Flow similarity model predicts allometric relationships among Acer platanoides L. branches

Using physical models to predict patterns of plant growth has been a long-standing goal for biologists. Most approaches invoke either thermodynamic, biomechanical or hydraulic principles and assume the mechanism of interest applies similarly throughout the plant branching architecture. A recent effort, the flow similarity model, predicts numerous aspects of branching physiology and morphology and argues that the physiological constraints experienced by plants change as a function of branch order and size, with more basal portions satisfying more biomechanical constraints, and more distal portions, hydraulic ones. Distal branches are expected to have a strong influence on allometric relationships within plants due to their numerical abundance. Here we evaluate the predictions of the flow similarity model and a well-known alternative fractal branching model, using data on the dimensions of 3,484 individual stem internodes across four individual Acer platanoides trees. Overall, we find strong agreement between model predictions and the allometric exponents describing tree branch allometry. Further the predicted curvature in allometric relationships is found in all 24 cases examined and the frequency distributions of branch lengths and diameters are consistent with model expectations in 6/8 cases. We also find the area ratios are consistent with the model assumption of area-preserving branching. Collectively, our data and analysis provide strong support for the flow similarity model, and identifies several areas in need of subsequent inquiry.