Integrating simulation of architectural development and source-sink behaviour of peach trees by incorporating Markov chains and physiological organ function submodels into L-PEACH

Modeling Xylem Functionality Aspects

Depending on the questions to be answered, water flow in the xylem can be modelled following different approaches with varying spatial and temporal resolution. When focussing on the influence of hydraulic architecture upon flow dynamics, distribution of water potentials in a tree crown or questions of vulnerability of the hydraulic system, functional-structural plant models, which link representations of morphological structure with simulated processes and with a virtual environment, can be a promising tool. Such a model will then include a network of idealized xylem segments, each representing the conducting part of a stem or branch segment, and a numerical machinery suitable for solving a system of differential equations on it reflecting the hydrodynamic laws, which are the basis of the broadly accepted cohesion-tension theory of water flow in plants. We will discuss functional-structural plant models, the simplifications that are useful for hydraulic simulations within this framework, the deduction of the used differential equations from basic physical conservation laws, and their numerical solution, as well as additional necessary models of radiation, photosynthesis, and stomatal conductance. In some supplementary notes, we are shortly addressing some related questions, for example, about root systems or about the relation between macro-scale hydraulic parameters and fine-grained (anatomical) xylem structure.

Integrating terrestrial laser scanning with functional-structural plant models to investigate ecological and evolutionary processes of forest communities

BACKGROUND

Woody plants (trees and shrubs) play an important role in terrestrial ecosystems, but their size and longevity make them difficult subjects for traditional experiments. In the last 20 years functional-structural plant models (FSPMs) have evolved: they consider the interplay between plant modular structure, the immediate environment and internal functioning. However, computational constraints and data deficiency have long been limiting factors in a broader application of FSPMs, particularly at the scale of forest communities. Recently, terrestrial laser scanning (TLS), has emerged as an invaluable tool for capturing the 3-D structure of forest communities, thus opening up exciting opportunities to explore and predict forest dynamics with FSPMs.

SCOPE

The potential synergies between TLS-derived data and FSPMs have yet to be fully explored. Here, we summarize recent developments in FSPM and TLS research, with a specific focus on woody plants. We then evaluate the emerging opportunities for applying FSPMs in an ecological and evolutionary context, in light of TLS-derived data, with particular consideration of the challenges posed by scaling up from individual trees to whole forests. Finally, we propose guidelines for incorporating TLS data into the FSPM workflow to encourage overlap of practice amongst researchers.

CONCLUSIONS

We conclude that TLS is a feasible tool to help shift FSPMs from an individual-level modelling technique to a community-level one. The ability to scan multiple trees, of multiple species, in a short amount of time, is paramount to gathering the detailed structural information required for parameterizing FSPMs for forest communities. Conventional techniques, such as repeated manual forest surveys, have their limitations in explaining the driving mechanisms behind observed patterns in 3-D forest structure and dynamics. Therefore, other techniques are valuable to explore how forests might respond to environmental change. A robust synthesis between TLS and FSPMs provides the opportunity to virtually explore the spatial and temporal dynamics of forest communities.

V-Mango: a functional-structural model of mango tree growth, development and fruit production

BACKGROUND AND AIMS

Mango (Mangifera indica L.) is the fifth most widely produced fruit in the world. Its cultivation, mainly in tropical and sub-tropical regions, raises a number of issues such as the irregular fruit production across years, phenological asynchronisms that lead to long periods of pest and disease susceptibility, and the heterogeneity of fruit quality and maturity at harvest. To address these issues, we developed an integrative functional-structural plant model that synthesizes knowledge about the vegetative and reproductive development of the mango tree and opens up the possible simulation of cultivation practices.

METHODS

We designed a model of architectural development in order to precisely characterize the intricate developmental processes of the mango tree. The appearance of botanical entities was decomposed into elementary stochastic events describing occurrence, intensity and timing of development. These events were determined by structural (position and fate of botanical entities) and temporal (appearance dates) factors. Daily growth and development of growth units and inflorescences were modelled using empirical distributions and thermal time. Fruit growth was determined using an ecophysiological model that simulated carbon- and water-related processes at the fruiting branch scale.

