Parameter stability of the functional-structural plant model GREENLAB as affected by variation within populations, among seasons and among growth stages

BACKGROUND AND AIMS: It is increasingly accepted that crop models, if they are to simulate genotype-specific behaviour accurately, should simulate the morphogenetic process generating plant architecture. A functional-structural plant model, GREENLAB, was previously presented and validated for maize. The model is based on a recursive mathematical process, with parameters whose values cannot be measured directly and need to be optimized statistically. This study aims at evaluating the stability of GREENLAB parameters in response to three types of phenotype variability: (1) among individuals from a common population; (2) among populations subjected to different environments (seasons); and (3) among different development stages of the same plants. METHODS: Five field experiments were conducted in the course of 4 years on irrigated fields near Beijing, China. Detailed observations were conducted throughout the seasons on the dimensions and fresh biomass of all above-ground plant organs for each metamer. Growth stage-specific target files were assembled from the data for GREENLAB parameter optimization. Optimization was conducted for specific developmental stages or the entire growth cycle, for individual plants (replicates), and for different seasons. Parameter stability was evaluated by comparing their CV with that of phenotype observation for the different sources of variability. A reduced data set was developed for easier model parameterization using one season, and validated for the four other seasons. KEY RESULTS AND CONCLUSIONS: The analysis of parameter stability among plants sharing the same environment and among populations grown in different environments indicated that the model explains some of the inter-seasonal variability of phenotype (parameters varied less than the phenotype itself), but not inter-plant variability (parameter and phenotype variability were similar). Parameter variability among developmental stages was small, indicating that parameter values were largely development-stage independent. The authors suggest that the high level of parameter stability observed in GREENLAB can be used to conduct comparisons among genotypes and, ultimately, genetic analyses.     

A dynamic, architectural plant model simulating resource-dependent growth

BACKGROUND AND AIMS: Physiological and architectural plant models have originally been developed for different purposes and therefore have little in common, thus making combined applications difficult. There is, however, an increasing demand for crop models that simulate the genetic and resource-dependent variability of plant geometry and architecture, because man is increasingly able to transform plant production systems through combined genetic and environmental engineering. MODEL: GREENLAB is presented, a mathematical plant model that simulates interactions between plant structure and function. Dual-scale automaton is used to simulate plant organogenesis from germination to maturity on the basis of organogenetic growth cycles that have constant thermal time. Plant fresh biomass production is computed from transpiration, assuming transpiration efficiency to be constant and atmospheric demand to be the driving force, under non-limiting water supply. The fresh biomass is then distributed among expanding organs according to their relative demand. Demand for organ growth is estimated from allometric relationships (e.g. leaf surface to weight ratios) and kinetics of potential growth rate for each organ type. These are obtained through parameter optimization against empirical, morphological data sets by running the model in inverted mode. Potential growth rates are then used as estimates of relative sink strength in the model. These and other 'hidden' plant parameters are calibrated using the non-linear, least-square method. KEY RESULTS AND CONCLUSIONS: The model reproduced accurately the dynamics of plant growth, architecture and geometry of various annual and woody plants, enabling 3D visualization. It was also able to simulate the variability of leaf size on the plant and compensatory growth following pruning, as a result of internal competition for resources. The potential of the model's underlying concepts to predict the plant's phenotypic plasticity is discussed.     

Correlation between dynamic tomato fruit-set and source–sink ratio: a common relationship for different plant densities and seasons?

Background and Aims

It is widely accepted that fruit-set in plants is related to source–sink ratio. Despite its critical importance to yield, prediction of fruit-set remains an ongoing problem in crop models. Functional–structural plant models are potentially able to simulate organ-level plasticity of plants. To predict fruit-set, the quantitative link between source–sink ratio and fruit-set probability is analysed here via a functional–structural plant model, GreenLab.

