Simplifying the decision matrix for estimating fine root production by the sequential soil coring approach

Sequential soil coring is a commonly used approach to measure seasonal root biomass and necromass, from which root production can be estimated by maximum–minimum, sum of changes, compartment-flow model, and/or decision matrix methods. Among these methods, decision matrix is the most frequently used. However, the decision matrix, often underestimating fine root production, is frequently misused in research due to inadequate documentation of its underlying logic. In this paper, we reviewed the decision matrix method and provided mathematical logic for the development of the matrix, by which not only root production but also mortality and decomposition rates can be calculated. To ease its use for large datasets, we developed simplified equations to facilitate computation of root production, mortality and decomposition to be used in MS Excel or R. We also presented results from calculations by an example using empirical data from boreal forests to show proper calculations of root production, mortality and decomposition. The simplified decision matrix presented here shall promote its application in ecology, especially for large datasets.     

Calculating as many fluxes as possible in underdetermined metabolic networks

A frequently occurring problem in Metabolic Flux Analysis is that the linear equation systems are underdetermined. A procedure for determining which reaction velocities can be calculated in underdetermined metabolic systems from measured rates and computing these velocities is given. The method is based on the null-space matrix to the stoichiometry matrix corresponding to the reactions with unknown velocities. Moreover, an elementary representation of the null-space is presented. This representation enables one to find those sets of measurable velocities that allow calculation of a certain non-measurable rate. The approach is illustrated by an example from monosaccharide metabolism.     

Application of an enthalpy balance model of the relation between growth and respiration to temperature acclimation of Eucalyptus globulus seedlings

The enthalpy balance model of growth uses measurements of the rates of heat and CO(2) production to quantify rates of decarboxylation, oxidative phosphorylation and net anabolism. Enthalpy conversion efficiency (eta(H)) and the net rate of conservation of enthalpy in reduced biosynthetic products (R(SG)DeltaH(B)) can be calculated from metabolic heat rate (q) and CO(2) rate (R(CO2)). eta(H) is closely related to carbon conversion efficiency and the efficiency of conservation of available electrons in biosynthetic products. R(SG)DeltaH(B) and eta(H) can be used, together with biomass composition, to describe the rate and efficiency of growth of plant tissues. q is directly related to the rate of O(2) consumption and the ratio q:R(CO2) is inversely related to the respiratory quotient. We grew seedlings of Eucalyptus globulus at 16 and 28 degrees C for four to six weeks, then measured q and R(CO2) using isothermal calorimetry. Respiratory rate at a given temperature was increased by a lower growth temperature but eta(H) was unaffected. Enthalpy conversion efficiency - and, therefore, carbon conversion efficiency - decreased with increasing temperature from 15 to 35 degrees C. The ratio of oxidative phosphorylation to oxygen consumption (P/O ratio) was inferred in vivo from eta(H) and by assuming a constant ratio of growth to maintenance respiration with changing temperature. The P/O ratio decreased from 2.1 at 10-15 degrees C to less than 0.3 at 35 degrees C, suggesting that decreased efficiency was not only due to activity of the alternative oxidase pathway. In agreement with predictions from non-equilibrium thermodynamics, growth rate was maximal near 25 degrees C, where the calculated P/O ratio was about half maximum. We propose that less efficient pathways, such as the alternative oxidase pathway, are necessary to satisfy the condition of conductance matching whilst maintaining a near constant phosphorylation potential. These conditions minimize entropy production and maximize the efficiency of mitochondrial energy conversions as growing conditions change, while maintaining adequate finite rates of energy processing.     

Relationship between milk energy intake and growth rate in suckling mammalian young at peak lactation: an updated meta-analysis

The milk energy intakes and growth rates of suckling young at peak lactation of 62 mammalian species and subspecies, all measured using either the weigh–suckle–weigh, the isotope dilution or the isotope transfer method, were evaluated. The mean daily gross energy intakes (GEI) were as low as 12 kJ in a small rodent (mouse) to as high as 249 MJ in a phocid seal (hooded seal Cystophora cristata ), while the daily growth rates at peak lactation ranged from 0.4 to 5.9 kg. Several allometric equations were calculated to explore the relationships between gross energy intake via milk and body weight (BW), growth rate and BW, as well as between gross energy intake via milk and growth rate. The results suggest that both GEI via milk and growth rates are proportional to BW to the power of 0.82. Accordingly, the metabolic weight of suckling mammalian young should be expressed as BW^0.82. The predictive values of the calculated equations indicate that suckling young at peak lactation consume c . 883 kJ day⁻¹ kg⁻¹ BW^0.82 and have growth rates of 32 g day⁻¹ kg⁻¹ BW^0.82. However, large deviations for some species and few outliers were found. These equations could be used to predict values for species that have not been studied, provided that the BW falls within the range of weights used to derive the equations.     

