Seed Morphology in the Vitaceae Based on Geometric Models

Abstract

Morphometric methods based on artificial vision algorithms provide measurements for magnitudes descriptive of seed images (i.e., the length, width, area, and surface circularity index). Nevertheless, their results frequently omit the resemblance of the images to geometric figures that may be used as models. A complementary method based on the comparison of seed images with geometric models is applied to seeds of Vitis spp. The J index gives the percentage of similarity between a seed image and the model. Seven new geometric models are described based on the heart-shaped and piriform curves. Seeds of different species, subspecies and cultivars of Vitis adjust to different models. Models 1 and 3, the heart curve and the water drop, adjust better to seeds of V. amurensis, V. labrusca and V. rupestris than to V. vinifera. Model 6, the Fibonacci’s pear, adjusts well to seeds of V. vinifera, in general, and better to V. vinifera ssp. vinifera than to V. vinifera ssp. sylvestris. Seed morphology in species of Cissus and Parthenocissus, two relatives of Vitis in the Vitaceae, is also analysed. Geometric models are a tool for the description and identification of species and lower taxonomic levels complementing the results of morphometric analysis.

Seed Geometry in the Vitaceae

“…Seven geometric models for the description and quantification of seed shape in the Vitaceae were described before [ 45 ]. Models 1 to 5 were derived from modifications in the equations of the heart curve [ 63 ], Model 6 was derived from the pyriform curve [ 64 ], and Model 7 was obtained by the modification of two independent equations representing an ellipse, searching for the similarity with the seeds of cultivars of V. vinifera .…”

“…Water drops and lemniscates described well the seeds of some species in the Arecaceae [ 13 ]. The former adapt well to the bi-dimensional shape of well-oriented images in the Vitaceae [ 45 ]. Figure 3 shows examples of seeds resembling elongated water drops, see [ 45 ] for quantitative measurements in Cissus verticillata .…”

“…The equation describing the water drop is given in [ 13 , 45 ], while the equation describing the lemniscate is given in [ 13 ].…”

“…A family of equations will be described that simplify the design of new models according to the variety of seed types found in the Vitaceae [ 45 ]. The task of finding a model adapted to a new shape will be easier knowing which term of an existing equation may give the changes needed to obtain a given figure.…”

Taxonomic Revisiting and Phylogenetic Placement of Two Endangered Plant Species: Silene leucophylla Boiss. and Silene schimperiana Boiss. (Caryophyllaceae)

“…Phylogenetic analysis is essential for explaining structural, ecological, taxonomical, and functional biodiversity characteristics in an evolutionary background [ 26 , 27 ]. The critical species Silene leucophylla and S. schimperiana have been disregarded in recent phylogenetic and taxonomic studies of the genus Silene [ 4 , 28 ].…”