Introducing entropy-based metrics for quantifying edge- and macro-shape complexity in leaves and beyond

Leaf shape is a fundamental trait of plant ecological strategies, influencing biotic interactions and ecosystem functioning. However, established quantitative metrics fail to capture subtle variations and irregularities, require user-based reference points or are challenging to compare among taxa with broadly different leaf shapes. In addition, established metrics typically conflate (aggregate) leaf edge complexity and macro-shape complexity, despite their independent functional significance and genetic foundations. Here, we introduce an entropy-based framework to quantify two new complexity metrics: edge complexity and macro-shape complexity. Based on three case studies, we show that these metrics outperform aggregate metrics in predicting Quercus robur chemical traits, provide more intuitive interspecific classifications, and strongly align with human perception. In addition, edge and macro-shape complexity show high complementarity, while aggregate metrics are highly redundant and typically strongly related to leaf area. Emerging as the strongest predictor of leaf chemistry and key visual cue for complexity as perceived by humans, the effects of edge complexity highlight the under-appreciated functional significance of leaf margins. Our framework and the proposed entropy-based complexity metrics thus promise to help unlock the potential of growing digital image archives of leaves, including images from herbaria and fossils, and are technically readily applicable to shapes of algae, bacteria, pollen, and beyond. The accompanying package ShapeComplexity enables the broad application of entropy-based metrics, providing a powerful tool to explore how the shape of organisms and biological structures influences ecological strategies, biotic interactions, and ecosystem functioning while tracking spatial and temporal variation.