Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth

We study individual plant growth and size hierarchy formation in an experimental population of Arabidopsis thaliana, within an integrated analysis that explicitly accounts for size-dependent growth, size- and space-dependent competition, and environmental stochasticity. It is shown that a Gompertz-type stochastic differential equation (SDE) model, involving asymmetric competition kernels and a stochastic term which decreases with the logarithm of plant weight, efficiently describes individual plant growth, competition, and variability in the studied population. The model is evaluated within a Bayesian framework and compared to its deterministic counterpart, and to several simplified stochastic models, using distributional validation. We show that stochasticity is an important determinant of size hierarchy and that SDE models outperform the deterministic model if and only if structural components of competition (asymmetry; size- and space-dependence) are accounted for. Implications of these results are discussed in the context of plant ecology and in more general modelling situations.     

A simple model predicting individual weight change in humans

Excessive weight in adults is a national concern with over 2/3 of the US population deemed overweight. Because being overweight has been correlated to numerous diseases such as heart disease and type 2 diabetes, there is a need to understand mechanisms and predict outcomes of weight change and weight maintenance. A simple mathematical model that accurately predicts individual weight change offers opportunities to understand how individuals lose and gain weight and can be used to foster patient adherence to diets in clinical settings. For this purpose, we developed a one-dimensional differential equation model of weight change based on the energy balance equation paired to an algebraic relationship between fat-free mass and fat mass derived from a large nationally representative sample of recently released data collected by the Centers for Disease Control. We validate the model's ability to predict individual participants’ weight change by comparing model estimates of final weight data from two recent underfeeding studies and one overfeeding study. Mean absolute error and standard deviation between model predictions and observed measurements of final weights are less than 1.8±1.3 kg for the underfeeding studies and 2.5±1.6 kg for the overfeeding study. Comparison of the model predictions to other one-dimensional models of weight change shows improvement in mean absolute error, standard deviation of mean absolute error, and group mean predictions. The maximum absolute individual error decreased by approximately 60% substantiating reliability in individual weight-change predictions. The model provides a viable method for estimating individual weight change as a result of changes in intake and determining individual dietary adherence during weight-change studies.     

A model for relating troop size and home range area in a primate species

For relating troop size (N) and home range area (R), a simple model,QR=αN, whereQ denotes habitat quality and α is a constant, was examined using published field data forMacaca fuscata, M. mulatta andColobus guereza. In particular, theN-R direct proportionality of the model was tested for its validity and usefulness in comparison with a few less simple models. The implications of the present model are discussed in relation to bioenergetics and population dynamics.     

Pulsed electromagnetic field: an organic compatible method to promote plant growth and yield in two corn types

Pre-sowing treatment of pulsed electromagnetic fields was used in corn seeds, in both indoor and outdoor conditions, in order to investigate the effect on plant growth and yield. The results of this research showed that pulsed electromagnetic fields can enhance plant characteristics, both under controlled environmental conditions and uncontrolled field conditions. The two varieties responded differently in the duration of magnetic field. Seeds were treated for 0, 15, 30, and 45 min with pulsed electromagnetic field (MF-0, MF-15, MF-30, and MF-45). Common corn variety performed better results in MF-30 treatment, while sweet corn variety performed better in MF-45 treatment. Magnetic field improved germination percentage, vigor, chlorophyll content, leaf area, plant fresh and dry weight, and finally yields. In the very interesting measurement of yield, seeds that have been exposed to magnetic field for 30 and 45 min have been found to perform the best results with no statistical differences among them. Another interesting finding was in root dry weight measurements, where magnetic field has a negative impact in MF-30 treatment in both hybrids, however without affecting other measurements. Enhancements on plant characteristics with economic impact on producer's income could be the future of a modern, organic, and sustainable agriculture.     

