The silhouettes of bi-dimensional images of seeds often resemble geometric figures that can be used as models for the description and quantification of seed shape in plant families. A recent review of the geometry of seeds in the Arecaceae described a series of models useful for the analysis of seed shape in this family [13]. Geometric models included the ellipses (the circle is a particular type of ellipse), ovals, lemniscates, superellipses, cardioid and derivatives, lenses and the water drop curve [13]. The reader is referred to this review for the algebraic description of the models and their application in the morphometry of seeds in the Arecaceae. The application of geometric models in morphometry is based on the comparison of bi-dimensional images of well oriented seeds with these figures by means of image programs working in two layers (Adobe Photoshop, Corel Photo Paint…). The two images (seed and model) can be superimposed searching for a maximum similarity and the ratio between shared and total surface areas, that we have termed J index, is calculated with the data obtained in ImageJ ^[14][15]. J index measures the percent of similarity between two images (the seed and the model) and provides information on overall seed shape ^[15][16][16,17]. Bidimensional seed images of many plant species adjust well to one of three morphological types: the ellipse, the oval and the cardioid ^[17][18]. The seeds of the model plant Arabidopsis thaliana (L.) Heynh., those of the model legumes Lotus japonicus (Regel) K.Larsen and Medicago truncatula Gaertn., as well as the seeds of Capparis spinosa L., in the Capparaceae and Rhus tripartita DC. in the Anacardiaceae adjust well to cardioids or modified cardioids ^{[18][19][20][21][22]}[19,20,21,22,23]. The seeds of Ricinus communis L. and Jatropha curcas L. in the Euphorbiaceae and those of cultivars of Triticum sp. in the Poaceae adjust well to ellipses of varied x/y ratio ^[23][24][25][24,25,26]. Oval shaped seeds occur frequently in the Cucurbitaceae, Berberidaceae, Eupteleaceae and Lardizabalaceae ^[26][27][27,28], while the cardioid is more common in Papaveraceae ^[27][28]. A given geometric type is sometimes associated with other morphological or ecological characteristics. For example, cardioid-type seeds were observed to be more frequent in small-sized seeds, while elliptic shape is more frequent in larger seeds ^[17][18]. In the Malvaceae, cardioid type seeds are associated with small herbs of annual cycle ^[28][29].

2.2. Seed Morphology in the Vitaceae

Seed shape in the Vitaceae is variable and seeds resembling geometric figures are frequent in this family. The seeds of Ampelocissus are pyriform, oval, or round in dorsal or ventral view ^[29][30]. The seeds of Cissus species are often described as globose with a pointed base, elliptic in outline or oblong (see, for example, ^[30][31][32][33,34,35]). These adjectives and other like sub-globose or terete are also applied to seed descriptions in other genera suggesting two important points: (1) The seeds of the Vitaceae are suitable for the comparison with geometric figures used as models. (2) The comparison may be quantitative, yielding measures that contribute to taxonomy. Table 2 contains a list of 131 species in the Vitaceae whose seeds have been observed for this work.

Table 2. A summary of the 131 species for which seed shape has been analysed in this work.

Tribe (Species Observed/Total)	Genera (Species Observed/Total)	Species (References for the Images)
I. Ampelopsideae (15/47)	Ampelopsis Michx.
,
62
]
,
V. wilsoniae
[
35
]
[
39	]	[31,41]

 

Table 3 contains a summary of groups based on morphological seed types for the analysed species .

Table 3. A summary of groups based on morphological seed types for the analysed species in the Vitaceae. The number of cases found in each group is given between dashes.