Determining the parametric structure of models

In this paper we develop a comprehensive approach to determining the parametric structure of models. This involves considering whether a model is parameter redundant or not and investigating model identifiability. The approach adopted makes use of exhaustive summaries, quantities that uniquely define the model. We review and generalise previous work on evaluating the symbolic rank of an appropriate derivative matrix to detect parameter redundancy, and then develop further tools for use within this framework, based on a matrix decomposition. Complex models, where the symbolic rank is difficult to calculate, may be simplified structurally using reparameterisation and by finding a reduced-form exhaustive summary. The approach of the paper is illustrated using examples from ecology, compartment modelling and Bayes networks. This work is topical as models in the biosciences and elsewhere are becoming increasingly complex.     

Calculability analysis in underdetermined metabolic networks illustrated by a model of the central metabolism in purple nonsulfur bacteria

Metabolite balancing has turned out to be a powerful computational tool in metabolic engineering. However, the linear equation systems occurring in this analysis are often underdetermined. If it is difficult or impossible to find the missing constraints, it is nevertheless feasible in some cases to determine the values of a subset of the unknown rates. Here, a procedure for finding out which reaction rates can be uniquely calculated in underdetermined metabolic networks and computing these rates is given. The method is based on the null space to the stoichiometry matrix corresponding to the reactions with unknown rates. It is shown that this method is considerably easier to handle than an algorithm given previously (Van der Heijden et al., 1994a). Furthermore, a useful elementary representation of the null space is presented which is closely related with the elementary flux modes. This unique representation is central to a more general approach to observability/calculability analysis. In particular, it allows one to find, in an easy way, those sets of measurable rates that enable a calculation of a certain unknown rate. Besides, rates which are never calculable by metabolite balancing may be easily detected by this method. The applicability of these methods is illustrated by a model of the central metabolism in purple nonsulfur bacteria. The photoheterotrophic growth of these representatives of anoxygenic photosynthetic bacteria is stoichiometrically analyzed. Interesting metabolic constraints caused by the necessary balancing of NADPH can be detected in a highly underdetermined system. This is, to our knowledge, the first application of stoichiometric analysis to the metabolic network in this bacteria group using metabolite balancing techniques. A new software tool, the FluxAnalyzer, is introduced. It allows quantitative and structural analysis of metabolic networks in a graphical user interface.     

Inference of S-system models of genetic networks by solving one-dimensional function optimization problems

Voit and Almeida have proposed the decoupling approach as a method for inferring the S-system models of genetic networks. The decoupling approach defines the inference of a genetic network as a problem requiring the solutions of sets of algebraic equations. The computation can be accomplished in a very short time, as the approach estimates S-system parameters without solving any of the differential equations. Yet the defined algebraic equations are non-linear, which sometimes prevents us from finding reasonable S-system parameters. In this study, we propose a new technique to overcome this drawback of the decoupling approach. This technique transforms the problem of solving each set of algebraic equations into a one-dimensional function optimization problem. The computation can still be accomplished in a relatively short time, as the problem is transformed by solving a linear programming problem. We confirm the effectiveness of the proposed approach through numerical experiments.     

Motif recognition and alignment for many sequences by comparison of dot-matrices

Calculation of dot-matrices is a widespread tool in the search for sequence similarities. When sequences are distant, even this approach may fail to point out common regions. If several plots calculated for all members of a sequence set consistently displayed a similarity between them, this would increase its credibility. We present an algorithm to delineate dot-plot agreement. A novel procedure based on matrix multiplication is developed to identify common patterns and reliably aligned regions in a set of distantly related sequences. The algorithm finds motifs independent of input sequence lengths and reduces the dependence on gap penalties. When sequences share greater similarity, the same approach converts to a multiple sequence alignment procedure.     

