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.     

Control of kernel weight and kernel water relations by post-flowering source-sink ratio in maize

The maize (Zea mays L.) kernel undergoes large changes in water content during its development. Whether such changes regulate the pattern of kernel development or are simply a consequence of it has not yet been established because other factors, such as assimilate supply, can also affect the rate and duration of kernel growth. This study was conducted to determine whether variation in kernel weight (KW) in response to source-sink treatments is mediated by a change in kernel water relations. Two hybrids were sown at three stand densities (one, eight and 18 plants m-2), and kernel numbers were restricted to control the post-flowering source-sink ratio within each stand density. Kernel development and water relations [water content, water potential (psiw), osmotic potential (psis) and turgor] were monitored throughout grain filling. Final KW varied from 253 to 372 mg per kernel in response to source-sink treatments. For both genotypes, variation in KW was a result of a change in kernel growth rate (r2 = 0.91; P < 0.001) and not in the duration of kernel filling. Final KW was closely correlated with maximum kernel water content (r2 = 0.94; P < 0.001) achieved during rapid dry matter accumulation. However, variation in KW was not reflected in kernel water status parameters (psiw, psis or turgor), which remained fairly stable across treatments. These results indicate that maximum water content provides an easily quantifiable measure of kernel sink capacity in maize. Kernel water status parameters may affect the duration of grain filling, but have no discernible impact on kernel growth rate.     

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.     

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.     

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 %.     

Cessation of tillering in spring wheat in relation to light interception and red : far-red ratio

BACKGROUND AND AIMS: The production of axillary shoots (tillering) in spring wheat (Triticum aestivum) depends on intraspecific competition. The mechanisms that underlie this competition are complex, but light within the wheat canopy plays a key role. The main objectives of this paper are to analyse the effects of plant population density and shade on tillering dynamics of spring wheat, to assess the canopy conditions quantitatively at the time of tillering cessation, and to analyse the relationship between the tiller bud and the leaf on the same phytomer. METHODS: Spring wheat plants were grown at three plant population densities and under two light regimes (25 % and 100 % light). Tiller appearance, fraction of the light intercepted, and red : far-red ratio at soil level were recorded. On six sampling dates the growth status of axillary buds was analysed. KEY RESULTS: Tillering ceased earlier at high population densities and ceased earlier in the shade than in full sunlight. At cessation of tillering, both the fraction of light intercepted and the red : far-red ratio at soil level were similar in all treatments. Leaves on the same phytomer of buds that grew out showed more leaf mass per unit area than those on the same phytomer of buds that remained dormant. CONCLUSIONS: Tillering ceases at specific light conditions within the wheat canopy, independent of population density, and to a lesser extent independent of light intensity. It is suggested that cessation of tillering is induced when the fraction of PAR intercepted by the canopy exceeds a specific threshold (0.40-0.45) and red : far-red ratio drops below 0.35-0.40.     

A functional-structural model for radiata pine (Pinus radiata) focusing on tree architecture and wood quality

Backgrounds and Aims

Functional–structural models are interesting tools to relate environmental and management conditions with forest growth. Their three-dimensional images can reveal important characteristics of wood used for industrial products. Like virtual laboratories, they can be used to evaluate relationships among species, sites and management, and to support silvicultural design and decision processes. Our aim was to develop a functional–structural model for radiata pine (Pinus radiata) given its economic importance in many countries.

Methods

The plant model uses the L-system language. The structure of the model is based on operational units, which obey particular rules, and execute photosynthesis, respiration and morphogenesis, according to their particular characteristics. Plant allometry is adhered to so that harmonic growth and plant development are achieved. Environmental signals for morphogenesis are used. Dynamic turnover guides the normal evolution of the tree. Monthly steps allow for detailed information of wood characteristics. The model is independent of traditional forest inventory relationships and is conceived as a mechanistic model. For model parameterization, three databases which generated new information relating to P. radiata were analysed and incorporated.

Key Results

Simulations under different and contrasting environmental and management conditions were run and statistically tested. The model was validated against forest inventory data for the same sites and times and against true crown architectural data. The performance of the model for 6-year-old trees was encouraging. Total height, diameter and lengths of growth units were adequately estimated. Branch diameters were slightly overestimated. Wood density values were not satisfactory, but the cyclical pattern and increase of growth rings were reasonably well modelled.

Conclusions

The model was able to reproduce the development and growth of the species based on mechanistic formulations. It may be valuable in assessing stand behaviour under different environmental and management conditions, assisting in decision-making with regard to management, and as a research tool to formulate hypothesis regarding forest tree growth and development.     