Methods

Two experiments, each with four plant densities, were carried out in a solar greenhouse during two growth seasons (started in spring and autumn). Dynamic fruit-set probability was estimated by frequent observation on inflorescences. Source and sink parameter values were obtained by fitting GreenLab outputs for the biomass of plant parts (lamina, petiole, internode, fruit), at both organ and plant level, to corresponding destructive measurements at six dates from real plants. The dynamic source–sink ratio was calculated as the ratio between biomass production and plant demand (sum of all organ sink strength) per growth cycle, both being outputs of the model.

Key Results and Conclusions

Most sink parameters were stable over multiple planting densities and seasons. From planting, source–sink ratio increased in the vegetative stage and reached a peak after fruit-set commenced, followed by a decrease of leaf appearance rate. Fruit-set probability was correlated with the source–sink ratio after the appearance of flower buds. The relationship between fruit-set probability and the most correlated source–sink ratio could be quantified by a single regression line for both experiments. The current work paves the way to predicting dynamic fruit-set using a functional structure model.     

Does the Structure–Function Model GREENLAB Deal with Crop Phenotypic Plasticity Induced by Plant Spacing? A Case Study on Tomato

BACKGROUND AND AIMS: Plant growth models able to simulate phenotypic plasticity are increasingly required because (1) they should enable better predictions of the observed variations in crop production, yield and quality, and (2) their parameters are expected to have a more robust genetic basis, with possible implications for selection of quantitative traits such as growth- and allocation-related processes. The structure-function plant model, GREENLAB, simulates resource-dependent plasticity of plant architecture. Evidence for its generality has been previously reported, but always for plants grown in a limited range of environments. This paper aims to test the model concept to its limits by using plant spacing as a means to generate a gradient of competition for light, and by using a new crop species, tomato, known to exhibit a strong photomorphogenetic response. METHODS: A greenhouse experiment was carried out with three homogeneous planting densities (plant spacing = 0.3, 0.6 and 1 m). Detailed records of plant development, plant architecture and organ growth were made throughout the growing period. Model calibration was performed for each situation using a statistical optimization procedure (multi-fitting). KEY RESULTS AND CONCLUSIONS: Obvious limitations of the present version of the model appeared to account fully for the plant plasticity induced by inter-plant competition for light. A lack of stability was identified for some model parameters at very high planting density. In particular, those parameters characterizing organ sink strengths and governing light interception proved to be environment-dependent. Remarkably, however, responses of the parameter values concerned were consistent with actual growth measurements and with previously reported results. Furthermore, modifications of total biomass production and of allocation patterns induced by the planting-density treatments were accurately simulated using the sets of optimized parameters. These results demonstrate that the overall model structure is potentially able to reproduce the observed plant plasticity and suggest that sound biologically based adaptations could overcome the present model limitations. Potential options for model improvement are proposed, and the possibility of using the kernel algorithm currently available as a fitting tool to build up more sophisticated model versions is advocated.     

The derivation of sink functions of wheat organs using the GREENLAB model

BACKGROUND AND AIMS: In traditional crop growth models assimilate production and partitioning are described with empirical equations. In the GREENLAB functional-structural model, however, allocation of carbon to different kinds of organs depends on the number and relative sink strengths of growing organs present in the crop architecture. The aim of this study is to generate sink functions of wheat (Triticum aestivum) organs by calibrating the GREENLAB model using a dedicated data set, consisting of time series on the mass of individual organs (the 'target data'). METHODS: An experiment was conducted on spring wheat (Triticum aestivum, 'Minaret'), in a growth chamber from, 2004 to, 2005. Four harvests were made of six plants each to determine the size and mass of individual organs, including the root system, leaf blades, sheaths, internodes and ears of the main stem and different tillers. Leaf status (appearance, expansion, maturity and death) of these 24 plants was recorded. With the structures and mass of organs of four individual sample plants, the GREENLAB model was calibrated using a non-linear least-square-root fitting method, the aim of which was to minimize the difference in mass of the organs between measured data and model output, and to provide the parameter values of the model (the sink strengths of organs of each type, age and tiller order, and two empirical parameters linked to biomass production). KEY RESULTS AND CONCLUSIONS: The masses of all measured organs from one plant from each harvest were fitted simultaneously. With estimated parameters for sink and source functions, the model predicted the mass and size of individual organs at each position of the wheat structure in a mechanistic way. In addition, there was close agreement between experimentally observed and simulated values of leaf area index.     

