A new way to account for the effect of source-sink spatial relationships in whole plant carbon allocation models

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Abstract
To improve source–sink relationship based carbon-allocation models, the basic proportional model was extended to account for a well-known effect of individual source to sink distances: among different sinks of similar characteristics, the more distant from the source, the lower the allocation coefficient. This was achieved through multiplication of the sink strength value by a coefficient that is proportional to a decreasing, simple function of distance, f; the power form was chosen for both simplicity and theoretical reasons. The resulting model was parameterized and evaluated on the empirical allocation matrix of the ECOPHYS model, after grouping together several individual, small sinks of similar nature and close location to remove any phyllotaxy-related bias. Both goodness of fit and predictive value were significantly improved compared with the basic proportional model (f = constant). The f-extended model yielded even better results if segments of different nature or age on the source to sink pathway were assigned different weights in the expression of distance, whereas the default expression of f, with an exponent of –1 and no additive constant, was optimal with no further parameter required. Thus, only 7 parameters (3 for pathway segment weights and 4 for sink strength values) were sufficient to retrieve the original 68 independent experimental allocation coefficients with a reasonable degree of accuracy. Pathway segment weights likely reflect both intrinsic transport pathway properties and situation within the plant architecture; this is discussed in relation to the possibilities of generalization and practical use of the model.