Exploring the spatial distribution of light interception and photosynthesis of canopies by means of a functional-structural plant model

Background and Aims

At present most process-based models and the majority of three-dimensional models include simplifications of plant architecture that can compromise the accuracy of light interception simulations and, accordingly, canopy photosynthesis. The aim of this paper is to analyse canopy heterogeneity of an explicitly described tomato canopy in relation to temporal dynamics of horizontal and vertical light distribution and photosynthesis under direct- and diffuse-light conditions.

Methods

Detailed measurements of canopy architecture, light interception and leaf photosynthesis were carried out on a tomato crop. These data were used for the development and calibration of a functional–structural tomato model. The model consisted of an architectural static virtual plant coupled with a nested radiosity model for light calculations and a leaf photosynthesis module. Different scenarios of horizontal and vertical distribution of light interception, incident light and photosynthesis were investigated under diffuse and direct light conditions.

Key Results

Simulated light interception showed a good correspondence to the measured values. Explicitly described leaf angles resulted in higher light interception in the middle of the plant canopy compared with fixed and ellipsoidal leaf-angle distribution models, although the total light interception remained the same. The fraction of light intercepted at a north–south orientation of rows differed from east–west orientation by 10 % on winter and 23 % on summer days. The horizontal distribution of photosynthesis differed significantly between the top, middle and lower canopy layer. Taking into account the vertical variation of leaf photosynthetic parameters in the canopy, led to approx. 8 % increase on simulated canopy photosynthesis.

Conclusions

Leaf angles of heterogeneous canopies should be explicitly described as they have a big impact both on light distribution and photosynthesis. Especially, the vertical variation of photosynthesis in canopy is such that the experimental approach of photosynthesis measurements for model parameterization should be revised.     

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.     

Simulation of the evolution of root water foraging strategies in dry and shallow soils

Background and Aims

The dynamic structural development of plants can be seen as a strategy for exploiting the limited resources available within their environment, and we would expect that evolution would lead to efficient strategies that reduce costs while maximizing resource acquisition. In particular, perennial species endemic to habitats with shallow soils in seasonally dry environments have been shown to have a specialized root system morphology that may enhance access to water resources in the underlying rock. This study aimed to explore these hypotheses by applying evolutionary algorithms to a functional–structural root growth model.

Methods

A simulation model of a plant''s root system was developed, which represents the dynamics of water uptake and structural growth. The model is simple enough for evolutionary optimization to be computationally feasible, yet flexible enough to allow a range of structural development strategies to be explored. The model was combined with an evolutionary algorithm in order to investigate a case study habitat with a highly heterogeneous distribution of resources, both spatially and temporally – the situation of perennial plants occurring on shallow soils in seasonally dry environments. Evolution was simulated under two contrasting fitness criteria: (1) the ability to find wet cracks in underlying rock, and (2) maximizing above-ground biomass.

Key Results

The novel approach successfully resulted in the evolution of more efficient structural development strategies for both fitness criteria. Different rooting strategies evolved when different criteria were applied, and each evolved strategy made ecological sense in terms of the corresponding fitness criterion. Evolution selected for root system morphologies which matched those of real species from corresponding habitats.

Conclusions

Specialized root morphology with deeper rather than shallower lateral branching enhances access to water resources in underlying rock. More generally, the approach provides insights into both evolutionary processes and ecological costs and benefits of different plant growth strategies.     

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.     

Experiments and a model examining learning in the area-restricted search behavior of ferrets (Mustela putorius furo)

Area-restricted searches have been described as important componentsof the foraging behavior of many organisms. It is unclear, however,whether individual foragers can use learning to fine-tune theirsearches, or even whether these searches are efficiently performed.I used a simulation model to make qualitative predictions aboutsearch behavior in a laboratory system. The simulation modelindicates that the sinuosity and path length of searches stronglyaffect search efficiency. The model predicts that, for a rate-maximizingforager, path length should increase and search sinuosity shoulddecrease as prey become less clumped. Foraging animals may thereforebe selected to learn the path length and sinuosity of searchesin response to changing degrees of dumping of prey. These predictionswere tested in a laboratory system involving ferrets (Mustelaputorius furo) foraging for oil-drop "prey items." Search pathschanged in a graded manner to experimental manipulations ofthe dumping of prey. As predicted by the model, ferrets learnedto perform longer and less sinuous search paths as prey becameless clumped. This study provides the first evidence that area-restrictedsearch behavior is learned and can be fine-tuned to efficientlyexploit different spatial distributions of food.     

