Introducing MuSCA, the multi-scale carbon allocation model

MuSCA reveals that the topological scale has a major influence on the simulation of carbon allocation.

How is carbon allocated in a plant? The answer to that question might depend on the scale that you’re looking at. In the past, that has meant that the answer is in some way, dependent on how you ask the question. MuSCA, a multi-scale source-sink carbon allocation model produced by Francesco Reyes and colleagues, is a new model that can work at multiple scales.

Simulation of C allocation and fruit growth on a tree structure represented at different spatial scales during one day. Image: Reyes et al. 2019.

Why would you need a model, when you can look at an actual plant? As Francesco Reyes explained, the model is used to see if you understand what is going on in a plant. “Plant models are simplified representations of some plant characteristics or functioning. Scopes of these models can be to verify if our knowledge about plant functioning is consistent with reality and to predict plant responses in response to variable environmental conditions and management. When representing a plant in a model, you may opt to describe the plant at a higher or lower resolution. The plant structure can be described as roughly as, e.g. a sequence of the main axis or in higher detail, e.g. identifying every leaf, internode or fruit.”

“Despite several carbon allocation models that exist in the literature, each one of them represents the plant structure in a different way. Now, plant model results are influenced both by the way (in a simplistic manner the “resolution”) at which the plant structure is described and by the description of the physiological processes. The multi-scale carbon allocation model we created allows us to disentangle the effects due to these two factors. This is because it will enable us to use the same set of physiological rules while describing the same plant at different spatial scales, defined by the user.”

Scale can matter as detail comes at a cost in computational time. Dr Reyes said that MuSCA allows the user to evaluate better how much detail they need. “The plant topology is newly discretized based on rules provided by the user to group plant metamers into coarser ones (e.g. main axis, or shoots, ….). This is followed by a re-calculation of distances among the newly defined plant components, which will be used for computing carbon movement from leaves to the other organs.”

Switching between one scale and another is not simple, and the model took quite a bit work to make it reliable. “The first results were quite different from our final ones. It took a lot of work to get a model consistently representing carbon allocation at different spatial scales. The interactions between the discretion of a plant topology and carbon flow rules are not trivial.”

The result of the tuning means that the model is set to replicate one particular apple variety, but it is flexible, Dr Reyes said. “The model is calibrated for the apple tree fuji cultivar, but its structure and modules are non-species specific. It is sufficient to recalibrate a few modules (mainly maximal potential growth curves and photosynthesis) to adapt it to a different tree species. The model is totally independent of the individual plant. The individual plant structure, fruit and leaf distributions are inputs, and the model operates on them to produce an output.”

While the model is primarily for research purposes, it can be used to answer questions about the influence of the distribution of fruits on a tree on their harvest size, which may be very important for a grower.

“In a broad sense, this model makes us reflecting on the fundamental fact that, as any model is a simplification of reality, no model is ever fully correct,” Dr Reyes said. “Wrong or excessive simplifications of reality in a mental (or mathematical) models can lead to important distortions in the way we may further interpret and interact with the real world.”

“This model may help the research community defining guidelines for the representation of plant structures in the source-sink plant modelling domain. Questions such as how the specific plant topology may interact with the choice of a specific spatial scale may also lead to relevant research.”

However, the research may also have relevance far beyond botany, Dr Reyes said. “The multi-scale formalism for re-discretizing the plant topology and assessing distances among topological components, here used for carbon movement, may also be used in other domains (e.g. logistics?) as it is related to a general topological structure, and not necessarily to a plant.”

“It’s crazy tripping through a theoretical plant structure governed by non-linear mathematical rules while questioning if the plant would really behave the same in reality,” said Dr Reyes. Other researchers wish to work with the model should be able to do so with a little training, he added.

Further reading

Reyes, F., Pallas, B., Pradal, C., Vaggi, F., Zanotelli, D., Tagliavini, M., … Costes, E. (2019). MuSCA: a multi-scale source–sink carbon allocation model to explore carbon allocation in plants. An application to static apple tree structures. Annals of Botany. https://doi.org/10.1093/aob/mcz122