Curvature Analysis of Seed Silhouettes in Silene L.

Abstract

The application of seed morphology to descriptive systematics requires methods for shape analysis and quantification. The complexity of lateral and dorsal views of seeds of Silene species is investigated here by the application of the Elliptic Fourier Transform (EFT) to representative seeds of four morphological types: smooth, rugose, echinate and papillose. The silhouettes of seed images in the lateral and dorsal views are converted to trigonometric functions, whose graphical representations reproduce them with different levels of accuracy depending on the number of harmonics. A general definition of seed shape in Silene species is obtained by equations based on 40 points and 20 harmonics, while the detailed representation of individual tubercles in each seed image requires between 100 and 200 points and 60–80 harmonics depending on their number and complexity. Smooth-type seeds are accurately represented with a low number of harmonics, while rugose, echinate and papillose seeds require a higher number. Fourier equations provide information about tubercle number and distribution and allow the analysis of curvature. Further estimation of curvature values in individual tubercles reveals differences between seeds, with higher values of curvature in S. latifolia, representative of echinate seeds, and lower in S. chlorifolia with rugose seeds.

Quantitative Analysis of Seed Surface Tubercles in Silene Species

“…Both types of seed tubercle may be thoroughly differentiated via curvature analysis. Curvature is the magnitude that indicates the rate of change in the slope through the points of a curve [37][38][39][40][41]. This has a constant value in a circumference, which equals the inverse of its radius with units of length −1 .…”

“…In some instances, tubercle shape is associated with a given phylogenetic group or a particular geographic location [6,10,[49][50][51]. The seeds of Moheringia L. species with long tubercles (papillate) have been described in warm-winter Maximum absolute values and average curvatures were determined for individual tubercles of each species according to established procedures [37][38][39][40][41] (See Supplementary Materials). In the measurements of curvature for individual tubercles, the points were taken automatically with the function, Analyze line graph, of Image J.…”

“…A direct quantitative analysis of tubercle geometrics based on their width, height and curvature values is given for the first time in this work. Curvature represents the rate at which the unit tangent vector is changing with respect to arc length [37][38][39][40][41]. Curvature measurements are based on previous methods developed for roots analysis in Arabidopsis Heynh.…”

“…(Brassicaceae) [37,38], as well as in wheat and grape seeds [39,40]. Curvature was measured in Silene seeds [41] and curvature values in the tubercles of S. chlorifolia Sm., a representative of rugose seeds, were compared with those in a population of S. latifolia Poir. Maximum and mean curvature values were higher in S. latifolia, suggesting that higher curvature values may be a property of echinate seeds in contrast with rugose seeds.…”

Plant Morphology and Function, Geometric Morphometrics, and Modelling: Decoding the Mathematical Secrets of Plants

“…Different species of Silene seeds with distinct morphologies exhibit varying harmonic numbers when analyzed using the elliptical Fourier transform (EFT) model [1]. Smoother seeds have fewer harmonic numbers, while wrinkled, spiky, and papillate seeds require more harmonic numbers.…”