A simple model for nitrogen-limited plant growth and nitrogen allocation

BACKGROUND: and Aims In many studies of nitrogen-limited plant growth a linear relationship has been found between relative growth rate and plant nitrogen concentration, showing a negative intercept at a plant nitrogen concentration of zero. This relationship forms the basis of the nitrogen productivity theory. On the basis of empirical findings, several authors have suggested that there is also a distinctive relationship between allocation and plant nitrogen concentration. The primary aim of this paper is to develop a simple plant growth model that quantifies this relationship in mathematical terms. The model was focused on nitrogen allocation to avoid the complexity of differences in nitrogen concentrations in the different plant compartments. The secondary aim is to use the model for examining the processes that underlie the empirically based nitrogen productivity theory. METHODS: In the construction of the model we focused on the formation and degradation of biologically active nitrogen in enzymes involved in the photosynthetic process (photosynthetic nitrogen). It was assumed that, in nitrogen-limiting conditions, the formation of photosynthetic nitrogen is proportional to nitrogen uptake. Furthermore it was assumed that the degradation of photosynthetic nitrogen is governed by first-order kinetics. Model predictions of nitrogen allocation were compared with data from literature describing four studies of growth. Model predictions of whole plant growth were compared with the above-mentioned nitrogen productivity theory. KEY RESULTS: Allocation predictions agreed well with the investigated empirical data. The ratio of leaf nitrogen and plant nitrogen declines linearly with the inverse of plant nitrogen concentration. Nitrogen productivity is proportional to this ratio. Predictions for whole-plant growth were in accordance with the nitrogen productivity theory. CONCLUSIONS: The agreement between model predictions and empirical findings suggests that the derived equation for nitrogen allocation and its relationship to plant nitrogen concentration might be generally applicable. The negative intercept in the linear relationship between relative growth rate and plant nitrogen concentration is interpreted as being equal to the degradation constant of photosynthetic nitrogen.     

A model for predicting growth responses in plants to changes in external water potential: Zea mays primary roots

In response to osmotic step changes, three distinct phases have been noted in the growth response of Zea mays primary roots. They are cessation or slowing of growth over a period of 15–20 minutes, tissue contraction, and a damped oscillatory return to nearly normal growth rate, all within a period of about one hour. A system model of the tissue response is presented to explain such behavior and to serve in a predictive capacity to govern future experiments.It is supposed that for turgor pressure in excess of a cell wall yield threshold, plastic flow is the major component of wall deformation, and that when turgor falls below yield threshold, elastic deformation is dominant. The equations of the model describe growth rate as a function of time in terms of the following properties; plastic flow, elastic deformation, permeability to water, and solute uptake. They are derived from basic equations of feedback interactions between internal osmotic pressure and growth rate, and between wall softening, turgor and growth rate.The model predicts oscillatory growth rate regulation, and phase and amplitude relationships between turgor pressure and growth rate. The simplest model which accounts for all observations is that of biphasic deformation, two modes of wall softening, and a dual feedback system involving osmotic and yield threshold control of growth rate.It should be noted that to predict the time course of turgor pressure, osmotic pressure, yield pressure, and growth rate, two initial conditions and six system parameter values are sufficient. So far only the initial values of growth rate and its derivative can be obtained for Zea mays primary roots. However, values for wall softening and hardening coefficients (including the strain and turgor independent component), plastic extensibility, water permeability and dilution rate coefficients have not been obtained as yet for Zea roots. Values for some of these parameters have been obtained for other roots, coleoptiles, and giant algal cells.Lest the reader despair, it should be pointed out that experimental observations coupled with simulation studies will help establish restricted ranges of values that the system parameters might assume. These can then be compared with known values in the literature and values experimentally obtained in the future.     

A simple, leaky cell growth model for plant cell aggregates

A simple growth model is proposed for plant cell aggregates which accounts for leakage of a single intermediate metabolite from the aggregates to the medium. This model predicts a lag phase in the growth curve whose extent is determined by the intermediate metabolite leakage coefficient and its equilibrium distribution coefficient between the medium and the cell aggregates, the size of the inoculum relative to the system total water content, and the initial intermediate metabolite content in the medium. The model thus provides for an interaction between growing plant cells and their environment in a way that has heretofore been unquantified. Preliminary validation of the model has been made against literature data of Dioscorea deltoidea grown in batch suspension cell culture on sucrose, yielding a correlation coefficient of 0.997. The predicted glucose + fructose concentration in the medium agrees reasonably well with experimental measurements after ca, 3.5 days of culture, although a discrepancy exists between model prediction and experiment immediately after startup. Further validation of the model is suggested on this and other plant species.     