Group (Geometric Model)	Examples
(13/18)
Group I (Lenses)-3-	Cissus quadrangularis [42][44], C. sterculiifolia [35][31], Tetrastigma petraeum [50][52]	Ampelopsis aconitifolia [33][36], A. arborea [34][37], A. bodinieri [33][36], A. cantoniensis [35][33][31,36], A. cordata [36][38], A. chaffanjoni [33][36], A. delavayana [35][31], A. denudata [29][30], A. glandulosa [37][39], A. grossedentata [35][31], A. humulifolia [33][36], A. japonica [33][36], A. megalophylla [35][33][31,36]
	Rhoicissus Planch. (2/14)
Group II (Superellipses)-7-	Ampelocissus bravoi [40][42], C. reniformis [35][39][31,41], Cyphostemma elephantopus [47][49], C. laza [35][31], Tetrastigma campylocarpum [50][52], T. caudatum [50][52], T. henryi [50][	Rhoicissus revoilii [35][31], R. rhomboidea [35][31]
52	]	II. Cisseae (33/300)	Cissus L. (33/300)
Group III (Elongated water drops)-15-	Ampelopsis arborea [34][37], Cayratia imerinensis [45][47], Cissus aralioides [32][38][35,40], C. cornifolia [38][40], C. erosa [41][43], C. integrifolia [38][40][40,42], C. petiolata [38][40], C. pileata [38][40], C. populnea [38][40], C. verticillata [35][39][40][43][31,41,42,45], C. sciaphila [38][40], C. smithiana [38][40], C. willardii [40][42], Cyphostemma junceum [35][31], V. vulpina [57][60][59,62]	Cissus antarctica [35][31], C. aralioides [32][38][35,40], C. barbeyana [38][40], C. bosseri [38][40], C. cactiformis [38][40], C. campestris [35][39][40][31,41,42], C. cornifolia [38][40], C. descoingsii, [35][39][31,41], C. diffusiflora [38][40], C. elongata [38][40], C. erosa [41][43], C. floribunda [38][40], C. fuliginea [35][31], C. granulosa [35][31], C. hastata [38][40], C. hypoglauca [35][31], C. integrifolia [38][40][40,42], C. leucophlea [38][40], C. penninervis [35][31], C. petiolata [38][40], C. pileata [38][40], C. populnea [38][40], C. quadrangularis [42][44], C. reniformis [35][39][31,41], C. repens [38][40], C. sciaphila [38][40], C. smithiana [38][40], C. sterculiifolia [35][31], C. subtetragona [38][40], C. trianae [35][31], C. tuberosa [40][42], C. verticillata [35][39][40][43][31,41,42,45], C. willardii [40][42],
III. Cayratieae (40/365)	Causonis
Group IV (Water drops, normal or rounded)-14-	Raf. (1/9)	Ampelopsis bodinieri [33][36], A. glandulosa [33][37][36,39], A. humulifolia [33][36], Cayratia cheniana [44][46], Cissus campestris [35][39][40][31,41,42], C. fuliginea [35][31], C. tuberosa [40][42], C. granulosa [35][31], Parthenocissus dalzielii [33][36], Tetrastigma triphyllum [35][50][31,52], Vitis amurensis [43][54][45,56], V. labrusca [43][52][57][45,54,59], V. palmata [58][60],	Causonis sp. [44][46]
V. rupestris	[43]		Cayratia Juss. (7/60)	Cayratia cheniana [44][46], C. geniculata [35][31], C. imerinensis [45][47], C. japonica [35][46][31,48], C. oligocarpa [35][31], C. saponaria [35][31], C. sp. [African, [44][46]]
	Cyphostemma (Planch.) Alston (3/200)	Cyphostemma elephantopus [47][49], C. laza [35][31], C. junceum [35][31]
[	45]
Group V (Heart curves normal or rounded)-19-	Ampelopsis aconitifolia [33][36], A. chaffanjoni [33][36], A. cordata [36][38], A. japonica [33][36], Parthenocissus heptaphylla [35][31], P. heterophylla [33][36], P. henryana [33][36], P. himalayana [50][51][52,53], P. quinquefolia [52][54], P. vitacea [35][31], P. tricuspidata [33][34][43][36,37,45], Rhoicissus revoilii [35][31], T. lanceolarium [29][30], Vitis cinerea [55][57], V. flexuosa [52][54], V. lanatoides [56][58], V. latisulcata [56][58], V. tsoi [35][31[39],41], V. wilsoniae [35][39][31,41]
Group VI (Elongated Heart curves)-6-	Ampelocissus acapulcensis [29][30], Cissus oligocarpa [35][31]. V. eolabrusca [52][54], V. grayensis [56][58], V. pseudorotundifolia [52][54], V. tiliifolia [59][61]		Pseudocayratia J. Wen, L.M.Lu and Z.D.Chen (3/5)
Group VII (Other elongated types)-11-	Ampelopsis megalophylla [35][33][31,36], Causonis sp. [44][46], Cayratia saponaria [35][31], Cissus trianae [35][31], C. hypoglauca [35][31], Parthenocissus laetevirens [33][36], T. hypoglaucum [50][52] Vitis aestivalis [53][55], V. rotundifolia [35][39][52][31,41,54], Yua austro-orientalis [35][31], Y. chinensis [35][31]	Pseudocayratia dichromocarpa [48][50], P. pengiana [48][50], P. speciosa [48][49][50,51]
	Tetrastigma (Miq.) Planch. (26/100)