An excision and squash technique for analysis of the cell cycle in the root quiescent centre of maize

The quiescent centre of primary roots of Zea mays L. (cvs LG 11 and Golden Bantam) consists of a population of slowly cycling diploid cells. These metabolically inactive cells may be triggered to synthesise DNA under specific conditions and constitute a good model for studying the regulation of the cell cycle. An excision and squash technique is described for the quiescent centre which, when coupled with Feulgen and fluorochrome staining, allows nuclear DNA contents to be determined by microdensitometry in less than a day. This technique was coupled with experiments in which excised quiescent centres were placed on solid culture medium into which hormones and radioactive DNA precursors were incorporated. In complementary and control experiments [methyl-³H]thymidine was supplied to intact roots (with or without root caps) by means of fibre-glass cubes as donors.
Progression of the cell cycle was followed by microdensitometry and autoradiography. Distribution of DNA content was similar in excised and squashed quiescent centres and in histological sections. Labelling experiments showed that the quiescent centre is made up of cells that differ in their cycle time. While some labelled cells had reached mitosis after 8 h, others were still in G₂ after 16 h of continuous labelling. Excision and culture of the quiescent centre resulted in a dramatic activation of the cell cycle as shown by the labelling index that increased from 15% in intact roots fed during 16 h with [methyl-³H]thymidine to 31% in excised quiescent centres to which radioactive precursor was supplied during the same time. Supplying hormones (50 μ M abscisic acid [ABA], 0. 1 μ M zeatin, 1 μ M zeatin riboside) to quiescent centres via the culture medium restored their inactivity (labelling indices dropped to 1% after ABA. and to 11% after zeatin and zeatin riboside treatments. respectively).     

Towards a functional-structural plant model of cut-rose: simulation of light environment, light absorption, photosynthesis and interference with the plant structure

Background and Aims

The production system of cut-rose (Rosa × hybrida) involves a complex combination of plant material, management practice and environment. Plant structure is determined by bud break and shoot development while having an effect on local light climate. The aim of the present study is to cover selected aspects of the cut-rose system using functional–structural plant modelling (FSPM), in order to better understand processes contributing to produce quality and quantity.

Methods

The model describes the production system in three dimensions, including a virtual greenhouse environment with the crop, light sources (diffuse and direct sun light and lamps) and photosynthetically active radiation (PAR) sensors. The crop model is designed as a multiscaled FSPM with plant organs (axillary buds, leaves, internodes, flowers) as basic units, and local light interception and photosynthesis within each leaf. A Monte-Carlo light model was used to compute the local light climate for leaf photosynthesis, the latter described using a biochemical rate model.

Key Results

The model was able to reproduce PAR measurements taken at different canopy positions, different times of the day and different light regimes. Simulated incident and absorbed PAR as well as net assimilation rate in upright and bent shoots showed characteristic spatial and diurnal dynamics for different common cultivation scenarios.

Conclusions

The model of cut-rose presented allowed the creation of a range of initial structures thanks to interactive rules for pruning, cutting and bending. These static structures can be regarded as departure points for the dynamic simulation of production of flower canes. Furthermore, the model was able to predict local (per leaf) light absorption and photosynthesis. It can be used to investigate the physiology of ornamental plants, and provide support for the decisions of growers and consultants.     

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

Background and Aims

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

Methods

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

Key Results

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

Conclusions

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

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.     

Brood defense and brood size in the great tit (Parus major): a test of a model of unshared parental investment

To understand the interaction of the many contextual variablesthat affect parental behavior a number of static optimalitymodels have been developed. Among these the one by Lazarus andInglis (1986) is the only one to specifically predict the magnitudeof unshared parental investment (PI), i.e., of parental carethat carries a cost to the parent and that benefits all currentoffspring equally because it cannot be divided among them. Weinvestigated specifically how parent great tits (Parus major)gear their brood defense, a form of unshared PI, to the sizeof the brood at stake and to the risk incurred as a functionof the type of predator. The predators used were dummies ofthe great spotted woodpecker (Picoides major) and of the tawnyowl (Strix aluco). Normally, adults can approach the woodpeckerwith impunity; it had inflicted heavy losses to nestlings ofthe study populations of great tits near Wolfsburg, Lower Saxony.Parent great tits whose brood had been artificially reducedto two young responded to the dummy with less defense than dida control group with their pre-test brood size left intact.The nature of defense was qualitatively the same as that elicitedby a live woodpecker. Parents confronting the owl near theirbrood decreased their response with an artificial reductionin brood size much less. Because the owl used poses a seriousrisk to the defenders, as compared to the woodpecker, the resultlends powerful support to the "total loss" version of the modelof unshared PI; it predicts brood size to affect unshared PImore strongly when there is less risk to the parent. This interpretationis correct to the extent that one premise of the model, namelythat of uncompromised parentage, can be relaxed; great tit broodscontain a sizeable number of extrapair young. Males defendedtheir brood more strongly than did females. Sex and brood manipulationadded up linearly when affecting defense level, i.e., therewas no interaction.