KEY RESULTS

The model simulates the dynamics of the population of growth units, inflorescences and fruits at the tree scale during a growing cycle. Modelling the effects of structural and temporal factors makes it possible to simulate satisfactorily the complex interplays between vegetative and reproductive development. The model allowed the characterization of the susceptibility of mango tree to pests and the investigatation of the influence of tree architecture on fruit growth.

CONCLUSIONS

This integrative functional-structural model simulates mango tree vegetative and reproductive development over successive growing cycles, allowing a precise characterization of tree phenology and fruit growth and production. The next step is to integrate the effects of cultivation practices, such as pruning, into the model.

A Comparative Study on the Branching Pattern of Monocyclic and Bicyclic Shoots of Apple cv. "Fuji"

The development of tree architecture results from shoot growth and branching, but their relationship is still not fully understood. The goal of this study was to determine the effect of parent shoot growth characteristics on branching patterns in terms of polycyclism, growth duration (GD), and growth period (GP), considering apple tree as a case study. Weekly shoot growth records were collected from 227 shoots during their second year of growth and the resulting branching patterns from the following year. The branching patterns were compared between the different shoot categories, using hidden semi-Markov models. Our results showed that the branching pattern was similar in bicyclic and monocyclic shoots with a long GD. The number of floral laterals, and the frequency and length of the floral zones, increased with GD. Moreover, a long GD led to strong acrotony, due to the high occurrence of a vegetative zone with long laterals in the distal position of the shoot. In bicyclic shoots, an early GP of the second GU led to more frequent and longer floral zones than a late GP. Therefore, the GD was the strongest driver of the branching pattern, and GP modulated the flowering capacity. The main similarities among shoot categories resulted from the existence of latent buds and floral zones associated with growth cessation periods. Even though flowering was more abundant during the early GP, the positions of floral zones indicated that induction in axillary meristems can also occur late in the season. This study provides new knowledge regarding the relationships between the dynamics of parent shoot growth and axillary meristem fates, with key consequences on flowering abundance and positions.

Long proleptic and sylleptic shoots in peach (Prunus persica L. Batsch) trees have similar, predetermined, maximum numbers of nodes and bud fate patterns

BACKGROUND AND AIMS

In peach (Prunus persica) trees, three types of shoots can be distinguished depending on the time of their appearance: sylleptic, proleptic and epicormic. On proleptic shoots, an average of ten phytomers are preformed in dormant buds prior to shoot growth after bud-break, whereas all phytomers are considered neoformed in sylleptic and epicormic shoots. However, casual observations indicated that proleptic and sylleptic shoots appear quite similar in number of phytomers and structure in spite of their different origins. The goal of this research was to test the hypothesis that both proleptic and sylleptic shoots exhibit similar growth characteristics by analysing their node numbers and bud fate patterns. If their growth characteristics are similar, it would indicate that the structure of both types of shoots is primarily under genetic rather than environmental control.

METHODS

The number of phytomers and bud fate patterns of proleptic and sylleptic shoots of four peach cultivars grown in the same location (Winters, California) were analysed and characterized using hidden semi-Markov models. Field data were collected during winter 2016, just prior to floral bud-break.

KEY RESULTS

Sylleptic shoots tended to have slightly fewer phytomers than proleptic shoots of the same cultivars. The bud fate patterns along proleptic and sylleptic shoots were remarkably similar for all the cultivars, although proleptic shoots started growing earlier (at least 1 month) in the spring than sylleptic shoots.

CONCLUSIONS

This study provides strong evidence for the semi-deterministic nature of both proleptic and sylleptic shoots across four peach cultivars in terms of number of phytomers and bud fate patterns along shoots. It is apparent that the overall structure of shoots with similar numbers of phytomers was under similar genetic control for the two shoot types. Understanding shoot structural characteristics can aid in phenotypic characterization of vegetative growth of trees and in providing a foundation for vegetative management of fruit trees in horticultural settings.

