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# Process-based allometry describes the influence of management on orchard tree aboveground architecture

### Abstract

We evaluated allometric relationships in length, diameter, and mass of branches for two variably managed orchard tree species (tart cherry, Prunus cerasus; apple, Malus spp.). The empirically estimated allometric exponents (a) of the orchard trees were described in the context of two processed-based allometry models that make predictions for a: the West, Brown and Enquist fractal branching model (WBE) and the recently introduced Flow Similarity model (FS). These allometric models make predictions about relationships in plant morphology (e.g., branch mass, diameter, length, volume, surface area) based on constraints imposed on plant growth by physical and physiological processes. We compared our empirical estimates of a to the model predictions to interpret the physiological implications of pruning and management in orchard systems. Our study found strong allometric relationships among the species and individuals studied with limited agreement with the expectations of either model. The 83-power law prediction of the mass ∼ diameter relationship by the WBE, indicative of biomechanical limitations, was marginally supported by this study. Length-including allometric relationships deviated from predictions of both models, but shift toward the expectation of flow similarity. In this way, managed orchard trees deviated from strict adherence to the idealized expectations of the models, but still fall within the range of model expectations in many cases despite intensive management.

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