A three-dimensional carbon-nutrient functional balance model explains the formation of Root Economics Space

Root carbon (C)-nutrient functional balance underpins root economic strategies, yet previous models neglected the root-length dimension. Here, we develop a three-dimensional C-nutrient functional balance model for first-order roots that explicitly incorporates root length, and validates it using a global root trait dataset. For subtropical woody species, root cortex volume x root length scaled isometrically with the fourth power of stele diameter (slope{approx}1.0), supporting the model. Herbaceous species from the Qinghai-Tibetan plateau showed a significantly lower slope (0.61), likely due to extreme environmental impacts on transport or metabolism. Woody species preferentially invest in cortical area (thicker roots), supporting mycorrhizal symbiosis, whereas herbaceous species favor root length extension for autonomous soil exploration. By integrating root length, this model provides a novel mechanistic explanation for the formation of both the collaboration and conservation axes within the root economics space, advancing the theoretical framework of root functional strategies.