Estimating Sink Parameters of Stochastic Functional-Structural Plant Models Using Organic Series-Continuous and Rhythmic Development

Functional-structural plant models (FSPMs) generally simulate plant development and growth at the level of individual organs (leaves, flowers, internodes, etc.). Parameters that are not directly measurable, such as the sink strength of organs, can be estimated inversely by fitting the weights of organs along an axis (organic series) with the corresponding model output. To accommodate intracanopy variability among individual plants, stochastic FSPMs have been built by introducing the randomness in plant development; this presents a challenge in comparing model output and experimental data in parameter estimation since the plant axis contains individual organs with different amounts and weights. To achieve model calibration, the interaction between plant development and growth is disentangled by first computing the occurrence probabilities of each potential site of phytomer, as defined in the developmental model (potential structure). On this basis, the mean organic series is computed analytically to fit the organ-level target data. This process is applied for plants with continuous and rhythmic development simulated with different development parameter sets. The results are verified by Monte-Carlo simulation. Calibration tests are performed both in silico and on real plants. The analytical organic series are obtained for both continuous and rhythmic cases, and they match well with the results from Monte-Carlo simulation, and vice versa. This fitting process works well for both the simulated and real data sets; thus, the proposed method can solve the source-sink functions of stochastic plant architectures through a simplified approach to plant sampling. This work presents a generic method for estimating the sink parameters of a stochastic FSPM using statistical organ-level data, and it provides a method for sampling stems. The current work breaks a bottleneck in the application of FSPMs to real plants, creating the opportunity for broad applications.

Stochastic modelling of tree architecture and biomass allocation: application to teak (Tectona grandis L. f.), a tree species with polycyclic growth and leaf neoformation

Background and aims

For a given genotype, the observed variability of tree forms results from the stochasticity of meristem functioning and from changing and heterogeneous environmental factors affecting biomass formation and allocation. In response to climate change, trees adapt their architecture by adjusting growth processes such as pre- and neoformation, as well as polycyclic growth. This is the case for the teak tree. The aim of this work was to adapt the plant model, GreenLab, in order to take into consideration both these processes using existing data on this tree species.

Methods

This work adopted GreenLab formalism based on source-sink relationships at organ level that drive biomass production and partitioning within the whole plant over time. The stochastic aspect of phytomer production can be modelled by a Bernoulli process. The teak model was designed, parameterized and analysed using the architectural data from 2- to 5-year-old teak trees in open field stands.

Key results

Growth and development parameters were identified, fitting the observed compound organic series with the theoretical series, using generalized least squares methods. Phytomer distributions of growth units and branching pattern varied depending on their axis category, i.e. their physiological age. These emerging properties were in accordance with the observed growth patterns and biomass allocation dynamics during a growing season marked by a short dry season.

Conclusions

Annual growth patterns observed on teak, including shoot pre- and neoformation and polycyclism, were reproduced by the new version of the GreenLab model. However, further updating is discussed in order to ensure better consideration of radial variation in basic specific gravity of wood. Such upgrading of the model will enable teak ideotypes to be defined for improving wood production in terms of both volume and quality.

Use of computational modeling combined with advanced visualization to develop strategies for the design of crop ideotypes to address food security

Sustainable crop production is a contributing factor to current and future food security. Innovative technologies are needed to design strategies that will achieve higher crop yields on less land and with fewer resources. Computational modeling coupled with advanced scientific visualization enables researchers to explore and interact with complex agriculture, nutrition, and climate data to predict how crops will respond to untested environments. These virtual observations and predictions can direct the development of crop ideotypes designed to meet future yield and nutritional demands. This review surveys modeling strategies for the development of crop ideotypes and scientific visualization technologies that have led to discoveries in "big data" analysis. Combined modeling and visualization approaches have been used to realistically simulate crops and to guide selection that immediately enhances crop quantity and quality under challenging environmental conditions. This survey of current and developing technologies indicates that integrative modeling and advanced scientific visualization may help overcome challenges in agriculture and nutrition data as large-scale and multidimensional data become available in these fields.

Using numerical plant models and phenotypic correlation space to design achievable ideotypes

Numerical plant models can predict the outcome of plant traits modifications resulting from genetic variations, on plant performance, by simulating physiological processes and their interaction with the environment. Optimization methods complement those models to design ideotypes, that is, ideal values of a set of plant traits, resulting in optimal adaptation for given combinations of environment and management, mainly through the maximization of performance criteria (e.g. yield and light interception). As use of simulation models gains momentum in plant breeding, numerical experiments must be carefully engineered to provide accurate and attainable results, rooting them in biological reality. Here, we propose a multi-objective optimization formulation that includes a metric of performance, returned by the numerical model, and a metric of feasibility, accounting for correlations between traits based on field observations. We applied this approach to two contrasting models: a process-based crop model of sunflower and a functional-structural plant model of apple trees. In both cases, the method successfully characterized key plant traits and identified a continuum of optimal solutions, ranging from the most feasible to the most efficient. The present study thus provides successful proof of concept for this enhanced modelling approach, which identified paths for desirable trait modification, including direction and intensity.

