Ellipticalness index – a simple measure of the complexity of oval leaf shape

Abstract

Plants have diverse leaf shapes that have evolved to adapt to the environments they have experienced over their evolutionary history. Leaf shape and leaf size can greatly influence the growth rate, competitive ability, and productivity of plants. However, researchers have long struggled to decide how to properly quantify the complexity of leaf shape. Prior studies recommended the leaf roundness index (RI = 4πA/P 2 ) or dissection index (DI = √ ⁄), where P is leaf perimeter and A is leaf area. However, these two indices merely measure the extent of the deviation of leaf shape from a circle, which is usually invalid as leaves are seldom circular. In this study, we proposed a simple measure, named the ellipticalness index (EI), for quantifying the complexity of leaf shape based on the hypothesis that the shape of any oval leaf can be regarded as a variation from a standard ellipse. 2220 leaves from nine species of Magnoliaceae were sampled to check the validity of the EI. We also tested the validity of the Montgomery equation (ME), which assumes a proportional relationship between leaf area and the product of leaf length and width, because the EI actually comes from the proportionality coefficient of the ME. We also compared the ME with five other models of leaf area. The ME was found to be the best model for calculating leaf area based on consideration of the trade-off between model fit vs. complexity, which strongly supported the robustness of the EI for describing oval leaf shape. The new index can account for both leaf shape and size, and we conclude that it is a promising method for quantifying and comparing oval leaf shapes across species in future studies.

A nondestructive method of calculating the wing area of insects

“…In previous studies on leaf shapes, the leaf roundness index (RI = 4 πA / P 2 ) and leaf dissection index (DI = P/2) (where P is the leaf perimeter and A is the leaf area) were frequently used to describe the complexity of leaf shapes (Kincaid & Schneider, 1983; Niinemets, 1998; Peppe et al, 2011; Santiago & Kim, 2009; Thomas & Bazzaz, 1996). Li, Quinn, Niinemets, et al (2022) pointed out the shortcomings of RI and DI as parameters for description of leaf shapes, especially elliptical and oval leaf shapes that deviate significantly from a circular form. Indeed, these indices fail to reflect leaf shape.…”

Tree Size Influences Leaf Shape but Does Not Affect the Proportional Relationship Between Leaf Area and the Product of Length and Width

“…where a is the natural logarithm of MP. When the ME held true, EI could be used as an indicator of leaf shape ( Li et al, 2021b ). The MP has a relationship with EI as:…”

“…However, an accurate quantification of many elliptical, oval, and oboval leaves significantly deviates from circular leaves. Consequently, Li et al (2021b) proposed a new index, the leaf ellipticalness index (EI), based on the Montgomery equation (ME; see Montgomery, 1911 ), which assumes that leaf area is proportional to the product of leaf length and width. In contrast to the leaf roundness index, the EI reflects the extent to which an elliptical leaf deviates from an ellipse, and can be used to calculate leaf area provided that leaf length and width are known.…”

A High throughput method for egg size measurement inDrosophila

“…) which is the ratio of the area under the optical density profile of an object to the area of the closest elliptical profile (Li et al, 2022;Morales et al, 2020). Due to the elliptical shape of Drosophila egg, an egg aligned on the long axis has smaller W/L ratio than eggs aligned on the short axis (Fig.…”