Calculation of tilt angles for crystal specimen orientation adjustment using double-tilt and tilt-rotate holders

In this communication we wish to present a group of new equations which can be used to calculate the tilt angle for crystal specimen orientation adjustment in the transmission electron microscope. The experiments were concerned with double-tilt and tilt-rotate holders and the new equations deduced using matrix geometry. The specimen orientation adjustment using the tilt angles calculated by these equations is considered to be more convenient and less time-consuming than following the Kikuchi map method. Our method avoids the difficulties associated with orientation adjustment of severely strained and small grain size specimens using the Kikuchi map procedure. The algorithms for deducing the new equations, together with an experimental example using the equations, are described.     

Diagenetic stoichiometry and benthic nutrient fluxes at the sediment–water interface of Lake Illawarra, Australia

Benthic flux measurements of O₂, TCO₂ and inorganic nutrients were made at three stations (seagrass beds, shallow bare sand and deep mud) in Lake Illawarra (Australia) to compare the characteristics of diagenesis and benthic biogeochemical processes for different primary producers (seagrass or microphytobenthos, (MPB)) and/or sediment types (sand or mud).Seagrass beds exhibited the highest gross primary productivity while the lowest rates occurred at the deep mud station. At the shallow bare sand station only, the gross primary production (GPP) and respiration (R) were balanced, while at the other two stations, R exceeded GPP by as much as 2 fold, indicating more organic carbon was decomposed than produced at the time of sampling. In general, nutrient fluxes displayed typical diurnal variation.Organic carbon oxidation scenarios, evaluated by either calcium carbonate dissolution or sulfate reduction models, indicated that both models can represent organic matter mineralization. The difference of estimated total carbon oxidized in this lake using the two models was small, ranging from 0.2% at deep mud station to maximum of 21% at seagrass station. In addition, N₂ flux rates (net denitrification), estimated using carbon and nitrogen stoichiometry, were of similar magnitude as the rates estimated using LOICZ budget modeling or measured using the N₂/Ar technique.Finally, a comparison of calculated diffusive fluxes and measured fluxes using incubation cores indicated that the results were of similar magnitude at the deep mud station, but the incubation cores fluxes were much higher than the calculated diffusive fluxes at the other two stations. This may have been caused by bioturbation or bioirrigation.     

Measurement of pharyngeal cross-sectional area by finite element analysis.

A noninvasive measurement of pharyngeal cross-sectional area (CSA) during sleep would be advantageous for research studies. We hypothesized that CSA could be calculated from the measured pharyngeal pressure and flow by finite element analysis (FEA). The retropalatal airway was visualized by using a fiber-optic scope to obtain the measured CSA (mCSA). Flow was measured with a pneumotachometer, and pharyngeal pressure was measured with a pressure catheter at the palatal rim. FEA was performed as follows: by using a three-dimensional image of the upper airway, a mesh of finite elements was created. Specialized software was used to allow the simultaneous calculation of velocity and area for each element by using the measured pressure and flow. In the development phase, 677 simultaneous measurements of CSA, pressure, and flow from one subject during non-rapid eye movement (NREM) and rapid eye movement (REM) sleep were entered into the software to determine a series of equations, based on the continuity and momentum equations, that could calculate the CSA (cCSA). In the validation phase, the final equations were used to calculate the CSA from 1,767 simultaneous measurements of pressure and flow obtained during wakefulness, NREM, and REM sleep from 14 subjects. In both phases, mCSA and cCSA were compared by Bland-Altman analysis. For development breaths, the mean difference between mCSA and cCSA was 0.0 mm2 (95% CI, -0.1, 0.1 mm2). For NREM validation breaths, the mean difference between mCSA and cCSA was 1.1 mm2 (95% CI 1.3, 1.5 mm2). Pharyngeal CSA can be accurately calculated from measured pharyngeal pressure and flow by FEA.     

Stability and oscillations in coupled systems.

In this paper are given criteria for stability and oscillations in coupled systems. The criteria are calculated by the determination of eigenvalues of a coupling matrix of an input-output relation which can be described by a set of differential equations of 1st order.     

An EGS4 based Monte Carlo code for the calculation of organ equivalent dose to a modified Yale voxel phantom.

