Assessment of uncertainty in functional-structural plant models

Background and Aims

Constructing functional–structural plant models (FSPMs) is a valuable method for examining how physiology and morphology interact in determining plant processes. However, such models always have uncertainty concerned with whether model components have been selected and represented effectively, with the number of model outputs simulated and with the quality of data used in assessment. We provide a procedure for defining uncertainty of an FSPM and how this uncertainty can be reduced.

Methods

An important characteristic of FSPMs is that typically they calculate many variables. These can be variables that the model is designed to predict and also variables that give indications of how the model functions. Together these variables are used as criteria in a method of multi-criteria assessment. Expected ranges are defined and an evolutionary computation algorithm searches for model parameters that achieve criteria within these ranges. Typically, different combinations of model parameter values provide solutions achieving different combinations of variables within their specified ranges. We show how these solutions define a Pareto Frontier that can inform about the functioning of the model.

Key Results

The method of multi-criteria assessment is applied to development of BRANCHPRO, an FSPM for foliage reiteration on old-growth branches of Pseudotsuga menziesii. A geometric model utilizing probabilities for bud growth is developed into a causal explanation for the pattern of reiteration found on these branches and how this pattern may contribute to the longevity of this species.

Conclusions

FSPMs should be assessed by their ability to simulate multiple criteria simultaneously. When different combinations of parameter values achieve different groups of assessment criteria effectively a Pareto Frontier can be calculated and used to define the sources of model uncertainty.     

Plant growth and architectural modelling and its applications. Preface

Over the last decade, a growing number of scientists around the world have invested in research on plant growth and architectural modelling and applications (often abbreviated to plant modelling and applications, PMA). By combining physical and biological processes, spatially explicit models have shown their ability to help in understanding plant–environment interactions. This Special Issue on plant growth modelling presents new information within this topic, which are summarized in this preface. Research results for a variety of plant species growing in the field, in greenhouses and in natural environments are presented. Various models and simulation platforms are developed in this field of research, opening new features to a wider community of researchers and end users. New modelling technologies relating to the structure and function of plant shoots and root systems are explored from the cellular to the whole-plant and plant-community levels.     

A modelling framework to simulate foliar fungal epidemics using functional–structural plant models

Background and Aims

Sustainable agriculture requires the identification of new, environmentally responsible strategies of crop protection. Modelling of pathosystems can allow a better understanding of the major interactions inside these dynamic systems and may lead to innovative protection strategies. In particular, functional–structural plant models (FSPMs) have been identified as a means to optimize the use of architecture-related traits. A current limitation lies in the inherent complexity of this type of modelling, and thus the purpose of this paper is to provide a framework to both extend and simplify the modelling of pathosystems using FSPMs.

Methods

Different entities and interactions occurring in pathosystems were formalized in a conceptual model. A framework based on these concepts was then implemented within the open-source OpenAlea modelling platform, using the platform''s general strategy of modelling plant–environment interactions and extending it to handle plant interactions with pathogens. New developments include a generic data structure for representing lesions and dispersal units, and a series of generic protocols to communicate with objects representing the canopy and its microenvironment in the OpenAlea platform. Another development is the addition of a library of elementary models involved in pathosystem modelling. Several plant and physical models are already available in OpenAlea and can be combined in models of pathosystems using this framework approach.

Key Results

Two contrasting pathosystems are implemented using the framework and illustrate its generic utility. Simulations demonstrate the framework''s ability to simulate multiscaled interactions within pathosystems, and also show that models are modular components within the framework and can be extended. This is illustrated by testing the impact of canopy architectural traits on fungal dispersal.

Conclusions

This study provides a framework for modelling a large number of pathosystems using FSPMs. This structure can accommodate both previously developed models for individual aspects of pathosystems and new ones. Complex models are deconstructed into separate ‘knowledge sources’ originating from different specialist areas of expertise and these can be shared and reassembled into multidisciplinary models. The framework thus provides a beneficial tool for a potential diverse and dynamic research community.     