Characterization of the interactions between architecture and source-sink relationships in winter oilseed rape (Brassica napus) using the GreenLab model

Background and Aims

This study aimed to characterize the interaction between architecture and source–sink relationships in winter oilseed rape (WOSR): do the costs of ramification compromise the source–sink ratio during seed filling? The GreenLab model is a good candidate to address this question because it has been already used to describe interactions between source–sink relationships and architecture for other species. However, its adaptation to WOSR is a challenge because of the complexity of its developmental scheme, especially during the reproductive phase.

Methods

Equations were added in GreenLab to compute expansion delays for ramification, flowering of each axis and photosynthesis of pods including the energetic cost of oil synthesis. Experimental field data were used to estimate morphological parameters while source–sink parameters of the model were estimated by adjustment of model outputs to the data. Ecophysiological outputs were used to assess the sources/sink relationships during the whole growth cycle.

Key Results

First results indicated that, at the plant scale, the model correctly simulates the dynamics of organ growth. However, at the organ scale, errors were observed that could be explained either by secondary growth that was not incorporated or by uncertainties in morphological parameters (durations of expansion and life). Ecophysiological outputs highlighted the dramatic negative impact of ramification on the source–sink ratio, as well as the decrease in this ratio during seed filling despite pod envelope photosynthesis that allowed significant biomass production to be maintained.

Conclusions

This work is a promising first step in the construction of a structure–function model for a plant as complex as WOSR. Once tested for other environments and/or genotypes, the model can be used for studies on WOSR architectural plasticity.     

The potential for nitrification and nitrate uptake in the rhizosphere of wetland plants: a modelling study

BACKGROUND AND AIMS: It has recently found that lowland rice grown hydroponically is exceptionally efficient in absorbing NO3-, raising the possibility that rice and other wetland plants growing in flooded soil may absorb significant amounts of NO3- formed by nitrification of NH4+ in the rhizosphere. This is important because (a) this NO3- is otherwise lost through denitrification in the soil bulk; and (b) plant growth and yield are generally improved when plants absorb their nitrogen as a mixture of NO3- and NH4+ compared with growth on either N source on its own. A mathematical model is developed here with which to assess the extent of NO3- absorption from the rhizosphere by wetland plants growing in flooded soil, considering the important plant and soil processes operating. METHODS: The model considers rates of O2 transport away from an individual root and simultaneous O2 consumption in microbial and non-microbial processes; transport of NH4+ towards the root and its consumption in nitrification and uptake at the root surface; and transport of NO3- formed from NH4+ towards the root and its consumption in denitrification and uptake by the root. The sensitivity of the model's predictions to its input parameters is tested over the range of conditions in which wetland plants grow. KEY RESULTS: The model calculations show that substantial quantities of NO3- can be produced in the rhizosphere of wetland plants through nitrification and taken up by the roots under field conditions. The rates of NO3- uptake can be comparable with those of NH4+. The model also shows that rates of denitrification and subsequent loss of N from the soil remain small even where NO3- production and uptake are considerable. CONCLUSIONS: Nitrate uptake by wetland plants may be far more important than thought hitherto. This has implications for managing wetland soils and water, as discussed in this paper.     

Complementarity in root architecture for nutrient uptake in ancient maize/bean and maize/bean/squash polycultures

Background and Aims

During their domestication, maize, bean and squash evolved in polycultures grown by small-scale farmers in the Americas. Polycultures often overyield on low-fertility soils, which are a primary production constraint in low-input agriculture. We hypothesized that root architectural differences among these crops causes niche complementarity and thereby greater nutrient acquisition than corresponding monocultures.