Organ or tissue equivalent dose, the most important quantity in radiation protection, cannot be measured directly. Therefore it became common practice to calculate the quantity of interest with Monte Carlo methods applied to so-called human phantoms, which are virtual representations of the human body. The Monte Carlo computer code determines conversion coefficients, which are ratios between organ or tissue equivalent dose and measurable quantities. Conversion coefficients have been published by the ICRP (Report No. 74) for various types of radiation, energies and fields, which have been calculated, among others, with the mathematical phantoms ADAM and EVA. Since then progress of image processing, and of clock speed and memory capacity of computers made it possible to create so-called voxel phantoms, which are a far more realistic representation of the human body. Voxel (Volume pixel) phantoms are built from segmented CT and/or MRI images of real persons. A complete set of such images can be joined to a 3-dimensional representation of the human body, which can be linked to a Monte Carlo code allowing for particle transport calculations. A modified version of the VOX_TISS8 human voxel phantom (Yale University) has been connected to the EGS4 Monte Carlo code. The paper explains the modifications, which have been made, the method of coupling the voxel phantom with the code, and presents results as conversion coefficients between organ equivalent dose and kerma in air for external photon radiation. A comparison of the results with published data shows good agreement.     

Biometry of oospores and oogonia of Pythium (Oomycetes): the independent taxonomic value of calculated ratios

SHAHZAD, S., COE, R. & DICK, M. W., 1992. Biometry of oospores and oogonia of Pythium (Oomycetes): the independent taxonomic value of calculated ratios. The oogonia and oospores of 80 isolates, representing 40 species of Pythium , were examined to determine the taxonomic values of direct measurements and derived indices. It was demonstrated that 20 individual oogonia from an isolate provided a suitable data base, with acceptable levels for standard errors of the means. All four measurable and all three calculable variables showed continuous variation between isolates and species, so that no single criterion was able to effect taxonomic separation. The inadequacy of the traditional plerotic/aplerotic concept was revealed. Derived indices were shown to have a significant taxonomic value in addition to the measured parameters from which they were derived. When taken together, using canonical variate analysis, the variables enabled isolates to be grouped into their respective species without recourse to other taxonomic features. The enhanced precision of the assessment of oogonial characteristics has enabled a new approach to Pythium classification to be developed.     

Integrating two physiological approaches helps relate respiration to growth of Pinus radiata

Correlation methods originating in the growth and maintenance paradigm (GMP) are traditionally used to calculate a 'growth coefficient' (g) or the 'growth potential' (1/g) of entire plants. The enthalpy balance approach is usually applied to plant organs and relies on determination of both CO(2) release and O(2) reduction to provide a measure of instantaneous rates of enthalpic growth (R(SG)DeltaH(B)). Aspects of both the approaches to explore physiological mechanisms that govern enthalpic growth (variation in rates of CO(2) release versus rates of O(2) reduction) were combined. Respiration and growth rates of apical buds of Pinus radiata were affected strongly by canopy position, and moderately by branching order. A linear relation between enthalpic growth and CO(2) respiration explained 69% of the observed variation. Despite faster rates of growth, enthalpic growth potential (1/g(H)) was comparatively low in the upper canopy. Low enthalpic growth potential entailed comparatively low enthalpy conversion efficiency (eta(H), ratio of R(SG)DeltaH(B) to R(CO(2)) DeltaH(CO(2)); proportional to CO(2):O(2) and to carbon conversion efficiency epsilon) at large R(SG)DeltaH(B). Maximizing enthalpic growth requires a large capacity for O(2) reduction. Relations between R(SG)DeltaH(B) and eta(H) could be described by hyperbolae using two parameters. One parameter, P(1), is equivalent to enthalpic growth potential (1/g(H)).     

NMR structural refinement of a tandem G.A mismatched decamer d(CCAAGATTGG)2 via the hybrid matrix procedure

A complete relaxation matrix approach employing a matrix eigenvalue/eigenvector solution to the Bloch equations is used to evaluate the NMR solution structure of a tandemly positioned G.A double mismatch decamer oligodeoxyribonucleotide duplex, d(CCAAGATTGG)2. An iterative refinement method using a hybrid relaxation matrix combined with restrained molecular dynamics calculations is shown to provide structures having good agreement with the experimentally derived structures. Distances incorporated into the MD simulations have been calculated from the relaxation rate matrix evaluated from a hybrid NOESY volume matrix whose elements are obtained from the merging of experimental and calculated NOESY intensities. Starting from both A- and B-DNA and mismatch syn and anti models, it is possible to calculate structures that are in good atomic RMS agreement with each other (less than 1.6 A RMS) but differ from the reported crystal structure (greater than 3.6 A). Importantly, the hybrid matrix derived structures are in excellent agreement with the experimental solution conformation as determined by comparison of the 200-ms simulated and experimental NOESY spectra, while the crystallographic data provide spectra that are grossly different.     