Group VIII (Heart curves of the Cayratia and Pseudocayratia types)-7-	Cayratia japonica [35][46][31,48], Cayratia sp. [African, [44][46]], Pseudocayratia dichromocarpa [48][50], P. pengiana [48][50], P. speciosa [48][50][50,52], Tetrastigma formosanum [49][51], T. pedunculare [35][49][50][31,51,52]	Tetrastigma campylocarpum [50][52], T. cauliflorum [50][52], T. caudatum [50][52], T. delavayi [50][52], T. dichotomum [49][51], T. formosanum [50][52], T. harmandi [35][31], T. hemsleyanum [35][50][31,52], T. henryi [50][52], T. hypoglaucum [50][52], T. jinghongense [50][52], T. kwangsiense [29][35][30,31], T. lanceolarium [29][30], T. laoticum [50][52], T. obovatum [49][50][51,52], T. obtectum [49][50][51,52], T. pachyllylum [50][52], T. pedunculare [35][49][50][31,51,52], T. petraeum [50][52], T. retinervum [50][52], T. rumicispermum [35][49][50][31,51,52], T. serrulatum [50][52], T. sichouense [50][52], T. thorsborneorum [50][52], T. triphyllum [35][50][31,52], T. xishuangbannaense [35][50][31,52]
IV. Parthenocisseae (11/16)	Parthenocissus Planch.
Group IX (Heart curves of the SqHC type of Ampelocissus and Ampelopsis)-15-	(9/14)	Ampelocissus bombycina [29][30], A. cavicaulis [29][30], A. erdvendbergiana [29][30], A. grantii [29][30], A. javalensis [29][40][30,42], A. latifolia [29][30], A. macrocirrha [29][30], A. martinii [40][42], A. obtusata [29][30], A. ochracea [29][30], A. robinsonii [29][30], Ampelopsis cantoniensis [35][33][31,36], A. delavayana [35][31], A. denudata [29][30], A. grossedentata [35][31]	Parthenocissus dalzielii [33][36], P. heptaphylla [35][31], P. henryana [33][36], P. heterophylla [33][36], P. himalayana [51][53], P. laetevirens [33][36], P. quinquefolia [52][54], P. tricuspidata [33][34][43][36,37,45], P. vitacea [35][31]
	Yua C.L.Li (2/2)
Group X Elongated Superellipse-heart curves-16-	Cissus elongata [38][40], C. penninervis [35][31], Rhoicissus rhomboidea [35][31], Tetrastigma hemsleyanum [35][50][31,52], T. jinghongense [50][52], T. laoticum [50][52], T. cauliflorum [50][52], T. dichotomum [49][51], T. harmandi [35][31], T. pachyllylum [50][52], T. kwangsiense [29][35][30,31], T. obovatum [49][50][51,52], T. obtectum [49][50][51,52], T. retinervum [49][51], T. serrulatum [50][52], T. sichouense [50]	Yua austro-orientalis [35][31], Y. chinensis [35][31]
[	52]	V. Viteae (32/190)	Ampelocissus Planch. (13/115)
Undefined-18-	Cayratia geniculata [35][31], Cissus antarctica [35][31], C. barbeyana [38][40], C. bosseri [38][40], C. cactiformis [38][40], C. descoingsii, [35][39][31,41], C. diffusiflora [38][40], C. floribunda [38][40], C. hastata [38][40], C. leucophlea [38][40], C. repens [38][40], C. subtetragona [38][40], T. delavayi [50][52], T. rumicispermum [35][49][50][31,51,52], T. thorsborneorum [50][52], T. xishuangbannaense [35][50][31,52], V. brandoniana [52][54], V. rostrata [52][54]	Ampelocissus acapulcensis [29][30], A. bombycina [29][30], A. bravoi [40][42], A. cavicaulis [29][30], A. erdvendbergiana [29][30], A. grantii [29][30], A. javalensis [29][40][30,42], A. latifolia [29][30], A. macrocirrha [29][30], A. martinii [40][42], A. obtusata [29][30], A. ochracea [29][30], A. robinsonii [29][30]
	Vitis L. (19/75)	Vitis aestivalis [53][55], V. amurensis [43][54][45,56], V. brandoniana [52][54], V. cinerea [55][57], V. eolabrusca [52][54], V. flexuosa [52][54], V. grayensis [56][58], V. labrusca [43][52][57][45,54,59], V. lanatoides [56][58], V. latisulcata [56][58], V. palmata [58][60], V. pseudorotundifolia [52][54], V. rostrata [52][54], V. rotundifolia [35][39][52][31,41,54], V. rupestris [43][45], V. tiliifolia [59][61], V. tsoi [35][39][31,41], V. vulpina [57][60][59

 

Figure 1. The images of seeds of Cissus sterculiifolia ^[35][31], Tetrastigma petraeum ^[49][51] and Cissus quadrangularis ^[42][44] resemble lenses of different proportions.

In general, the distribution of morphological types is not in close agreement with the current taxonomic classification; nevertheless, some results may be summarized in this aspect. First, the seeds of the Elongated Superellipse-Heart Curves (ESHCs) type (Group X) are more frequent in Tetrastigma and have been observed in Rhoicissus and Cissus, but not in species of other genera. While many seeds in species of Ampelopsis, Parthenocissus and Vitis share the typical shapes of water drop and heart curves, the squared heart curve (SqHC) type (Group IX) has been predominantly observed in Ampelocissus and Ampelopsis. A number of species remain undefined due to one of these two reasons: First, their irregular seed shape making difficult the identification of an adequate model (Cayratia geniculata, Cissus antarctica) and, second, the seed images have geometric shapes but the identification of the model with the corresponding equation is pending (Tetrastigma delavayi, T. rumicispermum). In addition, further work will be done on the seeds of Vitis species.