Simulation of carbon allocation and organ growth variability in apple tree by connecting architectural and source-sink models

BACKGROUND AND AIMS

Plant growth depends on carbon availability and allocation among organs. QualiTree has been designed to simulate carbon allocation and partitioning in the peach tree (Prunus persica), whereas MappleT is dedicated to the simulation of apple tree (Malus × domestica) architecture. The objective of this study was to couple both models and adapt QualiTree to apple trees to simulate organ growth traits and their within-tree variability.

METHODS

MappleT was used to generate architectures corresponding to the 'Fuji' cultivar, accounting for the variability within and among individuals. These architectures were input into QualiTree to simulate shoot and fruit growth during a growth cycle. We modified QualiTree to account for the observed shoot polymorphism in apple trees, i.e. different classes (long, medium and short) that were characterized by different growth function parameters. Model outputs were compared with observed 3D tree geometries, considering shoot and final fruit size and growth dynamics.

KEY RESULTS

The modelling approach connecting MappleT and QualiTree was appropriate to the simulation of growth and architectural characteristics at the tree scale (plant leaf area, shoot number and types, fruit weight at harvest). At the shoot scale, mean fruit weight and its variability within trees was accurately simulated, whereas the model tended to overestimate individual shoot leaf area and underestimate its variability for each shoot type. Varying the parameter related to the intensity of carbon exchange between shoots revealed that behaviour intermediate between shoot autonomy and a common assimilate pool was required to properly simulate within-tree fruit growth variability. Moreover, the model correctly dealt with the crop load effect on organ growth.

CONCLUSIONS

This study provides understanding of the integration of shoot ontogenetic properties, carbon supply and transport between entities for simulating organ growth in trees. Further improvements regarding the integration of retroaction loops between carbon allocation and the resulting plant architecture are expected to allow multi-year simulations.

Integrating mixed-effect models into an architectural plant model to simulate inter- and intra-progeny variability: a case study on oil palm (Elaeis guineensis Jacq.)

Three-dimensional (3D) reconstruction of plants is time-consuming and involves considerable levels of data acquisition. This is possibly one reason why the integration of genetic variability into 3D architectural models has so far been largely overlooked. In this study, an allometry-based approach was developed to account for architectural variability in 3D architectural models of oil palm (Elaeis guineensis Jacq.) as a case study. Allometric relationships were used to model architectural traits from individual leaflets to the entire crown while accounting for ontogenetic and morphogenetic gradients. Inter- and intra-progeny variabilities were evaluated for each trait and mixed-effect models were used to estimate the mean and variance parameters required for complete 3D virtual plants. Significant differences in leaf geometry (petiole length, density of leaflets, and rachis curvature) and leaflet morphology (gradients of leaflet length and width) were detected between and within progenies and were modelled in order to generate populations of plants that were consistent with the observed populations. The application of mixed-effect models on allometric relationships highlighted an interesting trade-off between model accuracy and ease of defining parameters for the 3D reconstruction of plants while at the same time integrating their observed variability. Future research will be dedicated to sensitivity analyses coupling the structural model presented here with a radiative balance model in order to identify the key architectural traits involved in light interception efficiency.

Bud structure, position and fate generate various branching patterns along shoots of closely related Rosaceae species: a review

Branching in temperate plants is closely linked to bud fates, either floral or vegetative. Here, we review how the fate of meristematic tissues contained in buds and their position along a shoot imprint specific branching patterns which differ among species. Through examples chosen in closely related species in different genera of the Rosaceae family, a panorama of patterns is apparent. Patterns depend on whether vegetative and floral buds are borne individually or together in mixed buds, develop as the shoot grows or after a rest period, and are located in axillary or terminal positions along the parent shoot. The resulting branching patterns are conserved among varieties in a given species but progressively change with the parent shoot length during plant ontogeny. They can also be modulated by agronomic and environmental conditions. The existence of various organizations in the topology and fate of meristematic tissues and their appendages in closely related species questions the between-species conservation of physiological and molecular mechanisms leading to bud outgrowth vs. quiescence and to floral induction vs. vegetative development.