Estimation of Primary Productivity by Chlorophyll a in vivo Fluorescence in Freshwater Phytoplankton

Primary productivity in marine waters is widely estimated by the measurements of ¹⁴C incorporation, the underwater light climate, and the absorption spectra of phytoplankton. In bio-optical models the quantum efficiency of carbon fixation derived from ¹⁴C incorporation rates, the photosynthetically absorbed radiation derived from the underwater light climate, and the phytoplankton absorption spectra are used to calculate time- and depth-integrated primary productivity. Due to the increased sensitivity of commercially available fluorometers, chlorophyll a in vivo fluorescence became a new tool to assess the photosynthetic activity of phytoplankton. Since fluorescence data yield only relative photosynthetic electron transport rates, a direct conversion into absolute carbon fixation rates is not possible. Here, we report a procedure how this problem can be adressed in freshwater phytoplankton. We adapted a marine bio-optical model to the freshwater situation and tested if this model yields realistic results when applied to a hypertrophic freshwater reservoir. Comparison of primary productivity derived from ¹⁴C incorporation to primary productivity derived from Chl a fluorescence showed that the conversion of fluorescence data into carbon fixation rates is still an unsolved problem. Absolute electron transport rates calculated from fluorescence data tend to overestimate primary production. We propose that the observed differences are caused mainly by neglecting the package effect of pigments in phytoplankton cells and by non-carbon related electron flow (e.g., nitrogen fixation). On the other hand, the ¹⁴C incorporation rates can be artificially influenced by "bottle effects", especially near the water surface, where photoinhibition, photorespiration, and Mehler reaction can play a major role.     

Convergence of genetic distances in a migration matrix model

A recurring problem with the use of migration matrix models of genetic differentiation has to do with their convergence properties. In practice, predictions can be drawn from these models only at equilibrium; but in the case of the standard predictors (most of which are modifications of Wright's FST), it can take an unrealistically large number of generations to approach equilibrium. An alternative set of predictors, the set of all pairwise genetic distances among the populations that define the rows and columns of the migration matrix, is investigated here. These distances are shown analytically to converge much more rapidly than the more commonly used predictors. In an application of the model to migration data on a human population from Papua New Guinea, it takes only about three to four generations for the pairwise distances to converge, in contrast to more than 100 generations for one of the standard predictors. In this case, moreover, the distances predicted by the model at equilibrium are similar to those calculated from the available genetic data.     

用R法估计方差组分的原理、方法和应用

综述了R法估计方差组分的原理、方法和应用,目的是使该方法能够得到合理应用。R法是通过计算全数据集对亚数据集随机效应的回归因子（R）来估计方差组分的。利用一种基于一个变换矩阵的多变量迭代算法,结合先决条件的共扼梯度法求解混合模型方程组使R法的计算效率大为改善。R法的主要优点是计算成本低,同时可以得到方差组分估值的抽样误差和近似置信区间。其缺点是对于同样的数据,R法较其他方法的抽样误差大,而且在小样本中估计值往往有偏。做为一种可选方法,R法可以应用到大数据集的方差组分估计中,同时应进一步研究其理论特性,拓宽其应用范围。Abstract: Theory, method and application of Method R on estimation of (co)variance components were reviewed in order to make the method be reasonably used. Estimation requires R values,which are regressions of predicted random effects that are calculated using complete dataset on predicted random effects that are calculated using random subsets of the same data. By using multivariate iteration algorithm based on a transformation matrix,and combining with the preconditioned conjugate gradient to solve the mixed model equations, the computation efficiency of Method R is much improved. Method R is computationally inexpensive,and the sampling errors and approximate credible intervals of estimates can be obtained. Disadvantages of Method R include a larger sampling variance than other methods for the same data,and biased estimates in small datasets. As an alternative method, Method R can be used in larger datasets. It is necessary to study its theoretical properties and broaden its application range further.