A mathematical framework for modelling cambial surface evolution using a level set method

Limiting Effect of Self-Shading on the Height of Tradescantia fluminensis Mats

Tradescantia fluminensis is an invasive plant species in New Zealand, Australia and parts of the USA. It reproduces vegetatively and can grow to form dense mats up to 60 cm deep. Growth is limited by available light, and shading is one of the few effective methods of control. In this paper, we develop a dynamic model of a vertical cross section of a T. fluminensis mat, capturing vertical variation in its biomass and internal light intensity. We measure both variables at different heights in experimental mats of the species and use these data to parameterize the model. The model produces realistic vertical biomass and light intensity profiles. We show that the mat grows to a steady-state biomass that depends only on: (i) the light absorption coefficient, which we estimate from experimental data and (ii) the ratio of photosynthesis to respiration rate. This steady state undergoes a transcritical bifurcation; when the ambient light intensity falls below a critical level, the biomass shrinks to zero and the mat cannot survive.

A surface model of nonlinear, non-steady-state phloem transport

Phloem transport is the process by which carbohydrates produced by photosynthesis in the leaves get distributed in a plant. According to Münch, the osmotically generated hydrostatic phloem pressure is the force driving the long-distance transport of photoassimilates. Following Thompson and Holbrook[35]'s approach, we develop a mathematical model of coupled water-carbohydrate transport. It is first proven that the model presented here preserves the positivity. The model is then applied to simulate the flow of phloem sap for an organic tree shape, on a 3D surface and in a channel with orthotropic hydraulic properties. Those features represent an significant advance in modelling the pathway for carbohydrate transport in trees.

Using functional–structural plant models to study, understand and integrate plant development and ecophysiology

Functional–structural plant models (FSPMs) explore and integrate relationships between a plant’s structure and processes that underlie its growth and development. In recent years, the range of topics being addressed by scientists interested in functional–structural plant modelling has expanded greatly. FSPM techniques are now being used to dynamically simulate growth and development occurring at the microscopic scale involving cell division in plant meristems to the macroscopic scales of whole plants and plant communities. The plant types studied also cover a broad spectrum from algae to trees. FSPM is highly interdisciplinary and involves scientists with backgrounds in plant physiology, plant anatomy, plant morphology, mathematics, computer science, cellular biology, ecology and agronomy. This special issue of Annals of Botany features selected papers that provide examples of comprehensive functional–structural models, models of key processes such as partitioning of resources, software for modelling plants and plant environments, data acquisition and processing techniques and applications of functional–structural plant models for agronomic purposes.