A general leaf area geometric formula exists for plants - evidence from the simplified Gielis equation

Plant leaves exhibit diverse shapes that enable them to utilize a light resource maximally. If there were a general parametric model that could be used to calculate leaf area for different leaf shapes, it would help to elucidate the adaptive evolutional link among plants with the same or similar leaf shapes. We propose a simplified version of the original Gielis equation (SGE), which was developed to describe a variety of object shapes ranging from a droplet to an arbitrary polygon. We used this equation to fit the leaf profiles of 53 species (among which, 48 bamboo plants, 5 woody plants, and 10 geographical populations of a woody plant), totaling 3310 leaves. A third parameter (namely, the floating ratio c in leaf length) was introduced to account for the case when the theoretical leaf length deviates from the observed leaf length. For most datasets, the estimates of c were greater than zero but less than 10%, indicating that the leaf length predicted by the SGE was usually smaller than the actual length. However, the predicted leaf areas approximated their actual values after considering the floating ratios in leaf length. For most datasets, the mean percent errors of leaf areas were lower than 6%, except for a pooled dataset with 42 bamboo species. For the elliptical, lanceolate, linear, obovate, and ovate shapes, although the SGE did not fit the leaf edge perfectly, after adjusting the parameter c, there were small deviations of the predicted leaf areas from the actual values. This illustrates that leaves with different shapes might have similar functional features for photosynthesis, since the leaf areas can be described by the same equation. The anisotropy expressed as a difference in leaf shape for some plants might be an adaptive response to enable them to adapt to different habitats.