Flow similarity model characterizes hydraulic-mechanical trade-offs driving size-dependent allometric scaling across branch orders in oak trees.

Allometry is central to understanding resource allocation strategies in plant development, with branching networks serving as critical determinants of allometric scaling patterns. While current theoretical models propose frameworks for allometric variation, empirical evidence supporting their assumptions is limited. Here, we measured the branching architecture of 191 oak (Quercus and Lithocarpus) branches across different light and altitude environments, analyzed the relationship between branching structure and allometric scaling exponents, and examined size-dependent variation in scaling exponents via quadratic fitting. Our study reveals that the branch diameter scale factor a remains stable (a = 1/2), aligning precisely with the West-Brown-Enquist (WBE) model and Flow Similarity (FS) model predictions of constant flow velocity, whereas the length scale factor b significantly exceeds WBE predictions (b > 1/3). The FS model is further validated in explaining the continuous decline in length-diameter allometric scaling exponents from terminal twigs to entire branches via hydraulic-mechanical trade-offs, whereas exponents calculated from the Price-Enquist-Savage equations were significantly different from SMA-fitted exponents. Light intensity significantly regulates size-dependent variation in allometric scaling exponents, while altitude effects are limited. Our findings advance understanding of how woody plant allometries vary across branch orders, helping to clarify the hydraulic-mechanical trade-off mechanisms underlying this process.