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.

Measuring and modelling seasonal patterns of carbohydrate storage and mobilization in the trunks and root crowns of peach trees

BACKGROUND AND AIMS

Developing a conceptual and functional framework for simulating annual long-term carbohydrate storage and mobilization in trees has been a weak point for virtually all tree models. This paper provides a novel approach for solving this problem using empirical field data and details of structural components of simulated trees to estimate the total carbohydrate stored over a dormant season and available for mobilization during spring budbreak.

METHODS

The seasonal patterns of mobilization and storage of non-structural carbohydrates in bark and wood of the scion and rootstock crowns of the trunks of peach (Prunus persica) trees were analysed subsequent to treatments designed to maximize differences in source-sink behaviour during the growing season. Mature peach trees received one of three treatments (defruited and no pruning, severe pruning to 1·0 m, and unthinned with no pruning) in late winter, just prior to budbreak. Selected trees of each treatment were harvested at four times (March, June, August and November) and slices of trunk and root crown tissue above and below the graft union were removed for carbohydrate analysis. Inner bark and xylem tissues from the first to fifth rings were separated and analysed for non-structural carbohydrates. Data from these experiments were then used to estimate the amount of non-structural carbohydrates available for mobilization and to parameterize a carbohydrate storage sub-model in the functional-structural L-PEACH model.

KEY RESULTS

The mass fraction of carbohydrates in all sample tissues decreased from March to June, but the decrease was greatest in the severely pruned and unthinned treatments. November carbohydrate mass fractions in all tissues recovered to values similar to those in the previous March, except in the older xylem rings of the severely pruned and unthinned treatment. Carbohydrate storage sink capacity in trunks was empirically estimated from the mean maximum measured trunk non-structural carbohydrate mass fractions. The carbohydrate storage source available for mobilization was estimated from these maximum mass fractions and the early summer minimum mass fractions remaining in these tissues in the severe treatments that maximized mobilization of stored carbohydrates. The L-PEACH sink-source carbohydrate distribution framework was then used along with simulated tree structure to successfully simulate annual carbohydrate storage sink and source behaviour over years.

CONCLUSIONS

The sink-source concept of carbohydrate distribution within a tree was extended to include winter carbohydrate storage and spring mobilization by considering the storage sink and source as a function of the collective capacity of active xylem and phloem tissue of the tree, and its annual behaviour was effectively simulated using the L-PEACH functional-structural plant model.

Towards aspect-oriented functional--structural plant modelling

BACKGROUND AND AIMS

Functional-structural plant models (FSPMs) are used to integrate knowledge and test hypotheses of plant behaviour, and to aid in the development of decision support systems. A significant amount of effort is being put into providing a sound methodology for building them. Standard techniques, such as procedural or object-oriented programming, are not suited for clearly separating aspects of plant function that criss-cross between different components of plant structure, which makes it difficult to reuse and share their implementations. The aim of this paper is to present an aspect-oriented programming approach that helps to overcome this difficulty.

METHODS

The L-system-based plant modelling language L+C was used to develop an aspect-oriented approach to plant modelling based on multi-modules. Each element of the plant structure was represented by a sequence of L-system modules (rather than a single module), with each module representing an aspect of the element's function. Separate sets of productions were used for modelling each aspect, with context-sensitive rules facilitated by local lists of modules to consider/ignore. Aspect weaving or communication between aspects was made possible through the use of pseudo-L-systems, where the strict-predecessor of a production rule was specified as a multi-module.

KEY RESULTS

The new approach was used to integrate previously modelled aspects of carbon dynamics, apical dominance and biomechanics with a model of a developing kiwifruit shoot. These aspects were specified independently and their implementation was based on source code provided by the original authors without major changes.

CONCLUSIONS

This new aspect-oriented approach to plant modelling is well suited for studying complex phenomena in plant science, because it can be used to integrate separate models of individual aspects of plant development and function, both previously constructed and new, into clearly organized, comprehensive FSPMs. In a future work, this approach could be further extended into an aspect-oriented programming language for FSPMs.

