Modelling Stem Height and Diameter Growth in Plants

A model of stem height and diameter growth in plants is developed.This is formulated and implemented within the framework of anexisting tree plantation growth model: the ITE Edinburgh ForestModel. It is proposed that the height:diameter growth rate ratiois a function of a within-plant allocation ratio determinedby the transport-resistance model of partitioning, multipliedby a foliage turgor pressure modifier. First it is demonstratedthat the method leads to a stable long-term growth trajectory.Diurnal and seasonal dynamics are also examined. Predicted timecourses over 20 years of stem mass, stem height, height:diameterratio, and height:diameter growth rate ratio are presented forsix treatments: control, high nitrogen, increased atmosphericcarbon dioxide concentration, increased planting density, increasedtemperature and decreased rainfall. High nitrogen and increasedtemperature give initially higher stem height:diameter ratios,whereas high CO₂gives an initially lower stem height:diameterratio. However, the responses are complex, reflecting interactionsbetween factors which often have opposing influences on height:diameterratios, for example: stem density, competition for light andfor nitrogen; carbon dioxide and decreased water stress; rainfall,leaching and nitrogen nutrition. The approach relates stem heightand diameter growth variables via internal plant variables toenvironmental and management variables. Potentially, a coherentview of many observations which are sometimes in apparent conflictis provided. These aspects of plant growth can be consideredmore mechanistically than has hitherto been the case, providingan alternative to the empirical or teleonomic methods whichhave usually been employed.Copyright 1999 Annals of Botany Company Plant, stem, height, diameter, growth, model, forest, plantation, trees.     

Temperature Dependence of Plant and Crop Process

The quantitative effects of temperature on plant and crop processesare discussed and related to the underlying theory, by meansof a critical and expository essay which aims to provide a conceptualbasis for the consideration of these problems. The topics consideredinclude the Arrhenius equation and Q₁₀; the collision and transition-statetheories of the rate constant; models with a temperature optimum;models without a temperature optimum; phase changes; diffusion,viscosity and translocation; hybrid systems (biochemistry plustransport); photosynsthesis; respiration; and development withthe day-degree hypothesis. Temperature, model, plants, crops     

A Model to Describe the Partitioning of Photosynthate during Vegetative Plant Growth

An approach is described to the problem of modelling quantitativelythe partitioning of photosynthate during vegetative plant growth.Two plant processes are important in the scheme: the first ofthese is the utilization of substrate for growth and how thisutilization depends upon substrate concentration, the secondconcerns the transport of substrate between different plantparts and how this depends upon the substrate concentrationsin the plant parts. In both cases simple phenomenological relationshave been assumed which seem to be in reasonable accord withexperimental data and with more basic theoretical considerations.The model is able to describe some of the features of steady-statevegetative plant growth in a natural manner. The limitationsof the present formulation are considered, and the implicationsof this type of approach for whole-plant models are discussed.     

A Balanced Quantitative Model for Root: Shoot Ratios in Vegetative Plants

The vegetative growth of a two-component plant consisting ofroot and shoot only is considered in terms of the transportand utilization of two required substrates, one providing carbonand the other providing nitrogen. The model provides a quantitativescheme for examining how root: shoot ratios depend upon thespecific activities of root and shoot and hence environment.It has been shown that the total shoot activity is proportionalto the total root activity in a plant undergoing steady-stategrowth.     

The Tomato Fruit: Import, Growth, Respiration and Carbon Metabolism at Different Fruit Sizes and Temperatures

Measurements of a complete carbon balance sheet over a 48 hperiod for growing tomato fruits at different fruit sizes andtemperature have been carried out. The rates of carbon import,respiration, and growth have been calculated and related toeach other and to the levels of certain carbon metabolites inthe fruit. It was found that there is an excellent linear relationshipbetween the import rate and the sucrose level in the fruit,consistent with the hypothesis that, for the tomato fruit, carbonflows down the sucrose concentration gradient at a rate proportionalto the gradient. This agrees with the findings of Mason andMaskell in cotton. Moreover, the resistance to transport wasrelatively independent of fruit size and temperature. The usualanalysis of respiration in terms of growth and maintenance componentsallowed the determination of conversion efficiencies and maintenancecoefficients for different fruit sizes and temperatures. Asobserved by other authors with other plants, the growth conversionefficiencies were temperature-independent, whereas the maintenancecoefficients were strongly temperature-dependent. The overallconversion efficiency was optimum at 25°C. The specificgrowth rate and the starch level in the tomato fruit were foundto be related.     

Measuring the Canopy Net Photosynthesis of Glasshouse Crops

A null balance method is described for measuring net photosynthesisof mature canopies of cucumber and other protected crops overperiods of 10 min in a single-span glasshouse (c. 9m x 18m inarea). Accuracy of control of the CO₂ concentration in the greenhouseatmosphere is within ±10 vpm of the normal ambient level(c. 350 vpm). The amounts of CO₂ used in canopy net photosynthesisare measured with linear mass flowmeters accurate to within±0.80g. The total errors incurred in measuring canopynet photosynthesis at an ambient CO₂ level are estimated tobe of the order of ± 1·2% in bright light (350W m^–2, PAR)and ±3·6% in dull light (100W m^–2, PAR). Measurements of the rates of net photosynthesis of a maturecanopy of a cucumber crop were made at near-ambient CO₂ concentrationsover a range (0–350 W m^–2) of natural light fluxdensities. A model of light absorption and photosynthesis applicableto row crops was used to obtain a net photosynthesis versuslight response curve for the cucumber crop. At a light fluxdensity of 350 W m^–2 the fitted value of canopy net photosynthesiswas 2.65 mg CO₂ m^–2s^–1 (equivalent to over 95 kgCO₂ ha^–1h^–1). The results are discussed in relationto the need for CO₂ supplements to avoid depletion in both ventilatedand unventilated glasshouses during late spring and summer. Key words: Glasshouse crops, cucumber, measurement, canopy photosynthesis, light, CO₂     

A Catastrophe Model for the Switch from Vegetative to Reproductive Growth in the Shoot Apex

A mathematical model is constructed to describe the morphopneticswitch that occurs when a vegetative plant apex becomes reproductive.The cusp equation from catastrophe theory is modified, and isused to relate primordial size at initiation to apex size. Theresulting equation may be viewed as an equation of state definingthe allowed organizational modes of the shoot apex. The modelsimulates the growth of the apex from the vetative stage toearly reproductive growth, and makes reasonable predictionsabout apex size and growth rate, primordial sizes, and the lengthsof the plastochron. flowering, mathematical model, catastrophe theory, shoot apex     

A New Formulation of the Logistic Growth Equation and Its Application to Leaf Area Growth

A formulation of the logistic growth equation in terms of twodifferential equations is proposed; this permits the asymptoteto depend upon conditions during the growth period such as substratesupply (irradiance) and temperature. The application of themodel to leaf area growth is outlined, and it is shown how observedresponses of mature leaf area to irradiance and temperaturemay be simulated. Logistic, leaf area, model