An approach to multiscale modelling with graph grammars

Background and Aims

Functional–structural plant models (FSPMs) simulate biological processes at different spatial scales. Methods exist for multiscale data representation and modification, but the advantages of using multiple scales in the dynamic aspects of FSPMs remain unclear. Results from multiscale models in various other areas of science that share fundamental modelling issues with FSPMs suggest that potential advantages do exist, and this study therefore aims to introduce an approach to multiscale modelling in FSPMs.

Methods

A three-part graph data structure and grammar is revisited, and presented with a conceptual framework for multiscale modelling. The framework is used for identifying roles, categorizing and describing scale-to-scale interactions, thus allowing alternative approaches to model development as opposed to correlation-based modelling at a single scale. Reverse information flow (from macro- to micro-scale) is catered for in the framework. The methods are implemented within the programming language XL.

Key Results

Three example models are implemented using the proposed multiscale graph model and framework. The first illustrates the fundamental usage of the graph data structure and grammar, the second uses probabilistic modelling for organs at the fine scale in order to derive crown growth, and the third combines multiscale plant topology with ozone trends and metabolic network simulations in order to model juvenile beech stands under exposure to a toxic trace gas.

Conclusions

The graph data structure supports data representation and grammar operations at multiple scales. The results demonstrate that multiscale modelling is a viable method in FSPM and an alternative to correlation-based modelling. Advantages and disadvantages of multiscale modelling are illustrated by comparisons with single-scale implementations, leading to motivations for further research in sensitivity analysis and run-time efficiency for these models.     

A rule-based model of barley morphogenesis, with special respect to shading and gibberellic acid signal transduction

BACKGROUND AND AIMS: Functional-structural plant models (FSPM) constitute a paradigm in plant modelling that combines 3D structural and graphical modelling with the simulation of plant processes. While structural aspects of plant development could so far be represented using rule-based formalisms such as Lindenmayer systems, process models were traditionally written using a procedural code. The faithful representation of structures interacting with functions across scales, however, requires a new modelling formalism. Therefore relational growth grammars (RGG) were developed on the basis of Lindenmayer systems. METHODS: In order to implement and test RGG, a new modelling language, the eXtended L-system language (XL) was created. Models using XL are interpreted by the interactive, Java-based modelling platform GroIMP. Three models, a semi-quantitative gibberellic acid (GA) signal transduction model, and a phytochrome-based shade detection and object avoidance model, both coupled to an existing morphogenetic structural model of barley (Hordeum vulgare L.), serve as examples to demonstrate the versatility and suitability of RGG and XL to represent the interaction of diverse biological processes across hierarchical scales. KEY RESULTS: The dynamics of the concentrations in the signal transduction network could be modelled qualitatively and the phenotypes of GA-response mutants faithfully reproduced. The light model used here was simple to use yet effective enough to carry out local measurement of red:far-red ratios. Suppression of tillering at low red:far-red ratios could be simulated. CONCLUSIONS: The RGG formalism is suitable for implementation of multi-scaled FSPM of plants interacting with their environment via hormonal control. However, their ensuing complexity requires careful design. On the positive side, such an FSPM displays knowledge gaps better thereby guiding future experimental design.     

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.     

Modelling seagrass growth and development to evaluate transplanting strategies for restoration

Background and Aims

Seagrasses are important marine plants that are under threat globally. Restoration by transplanting vegetative fragments or seedlings into areas where seagrasses have been lost is possible, but long-term trial data are limited. The goal of this study is to use available short-term data to predict long-term outcomes of transplanting seagrass.

Methods

A functional–structural plant model of seagrass growth that integrates data collected from short-term trials and experiments is presented. The model was parameterized for the species Posidonia australis, a limited validation of the model against independent data and a sensitivity analysis were conducted and the model was used to conduct a preliminary evaluation of different transplanting strategies.

Key Results

The limited validation was successful, and reasonable long-term outcomes could be predicted, based only on short-term data.

Conclusions

This approach for modelling seagrass growth and development enables long-term predictions of the outcomes to be made from different strategies for transplanting seagrass, even when empirical long-term data are difficult or impossible to collect. More validation is required to improve confidence in the model''s predictions, and inclusion of more mechanism will extend the model''s usefulness. Marine restoration represents a novel application of functional–structural plant modelling.     

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.