Draft:Functional-Structural Plant Models

Functional-Structural Plant Models (FSP models, also FSPMs) are computational models that integrate a three-dimensional (3D) representation of plant architecture (structure) with physiological processes (function), such as photosynthesis, transpiration, water and nutrient uptake, or carbon allocation . These models are often used to study plant growth and development in response to environmental conditions and management practices . FSP models can be either static, representing a snapshot of plant structure and function at a given moment, or dynamic, simulating growth and physiological processes over time. FSP models can be identified as agent-based models, if the agents represent individual plant organs or plant building blocks .

Over the years, FSP models have been applied across a wide range of domains, including greenhouse horticulture, crop phenotyping, intercropping research, evolutionary biology, forestry, agricultural systems modeling, and virtual plant phenotyping. Their ability to simulate both form and function makes them powerful tools for understanding plant-environment interactions and optimizing performance under diverse biological and management contexts.

History and Development

The development of functional-structural plant models emerged from early mathematical and simulation-based models of plant architecture. Foundational work in the 1960s and 1970s introduced Lindenmayer systems (L-systems), which provided a formal framework for modeling branching structures in plants . In the 1990s and early 2000, these early structural models were extended by integrating physiological processes, such as photosynthesis and carbon allocation, resulting in the development of modern FSP models.

As computational power increased and data acquisition technologies like 3D imaging and high-throughput plant phenotyping evolved, FSP models became more refined and versatile. Alongside these technological improvements, several software platforms have been developed to support the design and simulation of FSP models. Notable examples include: L-studio/VLab, OpenAlea, GroIMP, VPL, CPlantBox, Helios. Each offers specific capabilities for modeling plant architecture, simulating physiological processes, or visualizing 3D structures.

Core Principles, Modelling Approaches, and Applications

FSP models are computational models that combine detailed representations of plant architecture with physiological processes to simulate how plants grow and function in three-dimensional space. At the heart of FSP models is a modular approach, in which a plant is represented as a network of individual organs—such as leaves, internodes, roots, and flowers—each with distinct structural roles and physiological functions. This organ-level granularity allows for the simulation of interactions within the plant and between the plant and its environment.

FSP models can be categorized as static and dynamic models.

• Static models provide a snapshot of the plant at a specific stage, often used to examine architectural traits, light interception, or spatial distribution of biomass under fixed conditions.
• Dynamic FSP models simulate the progression of plant growth and physiological processes over time, responding to varying environmental inputs such as light, temperature, and water availability.

These models allow researchers to explore development, competition, and adaptation in changing environments, and to track resource flows—like assimilates or water—according to physiological rules.

A defining feature of FSP models is their ability to simulate environmental interactions. Processes such as light interception, carbon assimilation, nutrient transport, and water uptake are tightly integrated with the plant’s structural model, enabling realistic exploration of how architecture influences function and how plants respond to management or environmental stress.

To achieve this level of detail, FSP models make use of a range of mathematical and computational tools. For modeling plant architecture, rule-based approaches such as Lindenmayer systems (L-systems) are often employed to simulate structural development. Depending on the focus of the model, additional techniques may be used—for example: Markov chains for probabilistic modeling of organ initiation, Finite element methods for mechanical or transport simulations, Differential equations to describe dynamic processes like photosynthesis and transpiration.

The plant structure is typically represented as a branching network, where concepts from graph theory can help manage connectivity and updates as the plant develops. In some models, agent-based modeling is used to treat individual organs as semi-autonomous units that interact locally with each other and their environment, allowing for emergent behavior at the whole-plant level.

Thanks to this flexible and integrative design, FSP models have found applications across a wide range of disciplines. In agriculture and horticulture, they are used to: Optimize crop management strategies, Support breeding for improved architectural traits, Inform precision farming practices.

In forestry, FSP models help analyze tree growth, competition, and stand dynamics under natural or managed conditions. In ecophysiology, they are valuable tools for understanding how plants respond to environmental stresses such as drought, nutrient limitation, or climate change.

Beyond production-focused domains, FSP models are also applied in urban greenery and landscape design, where they assist in modeling plant growth for aesthetic and ecological purposes. In virtual plant phenotyping, they support the development of high-throughput methods by generating realistic plant models for testing sensors and algorithms. Additionally, FSPM models are used in photosynthesis and light-use efficiency studies, where they help quantify how architectural traits influence light capture and carbon assimilation at the organ or canopy level.

Whether static or dynamic, FSP models offer a robust and versatile framework for investigating the complex interplay between plant structure and function, and for guiding innovations in sustainable agriculture, ecological modeling, and plant science.

Software and Implementation

Several software platforms support the development and simulation of FSP models, including:

• CPlantBox
• GroIMP
• Helios
• OpenAlea
• L-studio/VLab
• VPL

FSP models may also have a stand-alone implementation (i.e., without the use of a platform), such asOpenSimRoot. More stand-alone FSP model implementations, together with non-FSP models, can be found on the website Quantitative Plant

Platforms or models may be entirely or partially written in Java, C/C++, Matlab, Scilab, Python, or Julia.

Community and Resources

The Functional-Structural Plant Modeling Forum is an active online community where researchers, model developers, and students discuss topics related to FSP models, share tools and tutorials, and troubleshoot model implementation issues. It serves as a central hub for collaboration and knowledge exchange within the FSPM field.

Challenges and Future Directions

While Functional-Structural Plant Models (FSP models) offer powerful insights into plant growth and development, several challenges remain. Parameterization is often complex, as acquiring accurate physiological and structural data is labor-intensive. Computational demands can also be high, particularly for large or detailed simulations. Ensuring model validation through integration with experimental data is essential but remains a bottleneck. Additionally, FSP models often require an interdisciplinary approach, bridging plant science, computer modeling, and mathematics.

Looking forward, advancements in AI, remote sensing, and high-throughput phenotyping are expected to enhance model accuracy and scalability. Integrating FSP models with precision agriculture and digital twin technologies holds great promise for advancing both scientific understanding and sustainable crop production.

Examples of FSP Models

• FSP Model Dwarf tomatoes YouTube.

See Also

• Crop simulation model
• L-systems
• Computational biology
• Plant growth analysis
• Plant architecture
• Ecophysiology
• 3D computer graphics