A multi-scale model to explore carbon allocation in plants

Abstract

Understanding and simulating carbon allocation in plants is necessary to predict carbohydrates allocation among growing and competing organs and, plant growth and structure development in relation to climatic conditions. In this context, several carbon allocation models have been developed but no clear consensus exists on (i) the most appropriate topological scale (organ, metamer, compartment...) to represent this process on complex plant structures and (ii) the importance of distances between organs in carbon transport. Multi-scale tree graph (MTG) is a formalism allowing the representation of geometry and topology of a tree structure at different scales. In this study, a multi-scale model was built to compute carbon allocation at different and user-defined spatial scales, using the MTG formalism. The implementation takes into account the distances between sources and sinks, the strength of the sinks and the available carbohydrates, following the equations of two previously developed models: SIMWAL and QualiTree. This allows multiple scales (e.g., metamer, growing unit, branch) to be combined during the computation of carbon allocation. For instance, allocation could be computed alternatively among plant components represented at metamer scale, or among growing units and then redistributed from each growing unit to its component metamers. Simulations on simple shoots, represented at different scales, showed how the scales chosen to represent the system influence the results of the predicted carbon allocation. This modelling approach was first applied to apple tree to analyze the impact of the scale of representation (growth unit, metamer) on the predicted organ growth variability. The present work will be available through the OpenAlea platform and will provide existing Functional Structural Plant Models with a new generic model to simulate carbon allocation in plants, depending on user-defined biological hypotheses, such as the choice of the scale of representation or the effect of distance. Keywords: functional structural plant model, multiscale tree graph, Malus × domestica, sink strength, plant architecture INTRODUCTION Carbon allocation in plants has been described as the result of the osmotic flow (Munch theory) of carbon assimilates along the plant topology, and the capacity of individual plant components along the osmotic gradient to load and unload carbon. Because of difficulties related to its computational representation (Lacointe, 2000), the osmotic flow has only lately been incorporated into models of carbon partitioning, however not yet validated on whole plants (Minchin and Lacointe, 2005; Thorpe et al., 2011). Conversely, simplifying approaches in which carbon flows result from the interaction between sources and sinks, with or without (e.g., Greenlab, Guo et al., 2006) an explicit consideration of distances and resistances in the transport, found to date more widespread applications. Among the first group can be distinguished i) analogies to electric circuits, whose computational efficiency can benefit from folding/unfolding rules provided by L-systems formalisms (Prusinkiewicz et al., 2007) but often needs tedious calibrations of the represented resistances (e.g., Grossman and DeJong, 1994), and ii) models that more simply