Methods

A functional–structural plant model, SimRoot, was used to simulate the first 40 d of growth of these crops in monoculture and polyculture and to determine the effects of root competition on nutrient uptake and biomass production of each plant on low-nitrogen, -phosphorus and -potassium soils.

Key Results

Squash, the earliest domesticated crop, was most sensitive to low soil fertility, while bean, the most recently domesticated crop, was least sensitive to low soil fertility. Nitrate uptake and biomass production were up to 7 % greater in the polycultures than in the monocultures, but only when root architecture was taken into account. Enhanced nitrogen capture in polycultures was independent of nitrogen fixation by bean. Root competition had negligible effects on phosphorus or potassium uptake or biomass production.

Conclusions

We conclude that spatial niche differentiation caused by differences in root architecture allows polycultures to overyield when plants are competing for mobile soil resources. However, direct competition for immobile resources might be negligible in agricultural systems. Interspecies root spacing may also be too large to allow maize to benefit from root exudates of bean or squash. Above-ground competition for light, however, may have strong feedbacks on root foraging for immobile nutrients, which may increase cereal growth more than it will decrease the growth of the other crops. We note that the order of domestication of crops correlates with increasing nutrient efficiency, rather than production potential.     

Dynamic Model for the Effects of Soil P and Fertilizer P on Crop Growth, P Uptake and Soil P in Arable Cropping: Experimental Test of the Model for Field Vegetables

In a previous paper (Greenwood et al. Annals of Botany88: 279–291,2001), we described a mechanistic model that calculates theeffects of extractable soil P and fertilizer P on daily incrementsin dry matter yield and P uptake of field crops. This paperdescribes the calibration of that model for six different speciesand subsequent tests of the calibrated model against resultsof independent experiments on the same soil type. Calibrationsfor lettuce, carrot and turnip were obtained by altering onlyone parameter, the effective root radius, while for onion, leekand spinach, both this and one of the parameters linking growthrate to % P in the plant were altered. The validity of the calibratedmodel was tested against results of field experiments that wereharvested at the seedling stage and at commercial maturity.The model predictions of the shapes of the responses of dryweight and of % P to both extractable soil P and fertilizerP were generally not significantly different from those measured.The model also gave satisfactory predictions of the time courseof dry weight and plant % P from emergence to commercial harvestof two crops grown with optimum levels of P fertilizer. In anotherexperiment, reasonably good agreement was obtained between simulatedresponses of plant dry weight yield and % P in the dry matterof carrot at commercial maturity and mid-way through the growingseason. Values of the effective root radius and various rootparameters, and calculations of P fluxes through the soil tothe root surfaces during the course of the simulation were,with few exceptions, consistent with information in the literature.Simulated P responsiveness is very sensitive to changes in thevalues of plant parameters affecting the dependence of P uptakeon plant % P as well as those concerned with the ability ofroots to exploit the soil's reserves of P. Reasons for inter-speciesdifferences in P response are elucidated and weaknesses in themodel identified. The model could form the basis of a short-cutapproach to forecasting optimal fertilizer P practices for differentcrops on different soils. It runs interactively on the Internetat: www.qpais.co.uk/phosmod/phos.htm Copyright 2001 Annals ofBotany Company Vegetable crops, model, simulation, plant phosphate, phosphate fertilizer, soil phosphate, crop response, root radius, species comparison     

Dynamic root growth and architecture responses to limiting nutrient availability: linking physiological models and experimentation

