Geometric entropy of plant leaves: A measure of morphological complexity.

Shape is an objective characteristic of an object. A boundary separates a physical object from its surroundings. It defines the shape and regulates energy flux into and from an object. Visual perception of a definite shape (geometry) of physical objects is an abstraction. While the perceived geometry at an object's sharp interface (macro) creates a Euclidian illusion of actual shape, the notion of diffuse interfaces (micro) allows an understanding of the realistic form of objects. Here, we formulate a dimensionless geometric entropy of plant leaves (S_L) by a 2-D description of a phase-field function. We applied this method to 112 tropical plant leaf images. S_L was estimated from the leaf perimeter (P) and leaf area (A). It correlates positively with a fractal dimensional measure of leaf complexity, viz., segmental fractal complexity. Leaves with a higher P: A ratio have higher S_L and possess complex morphology. The univariate cluster analysis of S_L reveals the taxonomic relationship among the leaf shapes at the genus level. An increase in S_L of plant leaves could be an evolutionary strategy. The results of morphological complexity presented in this paper will trigger discussion on the causal links between leaf adaptive stability/efficiency and complexity. We present S_L as a derived plant trait to describe plant leaf complexity and adaptive stability. Integrating S_L into other leaf physiological measures will help to understand the dynamics of energy flow between plants and their environment. [ABSTRACT FROM AUTHOR]