The scaling relationship between perianth fresh mass and area: proof of concept using Magnolia × soulangeana Soul.-Bod

A significant scaling relationship between the perianth mass and area was detected using 306 flowers of Magnolia × soulangeana, and increases in mass failed to achieve proportional increases in area.

The scaling relationship between leaf lamina mass and area has been explored extensively. However, this relationship for floral parts, which are considered homologous with foliage leaves, has not been studied despite the implications of scaling theory and plant morphometry. Toward this goal, a total of 306 flowers and 2759 tepals of Magnolia × soulangeana were collected and measured. The area of each tepal was determined by digitizing its profile, and the perianth area (A_p) was empirically determined by summing the areas of all tepals per flower. The perianth fresh mass (FM) was also measured, and the Montgomery equation (ME) was used to estimate the tepal area (A_t) predicted as proportional to the product of tepal length (L) and width (W) to explore the feasibility of estimating A_t non-destructively. The scaling exponent of FM vs A_p significantly exceeded unity, i.e., increases in mass failed to achieve proportional increases in area, a phenomenon called “diminishing returns”. The estimated proportionality coefficient of ME for non-destructively calculating A_t approximately equaled 0.7 [i.e., A_t ≈ (3/4)LW], and the distributions of A_t, L, W/L, and the tepal centroid ratio were relatively concentrated. The data indicate that (1) scaling relationship between tepal mass and area is statistically indistinguishable from the phenomenon observed for foliage leaves, (2) tepal shape and leaf shape are similar, and (3) the ME predicts tepal area nondestructively. These results encourage the application of the ME to study tepal shape and geometry and support the serial homology between leaves and tepals for this Magnolia hybrid.