In recent years the study of root phenotypic plasticity in response to sub-optimal environmental factors and the genetic control of these responses have received renewed attention. As a path to increased productivity, in particular for low fertility soils, several applied research projects worldwide target the improvement of crop root traits both in plant breeding and biotechnology contexts. To assist these tasks and address the challenge of optimizing root growth and architecture for enhanced mineral resource use, the development of realistic simulation models is of great importance. We review this research field from a modeling perspective focusing particularly on nutrient acquisition strategies for crop production on low nitrogen and low phosphorous soils. Soil heterogeneity and the dynamics of nutrient availability in the soil pose a challenging environment in which plants have to forage efficiently for nutrients in order to maintain their internal nutrient homeostasis throughout their life cycle. Mathematical models assist in understanding plant growth strategies and associated root phenes that have potential to be tested and introduced in physiological breeding programs. At the same time, we stress that it is necessary to carefully consider model assumptions and development from a whole plant-resource allocation perspective and to introduce or refine modules simulating explicitly root growth and architecture dynamics through ontogeny with reference to key factors that constrain root growth. In this view it is important to understand negative feedbacks such as plant–plant competition. We conclude by briefly touching on available and developing technologies for quantitative root phenotyping from lab to field, from quantification of partial root profiles in the field to 3D reconstruction of whole root systems. Finally, we discuss how these approaches can and should be tightly linked to modeling to explore the root phenome.     

Phenotypic plasticity of the maize root system in response to heterogeneous nitrogen availability

Mineral nutrients are distributed in a non-uniform manner in the soil. Plasticity in root responses to the availability of mineral nutrients is believed to be important for optimizing nutrient acquisition. The response of root architecture to heterogeneous nutrient availability has been documented in various plant species, and the molecular mechanisms coordinating these responses have been investigated particularly in Arabidopsis, a model dicotyledonous plant. Recently, progress has been made in describing the phenotypic plasticity of root architecture in maize, a monocotyledonous crop. This article reviews aspects of phenotypic plasticity of maize root system architecture, with special emphasis on describing (1) the development of its complex root system; (2) phenotypic responses in root system architecture to heterogeneous N availability; (3) the importance of phenotypic plasticity for N acquisition; (4) different regulation of root growth and nutrients uptake by shoot; and (5) root traits in maize breeding. This knowledge will inform breeding strategies for root traits enabling more efficient acquisition of soil resources and synchronizing crop growth demand, root resource acquisition and fertilizer application during crop growing season, thereby maximizing crop yields and nutrient-use efficiency and minimizing environmental pollution.     

How plant architecture affects light absorption and photosynthesis in tomato: towards an ideotype for plant architecture using a functional-structural plant model

Background and Aims

Manipulation of plant structure can strongly affect light distribution in the canopy and photosynthesis. The aim of this paper is to find a plant ideotype for optimization of light absorption and canopy photosynthesis. Using a static functional structural plant model (FSPM), a range of different plant architectural characteristics was tested for two different seasons in order to find the optimal architecture with respect to light absorption and photosynthesis.

Methods

Simulations were performed with an FSPM of a greenhouse-grown tomato crop. Sensitivity analyses were carried out for leaf elevation angle, leaf phyllotaxis, leaflet angle, leaf shape, leaflet arrangement and internode length. From the results of this analysis two possible ideotypes were proposed. Four different vertical light distributions were also tested, while light absorption cumulated over the whole canopy was kept the same.

Key Results

Photosynthesis was augmented by 6 % in winter and reduced by 7 % in summer, when light absorption in the top part of the canopy was increased by 25 %, while not changing light absorption of the canopy as a whole. The measured plant structure was already optimal with respect to leaf elevation angle, leaflet angle and leaflet arrangement for both light absorption and photosynthesis while phyllotaxis had no effect. Increasing the length : width ratio of leaves by 1·5 or increasing internode length from 7 cm to 12 cm led to an increase of 6–10 % for light absorption and photosynthesis.

Conclusions

At high light intensities (summer) deeper penetration of light in the canopy improves crop photosynthesis, but not at low light intensities (winter). In particular, internode length and leaf shape affect the vertical distribution of light in the canopy. A new plant ideotype with more spacious canopy architecture due to long internodes and long and narrow leaves led to an increase in crop photosynthesis of up to 10 %.     

