An elliptical blade is not a true ellipse, but a superellipse–Evidence from two Michelia species

The shape of leaf laminae exhibits considerable diversity and complexity that reflects adaptations to environmental factors such as ambient light and precipitation as well as phyletic legacy. Many leaves appear to be elliptical which may represent a ‘default’ developmental condition. However, whether their geometry truly conforms to the ellipse equation (EE), i.e., ( x/a ) 2 + ( y/b ) 2 = 1, remains conjectural. One alternative is described by the superellipse equation (SE), a generalized version of EE, i.e., | x/a | n +| y/b | n = 1. To test the efficacy of EE versus SE to describe leaf geometry, the leaf shapes of two Michelia species (i.e., M. cavaleriei var. platypetala , and M. maudiae ), were investigated using 60 leaves from each species. Analysis shows that the majority of leaves (118 out of 120) had adjusted root-mean-square errors of