寒地春玉米生长发育及产量对花前夜间增温的响应

采用田间开放式夜间增温试验方法,研究雨养农区寒地春玉米生长发育及产量对花前夜间增温的响应.结果表明:夜间增温条件下,0 ～ 10 cm耕层土壤夜间温度升高1.7℃,土壤水分略有下降;夜间增温使春玉米物候期明显提前,花前生育期缩短ld,花后生育期延长1d;夜间增温明显促进春玉米幼苗生长,提高根系长度,单株绿叶面积和棒三叶面积分别比对照提高13.5％和14.6％;与对照相比,春玉米地上生物量和籽粒产量分别显著增高8.2％和9.3％,百粒重显著增高7.1％.东北地区气候变暖尤其是日最低温度升高对春玉米的直接影响效应可能以增产为主.     

Induced systemic resistance to tomato leaf curl virus and increased yield in tomato by plant growth promoting rhizobacteria under field conditions

The talc-based formulation of two Pseudomonas fluorescens strains (Pf1 and VPT10) and its mixture (with and without chitin) were tested against tomato leaf curl virus in tomato under greenhouse and field conditions. The mean percentage of tomato leaf curl virus infected plants were significantly lower (25%) with less symptom severity and delayed symptom expression up to nine additional days in Pseudomonas with chitin (VPT10 + chitin) treated tomato plants compared to non-bacterised control plants upon challenge inoculation with tomato leaf curl virus. Tomato leaf curl virus was partially purified and antiserum was developed. Using the antiserum the tomato leaf curl virus was detected in symptomatic leaves and in whitefly vector through direct antigen coating enzyme linked immunosorbent assay which revealed the low virus titre in Pseudomonas treated plants (VPT10 + chitin) and insect vector compared to untreated tomato plants. The results indicate the potentiality of plant growth promoting rhizobacteria strains and talc-powder formulations in the effective management of this tomato leaf curl virus in tomato under field conditions.     

A simple plant and tissue culture growth chamber for the regeneration of tobacco mesophyll protoplasts

The isolation and regeneration of tobacco mesophyll protoplasts from fully developed leaves, an important methodological step in plant genetic engineering as well as in plant cell biology and physiology, has been proven unreliable to the extent that it has become a significant setback to basic research. This unfortunate situation is primarily due to the suboptimal physiological state of greenhouse-grown protoplast donor plants. A technically simple and inexpensive method, based on the utilization of commercial Phototron units, is described for the production of suitable tobacco donor plants. Furthermore, a modified version of such a culture unit can be used to regenerate plants from protoplast-derived calli.     

Quantitative genetics and functional-structural plant growth models: simulation of quantitative trait loci detection for model parameters and application to potential yield optimization

BACKGROUND AND AIMS: Prediction of phenotypic traits from new genotypes under untested environmental conditions is crucial to build simulations of breeding strategies to improve target traits. Although the plant response to environmental stresses is characterized by both architectural and functional plasticity, recent attempts to integrate biological knowledge into genetics models have mainly concerned specific physiological processes or crop models without architecture, and thus may prove limited when studying genotype x environment interactions. Consequently, this paper presents a simulation study introducing genetics into a functional-structural growth model, which gives access to more fundamental traits for quantitative trait loci (QTL) detection and thus to promising tools for yield optimization. METHODS: The GREENLAB model was selected as a reasonable choice to link growth model parameters to QTL. Virtual genes and virtual chromosomes were defined to build a simple genetic model that drove the settings of the species-specific parameters of the model. The QTL Cartographer software was used to study QTL detection of simulated plant traits. A genetic algorithm was implemented to define the ideotype for yield maximization based on the model parameters and the associated allelic combination. KEY RESULTS AND CONCLUSIONS: By keeping the environmental factors constant and using a virtual population with a large number of individuals generated by a Mendelian genetic model, results for an ideal case could be simulated. Virtual QTL detection was compared in the case of phenotypic traits--such as cob weight--and when traits were model parameters, and was found to be more accurate in the latter case. The practical interest of this approach is illustrated by calculating the parameters (and the corresponding genotype) associated with yield optimization of a GREENLAB maize model. The paper discusses the potentials of GREENLAB to represent environment x genotype interactions, in particular through its main state variable, the ratio of biomass supply over demand.     

