Author summaryLeaf venation exhibits diverse network structures among taxa and conservation within taxa, reflecting complex evolutionary processes involving functional, developmental, and structural constraints. We used network features to characterize hierarchical and complex venation patterns for quantitatively understanding their morphological diversities and constraints. We analyzed 479 non-chemically treated leaves of five species and demonstrated that network features contain sufficient information for species classification. Furthermore, we identified biased distribution patterns in the leaf venation morphospace by characterizing leaf samples from both untreated and cleared leaf images. The biased distribution patterns corresponded to a one-dimensional curve, which was predicted by a theoretical study based on the functional trade-offs between optimizing transport efficiency, construction cost, and robustness to damage. These results improve our understanding of morphological constraints and functional trade-offs shaping divergence in leaf venation. Our approach provides a basis for similar analyses in various fields targeting reticulate networks, which are ubiquitous in nature, including biomimetics, generative design, and microfluidics. Despite substantial variation in leaf vein architectures among angiosperms, a typical hierarchical network pattern is shared within clades. Functional demands (e.g., hydraulic conductivity, transpiration efficiency, and tolerance to damage and blockage) constrain the network structure of leaf venation, generating a biased distribution in the morphospace. Although network structures and their diversity are crucial for understanding angiosperm venation, previous studies have relied on simple morphological measurements (e.g., length, diameter, branching angles, and areole area) and their derived statistics to quantify phenotypes. To better understand the morphological diversities and constraints on leaf vein networks, we developed a simple, high-throughput phenotyping workflow for the quantification of vein networks and identified leaf venation-specific morphospace patterns. The proposed method involves four processes: leaf image acquisition using a feasible system, leaf vein segmentation based on a deep neural network model, network extraction as an undirected graph, and network feature calculation. To demonstrate the proposed method, we applied it to images of non-chemically treated leaves of five species for classification based on network features alone, with an accuracy of 90.6. By dimensionality reduction, a one-dimensional morphospace, along which venation shows variation in loopiness, was identified for both untreated and cleared leaf images. Because the one-dimensional distribution patterns align with the Pareto front that optimizes transport efficiency, construction cost, and robustness to damage, as predicted by the earlier theoretical study, our findings suggested that venation patterns are determined by a functional trade-off. The proposed network feature-based method is a useful morphological descriptor, providing a quantitative representation of the topological aspects of venation and enabling inverse mapping to leaf vein structures. Accordingly, our approach is promising for analyses of the functional and structural properties of veins.
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