Linking water stress effects on carbon partitioning by introducing a xylem circuit into L-PEACH

BACKGROUND AND AIMS

Many physiological processes such as photosynthesis, respiration and transpiration can be strongly influenced by the diurnal patterns of within-tree water potential. Despite numerous experiments showing the effect of water potential on fruit-tree development and growth, there are very few models combining carbohydrate allocation with water transport. The aim of this work was to include a xylem circuit into the functional-structural L-PEACH model.

METHODS

The xylem modelling was based on an electrical circuit analogy and the Hagen-Poisseuille law for hydraulic conductance. Sub-models for leaf transpiration, soil water potential and the soil-plant interface were also incorporated to provide the driving force and pathway for water flow. The model was assessed by comparing model outputs to field measurements and published knowledge.

KEY RESULTS

The model was able to simulate both the water uptake over a season and the effect of different irrigation treatments on tree development, growth and fruit yield.

CONCLUSIONS

This work opens the way to a new field of modelling where complex interactions between water transport, carbohydrate allocation and physiological functions can be simulated at the organ level and describe functioning and behaviour at the tree scale.

Modelling the size and composition of fruit, grain and seed by process-based simulation models

Understanding what determines the size and composition of fruit, grain and seed in response to the environment and genotype is challenging, as these traits result from several linked processes controlled at different levels of organization, from the subcellular to the crop level, with subtle interactions occurring at or between the levels of organization. Process-based simulation models (PBSMs) implement algorithms to simulate metabolic and biophysical aspects of cell, tissue and organ behaviour. In this review, fruit, grain and seed PBSMs describing the main phases of growth, development and storage metabolism are discussed. From this concurrent work, it is possible to identify generic storage organ processes which can be modelled similarly for fruit, grain and seed. Spatial heterogeneity at the tissue and whole-plant level is found to be a key consideration in modelling the effects of the environment and genotype on fruit, grain and seed end-use value. In the future, PBSMs may well become the main link between studies at the molecular and whole-plant levels. To bridge this phenotype-to-genotype gap, future models need to remain plastic without becoming overparameterized.

Modelling photo-modulated internode elongation in growing glasshouse cucumber canopies

• Growing glasshouse plant canopies are exposed to natural fluctuations in light quantity, and the dynamically changing canopy architecture induces local variations in light quality. This modelling study aimed to analyse the importance of both light signals for an accurate prediction of individual internode lengths. • We conceptualized two model approaches for estimating final internode lengths (FILs). The first one is only photosynthetically active radiation (PAR)-sensitive and ignores canopy architecture, whereas the second approach uses a functional-structural growth model for considering variations in both PAR and red : far-red (R : FR) ratio (L-Cucumber). Internode lengths measured in three experiments were used for model parameterization and evaluation. • The overall trends for the simulated FILs using the exclusively PAR-sensitive model approach were already in line with the measured FILs, but they underestimated FILs at higher ranks. L-Cucumber provided considerably better FIL predictions under various light conditions and canopy architectures. • Both light signals are needed for an accurate estimation of the FILs, and only L-Cucumber is able to consider R : FR signals from the growing canopy. Yet this study highlights the significance of the PAR signal for predicting FILs as neighbour effects increase, which indicates a potential role of photosynthate signalling in internode elongation.

A functional-structural kiwifruit vine model integrating architecture, carbon dynamics and effects of the environment

BACKGROUND AND AIMS

Functional-structural modelling can be used to increase our understanding of how different aspects of plant structure and function interact, identify knowledge gaps and guide priorities for future experimentation. By integrating existing knowledge of the different aspects of the kiwifruit (Actinidia deliciosa) vine's architecture and physiology, our aim is to develop conceptual and mathematical hypotheses on several of the vine's features: (a) plasticity of the vine's architecture; (b) effects of organ position within the canopy on its size; (c) effects of environment and horticultural management on shoot growth, light distribution and organ size; and (d) role of carbon reserves in early shoot growth.

