Fractal dimension does not adequately describe the complexity of leaf margin in seedlings of Quercus species

Abstract

We quantified the complexity of leaf margin in a set of Quercus tree species using fractal dimension estimated by the box-counting method (FDb). Leaves were sampled from seedlings in a set of 15 Quercus species with a wide range of leaf morphology (Q. agrifolia, Q. alba, Q. cerris, Q. chrysolepis, Q. coccifera, Q.faginea, Q. frainetto, Q. ilex subsp. ballota, Q. ilex subsp. ilex, Q. petraea, Q. pyrenaica, Q. robur, Q. rubra, Q. suber, and Q. velutina). To describe leaf-edge roughness, we used simple indices: P/L - the ratio of leaf perimeter (P) to maximum leaf length (L) along the main nerve; P/A - the ratio of leaf perimeter to leaf-blade area (A) and its dimensionless version (P/A0'); and WM/Wm -the ratio of maximum distance from the lobe tip to the main nerve (WM) to minimum distance from the lobe incision to the main nerve (Wm). There was a strong positive relationship between FDb and P/A. Clustering analysis revealed the existence of three groups of leaves, namely those with: smooth or spiny margins (e.g., Q. coccifera, Q. velutina), shallow lobes (e.g., Q. petraea), and deep lobes (e.g., Q. pyrenaica). In the studied Quercus species, the ratio WM/Wm is a simple and suitable leaflobation index. It is suggested that the flux rate along the leaf edge is related to the complexity of this boundary.

Keywords

• complexity
• fractal dimension
• leaf lobation
• box-counting method
• oak