Topological Phenotypes Constitute a New Dimension in the Phenotypic Space of Leaf Venation Networks

Abstract

The leaves of angiosperms contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We describe a new phenotypic trait of reticulate vascular networks based on the topology of the nested loops. This phenotypic trait encodes information orthogonal to widely used geometric phenotypic traits, and thus constitutes a new dimension in the leaf venation phenotypic space. We apply our metric to a database of 186 leaves and leaflets representing 137 species, predominantly from the Burseraceae family, revealing diverse topological network traits even within this single family. We show that topological information significantly improves identification of leaves from fragments by calculating a “leaf venation fingerprint” from topology and geometry. Further, we present a phenomenological model suggesting that the topological traits can be explained by noise effects unique to specimen during development of each leaf which leave their imprint on the final network. This work opens the path to new quantitative identification techniques for leaves which go beyond simple geometric traits such as vein density and is directly applicable to other planar or sub-planar networks such as blood vessels in the brain.

Structural and defensive roles of angiosperm leaf venation network reticulation across an Andes–Amazon elevation gradient

“…Similarly, there have been studies focusing on freely ending veinlets, but only for small numbers of species (Fiorin, Brodribb, & Anfodillo, 2016). Other intensive studies of loop topology have primarily examined mathematical questions, for example, Ronellenfitsch, Lasser, Daly, and Katifori (2015).…”

Investigating the evolution and development of biological complexity under the framework of epigenetics

“…Alternatively, phenotypes can change without the need for complexity to change, modularity can lead to topological changes in organisms, wherein individual structures remain largely unmodified but their position or organization within body plans will change. The importance of topology of organs and structures within body plans, despite being a crucial aspect of morphological disparity and variability, has only recently been reconsidered in evolutionary biology (Esteve-Altava, 2017;Esteve-Altava & Rasskin-Gutman, 2015;Ronellenfitsch, Lasser, Daly, & Katifori, 2015). The morphological variation involving topological changes will not change complexity but may allow phenotypic variation for a fixed value of complexity within a lineage.…”

Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis

“…It is known that capillaries with insufficient blood circulation may atrophy and disappear. Pruning such blood vessels is an important mechanism to achieve a hierarchical vascular network with optimized transport, as recent global optimization and adaptation algorithms have shown for a number of biological vascular systems [23,24].…”