METHODS

Using the L-system modelling platform, a functional-structural plant model of a kiwifruit vine was created that integrates architectural development, mechanistic modelling of carbon transport and allocation, and environmental and management effects on vine and fruit growth. The branching pattern was captured at the individual shoot level by modelling axillary shoot development using a discrete-time Markov chain. An existing carbon transport resistance model was extended to account for several source/sink components of individual plant elements. A quasi-Monte Carlo path-tracing algorithm was used to estimate the absorbed irradiance of each leaf.

KEY RESULTS

Several simulations were performed to illustrate the model's potential to reproduce the major features of the vine's behaviour. The model simulated vine growth responses that were qualitatively similar to those observed in experiments, including the plastic response of shoot growth to local carbon supply, the branching patterns of two Actinidia species, the effect of carbon limitation and topological distance on fruit size and the complex behaviour of sink competition for carbon.

CONCLUSIONS

The model is able to reproduce differences in vine and fruit growth arising from various experimental treatments. This implies it will be a valuable tool for refining our understanding of kiwifruit growth and for identifying strategies to improve production.

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.

Modelling phloem transport within a pruned dwarf bean: a 2-source-3-sink system

A mechanistic model of carbon partitioning, based on the Münch hypothesis of phloem transport and implemented with PIAF-Münch modelling platform (Lacointe and Minchin 2008), was tested for an architecture more complex than any tested previously. Using 11C to label photosynthate, responses in transport of photosynthate within a heavily pruned dwarf bean plant (Phaseolus vulgaris L.) to changes in source and sink activities were compared with model predictions. The observed treatment responses were successfully predicted. However, the observations could not be completely explained if the modelled stem contained only one phloem pathway: tracer from a labelled leaf was always detected in both shoot apex and root, whichever of the two leaves was labelled. This shows that bidirectional flow occurred within the stem, with solute moving simultaneously in both directions. Nevertheless, a model architecture with very little more complexity could incorporate such bidirectional flow. We concluded that the model could explain the observations, and that the PIAF-Münch model platform can be expected to describe partitioning in even more complex architectures.

Adapting APSIM to model the physiology and genetics of complex adaptive traits in field crops

Progress in molecular plant breeding is limited by the ability to predict plant phenotype based on its genotype, especially for complex adaptive traits. Suitably constructed crop growth and development models have the potential to bridge this predictability gap. A generic cereal crop growth and development model is outlined here. It is designed to exhibit reliable predictive skill at the crop level while also introducing sufficient physiological rigour for complex phenotypic responses to become emergent properties of the model dynamics. The approach quantifies capture and use of radiation, water, and nitrogen within a framework that predicts the realized growth of major organs based on their potential and whether the supply of carbohydrate and nitrogen can satisfy that potential. The model builds on existing approaches within the APSIM software platform. Experiments on diverse genotypes of sorghum that underpin the development and testing of the adapted crop model are detailed. Genotypes differing in height were found to differ in biomass partitioning among organs and a tall hybrid had significantly increased radiation use efficiency: a novel finding in sorghum. Introducing these genetic effects associated with plant height into the model generated emergent simulated phenotypic differences in green leaf area retention during grain filling via effects associated with nitrogen dynamics. The relevance to plant breeding of this capability in complex trait dissection and simulation is discussed.

MAppleT: simulation of apple tree development using mixed stochastic and biomechanical models

Construction of tree architectural databases over years is time consuming and cannot easily capture event dynamics, especially when both tree topology and geometry are considered. The present project aimed to bring together models of topology and geometry in a single simulation such that the architecture of an apple tree may emerge from process interactions. This integration was performed using L-systems. A mixed approach was developed based on stochastic models to simulate plant topology and mechanistic model for the geometry. The succession of growth units (GUs) along axes and their branching structure were jointly modelled by a hierarchical hidden Markov model. A biomechanical model, derived from previous studies, was used to calculate stem form at the metamer scale, taking into account the intra-year dynamics of primary, secondary and fruit growth. Outputs consist of 3-D mock-ups - geometric models representing the progression of tree form over time. To asses these models, a sensitivity analysis was performed and descriptors were compared between simulated and digitised trees, including the total number of GUs in the entire tree, descriptors of shoot geometry (basal diameter, length), and descriptors of axis geometry (inclination, curvature). In conclusion, despite some limitations, MAppleT constitutes a useful tool for simulating development of apple trees in interaction with gravity.