Computing competition for light in the GREENLAB model of plant growth: a contribution to the study of the effects of density on resource acquisition and architectural development

BACKGROUND AND AIMS: The dynamical system of plant growth GREENLAB was originally developed for individual plants, without explicitly taking into account interplant competition for light. Inspired by the competition models developed in the context of forest science for mono-specific stands, we propose to adapt the method of crown projection onto the x-y plane to GREENLAB, in order to study the effects of density on resource acquisition and on architectural development. METHODS: The empirical production equation of GREENLAB is extrapolated to stands by computing the exposed photosynthetic foliage area of each plant. The computation is based on the combination of Poisson models of leaf distribution for all the neighbouring plants whose crown projection surfaces overlap. To study the effects of density on architectural development, we link the proposed competition model to the model of interaction between functional growth and structural development introduced by Mathieu (2006, PhD Thesis, Ecole Centrale de Paris, France). KEY RESULTS AND CONCLUSIONS: The model is applied to mono-specific field crops and forest stands. For high-density crops at full cover, the model is shown to be equivalent to the classical equation of field crop production (Howell and Musick, 1985, in Les besoins en eau des cultures; Paris: INRA Editions). However, our method is more accurate at the early stages of growth (before cover) or in the case of intermediate densities. It may potentially account for local effects, such as uneven spacing, variation in the time of plant emergence or variation in seed biomass. The application of the model to trees illustrates the expression of plant plasticity in response to competition for light. Density strongly impacts on tree architectural development through interactions with the source-sink balances during growth. The effects of density on tree height and radial growth that are commonly observed in real stands appear as emerging properties of the model.     

The theory and application of plant competition models: an agronomic perspective

Many studies of plant competition have been directed towards understanding how plants respond to density in monocultures and how the presence of weeds affects yield in crops. In this Botanical Briefing, the development and current understanding of plant competition is reviewed, with particular emphasis being placed on the theory of plant competition and the development and application of mathematical models to crop-weed competition and the dynamics of weeds in crops. By consolidating the results of past research in this manner, it is hoped to offer a context in which researchers can consider the potential directions for future research in competition studies and its application to integrated weed management.     

Modelling seedling growth rates of 18 temperate arable weed species as a function of the environment and plant traits

BACKGROUND AND AIMS: The early growth rate of seedlings in the exponential phase is an important eco- physiological trait in crop/weed competition models based on assessments of relative weed green area. An understanding of the role of various plant traits in determining early growth rate may also be useful for identifying contrasting weed strategies for establishment before canopy closure. METHODS: The response of seedling relative growth rate (RGR) to the environment was measured in outdoor sand beds in the autumn and the spring for 18 temperate annual weed species and two crops. Seedling growth was modelled using thermal time and effective day-degrees (combining the effect of temperature and radiation). The contribution of various plant traits in determining variability in RGR was investigated using regression analysis. KEY RESULTS: The effective day-degree model was more effective for describing early weed growth than thermal time. Variability in RGR measured in the autumn was largely determined by differences between the species in net assimilation rate (NAR), whereas in the spring leaf area ratio (LAR) played a larger part. There were differences between the broadleaf and grass species in the relative contribution of NAR and LAR to RGR in both seasons. RGR in the spring was negatively correlated with initial seedling size. CONCLUSIONS: The parameters derived in this study can be used to calibrate empirical models of crop yield loss based on relative weed green area to different growing seasons and assessment dates. The grass weeds, which tended to have large seeds, had a higher investment in roots in the seedling stage, potentially making them more competitive later in the season when resources become limiting.     

