A network model for determining decomposition, topology, and properties of the woody crown

The acquisition of resources and airspace of woody crown occur by way of axes supporting annexes. Regardless of age, size, or branching system (monopodial or sympodial), the woody crown shows branched leafy axes implementing an aerial network. We propose here to represent the woody crown through a network comprised of two components, the segments of woody axes named connectors (CO) delimited by nodes (NO) as the branching regions. CO may link NO of different categories (regular, initial, final, and emission) as defined by the relative position of the NO in a crown and how many CO the NO has. The woody crown network (WCN) is similar to a random network with the probability of NO having some CO following an exponential decay. The absence of loops and real hubs weakened the robustness of WCN against failure or attacks on NO. The quantities of NO and CO and the proportions between them were the features of decomposition, and the distances measured in some CO between types of NO captured the topological characteristics of WCN. By combining decomposition and topology, we disclosed some properties of WCN, such as navigability, vulnerability, symmetry, and complexity. Navigability and complexity increased, while vulnerability and symmetry decreased exponentially as the size (ΣNO) of WCN enlarged. The behavior of properties as a function of ΣNO exposed some limits to mitigate the inherent hydraulic resistance during WCN development. Decomposition, topology, and properties of WCN in trees of Cerrado vegetation were interrelated to other crown traits revealing the strategies for acquiring airspace.