The document analyzes global patterns in secondary (2°) and tertiary (3°) vein density in 547 species of leaves from 59 families. It finds that both 2° and 3° vein density are negatively correlated with leaf size, with 3° having a weaker correlation. Small leaves are more common than large leaves globally. The results support a model where 2° and 3° veins develop independently during leaf expansion and differentiation, with 3° veins having more variation due to developing later. Higher 3° vein density in small leaves may confer hydraulic benefits in arid habitats.