A general formula for calculating surface area of the similarly shaped leaves: Evidence from six Magnoliaceae species

Abstract Leaf area is an important indicator of photosynthetic capacity in plants. Knowledge of the variation of leaf shape at an individual level or a population level can help by accurately calculate leaf area. Such calculations can help us to understand the life history strategies of plants, and allow us to better understand the influence of climate change on mean leaf area as an indicator of leaf size, which is closely related to stand yields and ecological ecosystem services. The Montgomery equation (ME), which describes a proportional relationship between leaf surface area and the product of leaf length and width, has been demonstrated to hold true for many broad-leaved plants. The Magnoliaceae family has 17 genera covering ca. 300 species, of which some plants play important roles in the landscape. Many Magnoliaceae plants have similar leaf shapes, and little is known about whether ME can act as a general formula to calculate leaf surface area for these plants. This paper provides the evidence that ME can be used to measure the leaf area of Magnoliaceae species. More than 2500 mature leaves of six species within two genera (Magnolia and Michelia) of the Magnoliaceae family were selected as samples. The data of leaf length, width, and area were obtained from the scanned images. We used four models to fit these data, including (1) ME (which is actually a direct proportional function of leaf area vs. the product of leaf length and width), (2) a power-law function between leaf area and the product of leaf length and width, (3) a power function with an exponent of 2 between leaf area and leaf length, and (4) a power function between leaf area and leaf length. We found that ME and the second function have similar root-mean-square error values that are both lower than those of the other two equations. However, ME is better than the second equation because of the simplicity of its structure. We documented the validity of ME for calculating leaf area at a species level, a genus level, and even for the 6-species pooled data set. The estimated Montgomery parameter (i.e., the proportional coefficient in ME) is approximately equal to 0.68, which means that leaf area of the six investigated species can be approximated by 68% of the area of a rectangle with the leaf’s length and width as its sides. This study provides a convenient and fast approach for leaf-area calculation. In addition, we found that the Montgomery parameter can act as an indicator for measuring the similarity of leaves among different species, which provides a measurement standard for leaf morphology.