Modelling diverse root density dynamics and deep nitrogen uptake—A simple approach

We present a 2-D model for simulation of root density and plant nitrogen (N) uptake for crops grown in agricultural systems, based on a modification of the root density equation originally proposed by Gerwitz and Page in J Appl Ecol 11:773–781, (1974). A root system form parameter was introduced to describe the distribution of root length vertically and horizontally in the soil profile. The form parameter can vary from 0 where root density is evenly distributed through the soil profile, to 8 where practically all roots are found near the surface. The root model has other components describing root features, such as specific root length and plant N uptake kinetics. The same approach is used to distribute root length horizontally, allowing simulation of root growth and plant N uptake in row crops. The rooting depth penetration rate and depth distribution of root density were found to be the most important parameters controlling crop N uptake from deeper soil layers. The validity of the root distribution model was tested with field data for white cabbage, red beet, and leek. The model was able to simulate very different root distributions, but it was not able to simulate increasing root density with depth as seen in the experimental results for white cabbage. The model was able to simulate N depletion in different soil layers in two field studies. One included vegetable crops with very different rooting depths and the other compared effects of spring wheat and winter wheat. In both experiments variation in spring soil N availability and depth distribution was varied by the use of cover crops. This shows the model sensitivity to the form parameter value and the ability of the model to reproduce N depletion in soil layers. This work shows that the relatively simple root model developed, driven by degree days and simulated crop growth, can be used to simulate crop soil N uptake and depletion appropriately in low N input crop production systems, with a requirement of few measured parameters.     

Towards modelling the flexible timing of shoot development: simulation of maize organogenesis based on coordination within and between phytomers

Background and Aims

Experimental evidence challenges the approximation, central in crop models, that developmental events follow a fixed thermal time schedule, and indicates that leaf emergence events play a role in the timing of development. The objective of this study was to build a structural development model of maize (Zea mays) based on a set of coordination rules at organ level that regulate duration of elongation, and to show how the distribution of leaf sizes emerges from this.

Methods

A model of maize development was constructed based on three coordination rules between leaf emergence events and the dynamics of organ extension. The model was parameterized with data from maize grown at a low plant population density and tested using data from maize grown at high population density.

Key Results

The model gave a good account of the timing and duration of organ extension. By using initial conditions associated with high population density, the model reproduced well the increase in blade elongation duration and the delay in sheath extension in high-density populations compared with low-density populations. Predictions of the sizes of sheaths at high density were accurate, whereas predictions of the dynamics of blade length were accurate up to rank 9; moderate overestimation of blade length occurred at higher ranks.

Conclusions

A set of simple rules for coordinated growth of organs is sufficient to simulate the development of maize plant structure without taking into account any regulation by assimilates. In this model, whole-plant architecture is shaped through initial conditions that feed a cascade of coordination events.     

Development of the Monsi-Saeki theory on canopy structure and function

BACKGROUND AND AIMS: Monsi and Saeki (1953) published the first mathematical model of canopy photosynthesis that was based on the light attenuation within a canopy and a light response of leaf photosynthesis. This paper reviews the evolution and development of their theory. SCOPE: Monsi and Saeki showed that under full light conditions, canopy photosynthesis is maximized at a high leaf area index (LAI, total leaf area per unit ground area) with vertically inclined leaves, while under low light conditions, it is at a low LAI with horizontal leaves. They suggested that actual plants develop a stand structure to maximize canopy photosynthesis. Combination of the Monsi-Saeki model with the cost-benefit hypothesis in resource use led to a new canopy photosynthesis model, where leaf nitrogen distribution and associated photosynthetic capacity were taken into account. The gradient of leaf nitrogen in a canopy was shown to be a direct response to the gradient of light. This response enables plants to use light and nitrogen efficiently, two resources whose supply is limited in the natural environment. CONCLUSION: The canopy photosynthesis model stimulated studies to scale-up from chloroplast biochemistry to canopy carbon gain and to analyse the resource-use strategy of species and individuals growing at different light and nitrogen availabilities. Canopy photosynthesis models are useful to analyse the size structure of populations in plant communities and to predict the structure and function of future terrestrial ecosystems.