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To test whether it can sustain a quantitative comparison with actual venation patterns, we have developed and implemented a numerical model and statistically compare actual and simulated patterns. This appealing hypothesis naturally explains the existence of hierarchical structures with abundant closed loops. In this work, we explore the previously proposed idea that elastic stresses may play an important role in the development of venation patterns. Although the role of auxin in vein formation is well established, some issues are difficult to explain within this model, in particular, the abundance of loops of high-order veins. The accepted view of vein formation is the auxin canalization hypothesis: a high flow of the hormone auxin triggers cell differentiation to form veins. The initial vein generations are repetitive within the same species, while high-order vein generations are much more diverse but still show preserved statistical properties. A remarkable characteristic of these structures is the abundance of closed loops: the venation array divides the leaf surface into disconnected polygonal sectors. Leaf venation patterns of most angiosperm plants are hierarchical structures that develop during leaf growth. We argue that the agreement between actual and simulated patterns provides strong evidence for the role of mechanical effects on venation development. When applied to the structure of high-order veins, the numerical results show the same qualitative features as actual venation patterns and, furthermore, have the same statistical properties.

We present a model based on the existence of mechanical instabilities that leads very naturally to hierarchical patterns with a large number of closed loops. Although there is evidence that auxin plays a fundamental role in vein formation, the simple canalization mechanism may not be enough to explain some features observed in the vascular system of leaves, in particular, the abundance of vein loops. The current prevalent ‘canalization’ hypothesis for the formation of veins claims that the transport of the hormone auxin out of the leaves triggers cell differentiation to form veins. We explore the possible role of elastic mismatch between epidermis and mesophyll as a driving force for the development of leaf venation.

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