure models

Background and AimsBranch biomass and other attributes are important for estimating the carbon budget of forest stands and characterizing crown structure. As destructive measuring is time-consuming and labour-intensive, terrestrial laser scanning (TLS) as a solution has been used to estimate branch biomass quickly and non-destructively. However, branch information extraction from TLS data alone is challenging due to occlusion and other defects, especially for estimating individual branch attributes in coniferous trees.MethodsThis study presents a method, entitled TSM_tls, to estimate individual branch biomass non-destructively and accurately by combining tree structure models and TLS data. The TSM_tls method constructs the stem-taper curve from TLS data, then uses tree structure models to determine the number, basal area and biomass of individual branches at whorl level. We estimated the tree structural model parameters from 122 destructively measured Scots pine (Pinus sylvestris) trees and tested the method on six Scots pine trees that were first TLS-scanned and later destructively measured. Additionally, we estimated the branch biomass using other TLS-based approaches for comparison.Key ResultsTree-level branch biomass estimates derived from TSM_tls showed the best agreement with the destructive measurements [coefficient of variation of root mean square error (CV-RMSE) = 9.66 % and concordance correlation coefficient (CCC) = 0.99], outperforming the other TLS-based approaches (CV-RMSE 12.97–57.45 % and CCC 0.43–0.98 ). Whorl-level individual branch attributes estimates produced from TSM_tls showed more accurate results than those produced from TLS data directly.ConclusionsThe results showed that the TSM_tls method proposed in this study holds promise for extension to more species and larger areas.     

单木生物量模型估计区域尺度生物量的不确定性

采用系统抽样体系江西省固定样地杉木连续观测数据和生物量数据,通过Monte Carlo法反复模拟由单木生物量模型推算区域尺度地上生物量的过程,估计了江西省杉木地上总生物量。基于不同水平建模样本量n及不同决定系数R~2的设计,分别研究了单木生物量模型参数变异性及模型残差变异性对区域尺度生物量估计不确定性的影响。研究结果表明:2009年江西省杉木地上生物量估计值为(19.84±1.27)t/hm~2,不确定性占生物量估计值约6.41%。生物量估计值和不确定性值达到平稳状态所需的运算时间随建模样本量及决定系数R~2的增大而减小;相对于模型参数变异性,残差变异性对不确定性的影响更小。     

A program for simulation of nerve equations with branching geometries

A computer program has been developed for simulation of electrical activity in neurons with complex branching morphology, multiple channel types, and inhomogeneous channel distribution. The program is based around an interpreter and screen editor for flexible specification of nerve properties and analysis of simulation results. Efficient simulation of the nerve specification is accomplished with procedure calls to fast, compiled routines for integration of the nerve equations.     

Carbon allocation in a Costa Rican dry forest derived from tree ring analysis

The rising discussion on carbon balance of tropical forests often does not consider the sequestration potential of secondary dry forests, which are becoming an increasing importance due to land use change and reforestation. We have developed an easy applicable tool for the estimation of biomass increment of tropical secondary forest stands on the base of tree ring analysis. The existence of annual rings was shown by a combination of anatomical examination and radiocarbon estimations. With tree ring analysis, forest inventories and destructive sampling the above-ground biomass increment of secondary forest stands of age between 9 and 48 years in the dry forest region of Guanacaste, Costa Rica were estimated. The above-ground biomass increment of the tree layer varies between 2.4 and 3.2 Mg/ha yr in different stands. Lianas contribute with up to 23% additional production. Differences in productivity among the stands along a chronosequence were not significant. The measured carbon allocation potential of 1.7–2.1 Mg C/ha yr lies in the range of reported values from other tropical dry forests and old growth humid forests as well.