A minimal continuous model for simulating growth and development of plant root systems

Aims: This paper proposes a general and minimal continuous model of root growth that aggregates architectural and developmental information and that can be used at different spatial scales. Methods: The model is described by advection, diffusion and reaction operators, which are related to growth processes such as primary growth, branching, mortality and root death. Output variable is the number of root tips per unit volume of soil. Operator splitting techniques are used to fit, solve and analyze the model with regards to ontogeny. The modeling approach is illustrated on a 2D case study concerning a part of Eucalyptus root system. Results: Operator splitting is helpful to fit the model. Basic knowledge on root architecture and development allows decreasing the number of unknown parameters and defining ontogenic phases on which specific calibrations must be carried out. Simulation results reproduce quantitatively the dynamic evolution of root density distribution with a good accuracy. Conclusion: The proposed root growth model is based on a continuous formalism that can be easily coupled with other physical models, e.g. nutrient and water transfer. The equations are generic and allow simulating different root architectures and growth strategies. They can be efficiently solved using adapted numerical methods.     

The biophysics of plant growth in a reversed electrostatic field: A comparison with conventional electrostatic and electrokinetic field growth responses

The growth of corn and bean plants in a reversed electrostatic field (soil positive) was investigated with reference to previous data for growth in a conventional electrostatic field (soil negative) and an electrokinetic (a.c.) field. Plant and leaf tip damage was observed for high potential gradients in the reversed field. Spectroscopic analyses of the damaged plant sections revealed micro-chemical activity essentially identical to that observed for conventional electrostatic and electrokinetic field growth.While the plant and leaf polarities for all three modes of electrification were found to be essentially consistent,the severity of leaf damage for identical field conditions was less for plants grown in the reversed electrostatic field as compared with conventional field growth. Leakage currents were also higher in the reversed field environments.It appears that plant growth responses are influenced, to a large extent, by the magnitude of active current flow. A summarization of all existing data indicated that plant growth in an electric field, regardless of mode (static or dynamic) is generally retarded at leakage currents in excess of 10^–5 amp, and may be stimulated for currents of 10^–8 amp. Current levels of 10^–16 amp and lower appeared to have no measurable effect on plant physiology.

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Zusammenfassung Das Wachstum von Mais- und Bohnenpflanzen im umgekehrten elektrostatischen Feld wurde mit Bezug auf frühere Ergebnisse über das Wachstum in einem konventionellen elektrostatischen Feld (Boden neg.)und einem elektrokinetischen(~) Feld untersucht. Pflanzen- und Blattspitzenschäden wurden bei hohen Potentialgradienten im umgekehrten Feld beobachtet. Spektroskopische Analysen der geschädigten Pflanzenabschnitte ergaben gleiche mikrochemische Aktivität wie beim Wachstum im konventionellen elektrostatischen und elektrokinetischen Feld.Während die Pflanzen-und Blattpolaritäten für alle 3 Arten der Elektrifizierung gleich beständig gefunden wurden, war das Ausmass des Blattschadens bei identischen Feldbedingungen geringer bei Pflanzen, die im umgekehrten elektrostatischen Feld wuchsen, bezogen auf das Wachstum bei konventionellen Feldbedingungen.Verlustströme waren grösser im umgekehrten Feld. Es scheint, dass Pflanzenwachstumsreaktionen in starkem Masse von der Grösse des aktiven Stromflusses beeinflusst werden. Eine Zusammenfassung aller Ergebnisse zeigt, dass Pflanzenwachstum im elektrischen Feld unabhängig von der Art (statisch oder dynamisch) im allgemeinen verzögert wird bei Verlustströmen über 10^–5 amp und angeregt werden kann durch Ströme von 10^–8 amp. Stromstärken von 10^–16 amp und weniger scheinen keinen messbaren Effekt auf das Pflanzenwachstum zu haben.

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Resume On a examiné les conditions de croissance de plants de pois et de maïs dans un champ électrostatique renversé (sol positif)en les comparant à des valeurs antérieures, acquises dans un champ électrostatique conventionnel (sol négatif) et un champ électro-cinétique (alternatif). On a constaté des dégâts aux plantes et à la pointe des feuilles dans le cas de gradients potentiels élevés par champ renversé. L'analyse spectroscopique des parties endommagées a révélé une activité micro-chimique identique dans son ensemble à celle observée dans le cas de champs électrostatiques conventionnels ou électro-cinétiques. Alors que la polarité des plantes et des feuilles restait constante dans les trois cas, le degré de dommage aux feuilles était, pour des conditions de champ identiques,plus faible chez les plantes soumises à un champ renversé que pour celles qui poussaient dans un champ électrostatique conventionnel. Les fuites de charge furent par contre plus importantes dans un champ renversé. Il semble que les réactions de croissance des plantes sont influencées dans une large mesure par l'intensité du "courant actif".Une récapitulation de tous les résultats obtenus montre que la croissance des plantes dans un champ électrique, quel qu'en soit le genre (statique ou dynamique) est généralement ralentie par des fuites de charge de plus de 10^–5 amp et stimulée par des courants de 10^–8 amp. Des courants de 10^–16 amp et moins ne semblent pas avoir de conséquences mesurables sur la croissance des plantes.

