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BACKGROUND AND AIMS: Transport of carbohydrates and water are essential aspects of plant function. The aim of this study was to develop and test the methods for mechanistic modelling of quasi-stationary coupled phloem/xylem transport in the context of functional–structural plant modelling. METHODS: The novelty of this approach is in combining analytical and computational methods. The plant structure is modelled at a metamer level with the internodes represented by conduit elements and the lateral organs represented by sources and sinks. Transport equations are solved analytically for each internode and then the solutions are adjusted and ‘sewn’ together using an iterative computational procedure taking into account concentration-dependent sinks and sources. The model is implemented in L-studio and uses the aspect-oriented modelling approach for phloem/xylem coupling. KEY RESULTS: To our knowledge, this is the first transport model that provides continuous distributions of the system variables in a complex developing structure. The model takes into account non-linear dependence of phloem resistance and osmotic potential on the local carbohydrate concentration. The model solutions show excellent agreement with the existing results of other analytical and numerical models. These comparisons confirm the validity of the approximations made in the model. Combining analytical and computational methods made it possible to take into account continuous sink/source distribution within internodes without much increase in the complexity of the computational procedure, because the necessary changes in the model were mostly in the analytical part. The results emphasize sensitivity of phloem flux and lateral xylem flux to the presence of distributed sinks and sources along the transport system. CONCLUSIONS: The presented approach provides a new insight into mechanistic modelling of phloem/xylem transport in growing plants. It will be useful for both fine-scale modelling of carbohydrate dynamics and for creating simpler models at a growth unit level.

Background and Aims Functional–structural plant (FSP) models provide insights into the complex interactions between plant architecture and underlying developmental mechanisms. However, parameter estimation of FSP models remains challenging. We therefore used pattern-oriented modelling (POM) to test whether parameterization of FSP models can be made more efficient, systematic and powerful. With POM, a set of weak patterns is used to determine uncertain parameter values, instead of measuring them in experiments or observations, which often is infeasible. Methods We used an existing FSP model of avocado (Persea americana ‘Hass’) and tested whether POM parameterization would converge to an existing manual parameterization. The model was run for 10 000 parameter sets and model outputs were compared with verification patterns. Each verification pattern served as a filter for rejecting unrealistic parameter sets. The model was then validated by running it with the surviving parameter sets that passed all filters and then comparing their pooled model outputs with additional validation patterns that were not used for parameterization. Key Results POM calibration led to 22 surviving parameter sets. Within these sets, most individual parameters varied over a large range. One of the resulting sets was similar to the manually parameterized set. Using the entire suite of surviving parameter sets, the model successfully predicted all validation patterns. However, two of the surviving parameter sets could not make the model predict all validation patterns. Conclusions Our findings suggest strong interactions among model parameters and their corresponding processes, respectively. Using all surviving parameter sets takes these interactions into account fully, thereby improving model performance regarding validation and model output uncertainty. We conclude that POM calibration allows FSP models to be developed in a timely manner without having to rely on field or laboratory experiments, or on cumbersome manual parameterization. POM also increases the predictive power of FSP models.

Background and AimsMany experimental studies assume that some topological units are autonomous with regard to carbon because it is convenient. Some plant models simulate carbon allocation, employing complex approaches that require calibration and fitted parameters. For whole-tree canopy simulations, simpler carbon allocation models can provide useful insights.MethodsWe propose a new method for simulating carbon allocation in the whole tree canopy considering various scales of carbon autonomy, i.e. branchlets, branches, limbs, and no autonomy. This method was implemented in a functional–structural plant model of growth of individual organs for studying macadamia tree growth during one growing season.Key ResultsThis model allows the simulation of various scales of carbon autonomy in a simple tree canopy, showing organ within-tree variability according to the scale of autonomy. Using a real tree canopy, we observed differences in growth variability within the tree and in tree growth, with several scales of carbon autonomy. The simulations that assumed autonomy at branch scale, i.e. 2-year-old wood, showed the most realistic results.ConclusionsSimulations using this model were employed to investigate and explain aspects of differences in carbon autonomy between trees, organ growth variability, competition between shoot and fruit growth, and time of autonomy.

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.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.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.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.

Autoregulation of nodulation is a long-distance shoot-root signalling regulatory system that regulates nodule meristem proliferation in legume plants. However, due to the intricacy and subtleness of the signalling nature in plants, molecular and biochemical details underlying mechanisms of autoregulation of nodulation remain largely unknown. The purpose of this study is to use functional-structural plant modelling to investigate the complexity of this signalling system. There are two major challenges to be met: modelling the 3D architecture of legume roots with nodulation and co-ordinating signalling-developmental processes with various rates.Soybean (Glycine max) was chosen as the target legume. Its root system was observed to capture lateral root branching and nodule distribution patterns. L-studio, a software tool supporting context-sensitive L-system modelling, was used for the construction of the architectural model and integration with the internal signalling.A branching pattern with regular radial angles was found between soybean lateral roots, from which a root mapping method was developed to characterize the laterals. Nodules were mapped based on 'nodulation section' to reveal nodule distribution. A root elongation algorithm was then developed for simulation of root development. Based on the use of standard sub-modules, a synchronization algorithm was developed to co-ordinate multi-rate signalling and developmental processes.The modelling methods developed here not only allow recreation of legume root architecture with lateral branching and nodulation details, but also enable parameterization of internal signalling to produce different regulation results. This provides the basis for using virtual experiments to help in investigating the signalling mechanisms at work.

† Background and Aims Improving the competitive ability of crops is a sustainable method of weed management. This paper shows how a virtual plant model of competition between chickpea (Cicer arietinum) and sowthistle (Sonchus oleraceus) can be used as a framework for discovering and/or developing more competitive chickpea cultivars. † Methods The virtual plant models were developed using the L-systems formalism, parameterized according to measurements taken on plants at intervals during their development. A quasi-Monte Carlo light-environment model was used to model the effect of chickpea canopy on the development of sowthistle. The chickpea– light environment– sowthistle model (CLES model) captured the hypothesis that the architecture of chickpea plants modifies the light environment inside the canopy and determines sowthistle growth and development pattern. The resulting CLES model was parameterized for different chickpea cultivars (viz. ‘Macarena’, ‘Bumper’, ‘Jimbour’ and ‘99071-1001’) to compare their competitive ability with sowthistle. To validate the CLES model, an experiment was conducted using the same four chickpea cultivars as different treatments with a sowthistle growing under their canopy. † Results and Conclusions The growth of sowthistle, both in silico and in glasshouse experiments, was reduced most by ‘99071-1001’, a cultivar with a short phyllochron. The second rank of competitive ability belonged to ‘Macarena’ and ‘Bumper’, while ‘Jimbour’ was the least competitive cultivar. The architecture of virtual chickpea plants modified the light inside the canopy, which influenced the growth and development of the sowthistle plants in response to different cultivars. This is the first time that a virtual plant model of a crop – weed interaction has been developed. This virtual plant model can serve as a platform for a broad range of applications in the study of chickpea– weed interactions and their 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.