     

A viscoelastic model for use in predicting arterial pulse waves

In nonlinear mathematical models of the arterial circulation, the viscoelasticity of the vessel walls has generally been neglected or only taken into account in a highly approximate manner. A new method is proposed to simulate the nonlinear viscoelastic properties of the wall material with the aid of a convolution integral of the creep function and the pressure history. With this simulation it is possible to properly describe the measured characteristics of arterial viscoelasticity. Moreover, it is utilized in a mathematical model of arterial pulse propagation to study the influence of the internal wall friction on the shape, amplitude and mean value of pressure and flow pulses. The corresponding predictions are in much better agreement with in-vivo measurements, especially for the distal part of the circulation, than those obtained without viscoelasticity.     

A model for species-area relationships in plant communities

Abstract. A model is proposed for the fitting of species-area curves to data from the Stellenbosch region, South Africa. Basic assumptions of the model are finiteness of the number of species in a finite area, and random distribution of plant species over the region. The model involves a distribution of densities of different species, and the parameters of this distribution are useful for describing and classifying communities. The data of the Stellenbosch region suggest that the assumptions of the model break down in areas greater than 500 m².     

A phenomenological model for predicting fatigue life in bovine trabecular bone

Cyclic loading of bone during daily activities can lead to fatigue degradation and increased risk of fracture in both the young and elderly population. Damage processes under cyclic loading in trabecular bone result in the reduction of the elastic modulus and accumulation of residual strain. These effects increase with increasing stress levels, leading to a progressive reduction in fatigue life. The present work analyzes the effect of stress and strain variation on the above damage processes in bovine trabecular bone, and develops a phenomenological model relating fatigue life to the imposed stress level. The elastic modulus reduction of the bone specimens was observed to depend on the maximum compressive strain, while the rate of residual strain accumulation was a function of the stress level. A model was developed for the upper and lower bounds of bone elastic modulus reduction with increasing number of cycles, at each stress range. The experimental observations were described well by the model. The model predicted the bounds of the fatigue life with change in fatigue stress. The decrease in the fatigue life with increasing stress was related to corresponding increases in the residual strain accumulation rates at the elevated stress levels. The model shows the validity of fatigue predictions from relatively few cyclic experiments, by combining trends observed in the monotonic and the cyclic tests. The model also presents a relatively simple procedure for predicting the endurance limit for bovine trabecular bone specimens.     

A dynamic model of plant growth with interactions between development and functional mechanisms to study plant structural plasticity related to trophic competition

Background and Aims

The strong influence of environment and functioning on plant organogenesis has been well documented by botanists but is poorly reproduced in most functional–structural models. In this context, a model of interactions is proposed between plant organogenesis and plant functional mechanisms.

Methods

The GreenLab model derived from AMAP models was used. Organogenetic rules give the plant architecture, which defines an interconnected network of organs. The plant is considered as a collection of interacting ‘sinks’ that compete for the allocation of photosynthates coming from ‘sources’. A single variable characteristic of the balance between sources and sinks during plant growth controls different events in plant development, such as the number of branches or the fruit load.

Key Results

Variations in the environmental parameters related to light and density induce changes in plant morphogenesis. Architecture appears as the dynamic result of this balance, and plant plasticity expresses itself very simply at different levels: appearance of branches and reiteration, number of organs, fructification and adaptation of ecophysiological characteristics.

Conclusions

The modelling framework serves as a tool for theoretical botany to explore the emergence of specific morphological and architectural patterns and can help to understand plant phenotypic plasticity and its strategy in response to environmental changes.Key words: Trophic plasticity, plant growth, functional–structural models, dynamic system, interactions, GreenLab