horticulturae

Opinion Seed Shape Description and Quantification by Comparison with Geometric Models

Emilio Cervantes * and José Javier Martín Gómez

IRNASA-CSIC, Cordel de Merinas, 40, E-37008 Salamanca, Spain * Correspondence: [email protected]; Tel.: +34-9-2321-9606



Received: 21 May 2019; Accepted: 6 August 2019; Published: 19 August 2019


Abstract: Modern methods of image analysis are based on the coordinates of the points making the silhouette of an image and allow the comparison between seed shape in different species and varieties. Nevertheless, these methods miss an important reference point because they do not take into consideration the similarity of seeds with geometrical figures. We propose a method based on the comparison of the bi-dimensional images of seeds with geometric figures. First, we describe six geometric figures that may be used as models for shape description and quantification and later on, we give an overview with examples of some of the types of seed morphology in angiosperms including families of horticultural plants and addressing the question of how is the distribution of seed shape in these families. The relationship between seed shape and other characteristics of plant species is discussed.

Keywords: geometric curves; J index image analysis; morphology; seed; shape

1. Introduction Shape is an important property of plants that has been used for the description of organs and structures since the origins of botany. Some plant species were termed on the basis of the shape of their leaves (for example Drosera rotundifolia, Plantago ovata), others according to the shape of their fruits (Coronilla scorpioides, Eugenia pyriformis), and others following the forms of their seeds (Vicia platysperma). Seed shape is an interesting property that has been used in the taxonomy of the Caryophyllaceae [1–3], Orchidaceae [4], Papilionaceae [5], and Zingiberaceae [6]. Seed shape is related to dispersal. The potential for dispersal is increased by the growth of extra-ovular structures such as plumes, wings, hooks, oil bodies, and diverse types of arils [7] that complicate the analysis of seed morphology. But, leaving out such structures, seed description may be based on similarity to geometrical figures such as the oval, ellipse, cardioid, and others. The comparison of seed images with these figures gives a precise description that can be quantitative, allowing the comparison between genotypes or seeds grown in different conditions. Recent methods for the comparison of seed shapes depend on high-throughput systems based on digital image analysis [8,9]. The methods combine artificial vision technologies with statistical algorithms and may be very efficient for the discrimination of seeds and fruits in a range of plant species and varieties [10–13]. Nevertheless, these methods have two main drawbacks: (1) Their results do not give a magnitude that can be associated with seed shape for a particular group of seeds, and (2) they do not take into consideration the similarity of seeds with geometrical figures, missing an important reference point. This has resulted in a “gap” in the current scientific literature on seed shape. Current methods based on artificial vision, algorithms, and statistical analysis need to go back to the initial seed images, combining geometric models with quantitative and statistical methods to analyze seed shapes.

Horticulturae 2019, 5, 60; doi:10.3390/horticulturae5030060 www.mdpi.com/journal/horticulturae Horticulturae 2019, 5, 60 2 of 18

HorticulturaeIn this 2019 review,, 5, x FOR we PEER first REVIEW describe the geometric models that may be applied for seed shape2 of 19 quantification in diverse plant families including important horticultural plants. Then, we present somesome examplesexamples of of families families where where the the models models have have been been applied applied and discuss and discuss possible possible models inmodels families in offamilies interest of ininterest horticulture. in horticulture. Finally, Finally, we discuss we discuss the relationship the relationship between between seed shape seed andshape other and plantother characteristicsplant characteristics and the and potential the potential of seed of morphology seed morphology in taxonomy. in taxonomy.

2.2. GeometricGeometric ModelsModels FigureFigure1 1 presents presents a a summary summary of of the the geometric geometric models models used used for for the the description description and and quantification quantification ofof seedseed shape.shape. TheseThese are:are: The cardioid and derivatives;derivatives; thethe ellipse;ellipse; thethe oval;oval; thethe contourcontour ofof Fibonacci’sFibonacci’s spiral,spiral, heart-shapedheart-shaped curves,curves, andand lenseslenses ofof variedvaried proportions.proportions.

Figure 1. Main models used in the description and quantification of seeds. (1) Cardioid and derivatives; (2) ellipse; (3) oval and elongated oval; (4) the contour of Fibonacci’s spiral; (5) heart-shaped curves; Figure 1. Main models used in the description and quantification of seeds. (1) Cardioid and (6) lens. derivatives; (2) ellipse; (3) oval and elongated oval; (4) the contour of Fibonacci’s spiral; (5) heart- Inshaped this section, curves; ( we6) lens. describe each of these models. The origin of the images used is indicated in the AppendixA. In this section, we describe each of these models. The origin of the images used is indicated in 2.1.the Cardioidappendix A.

2.1. CardioidThe cardioid is the curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. Another definition is that of the envelope of a pencil of circles formed in a way thatThe theircardioid mid is points the curve lie on traced the perimeter by a point of the on fixedthe perimeter generator of circle a circle [14]. that The is cardioid rolling around has been a longfixed recognized circle of the as same a tool radius. to describe Another biological definition structures is that duringof the envelope development of a pencil because of itcircles corresponds formed toin thea way figure that generated their mid by points an organ lie on that the grows perimeter from of a fixedthe fixed point generator of insertion circle [15 [14].]. Thus, The plane cardioid figures has ofbeen animal long embryos, recognized leaves, as a and tool seeds to describe resemble biol theogical cardioid structures (Figure2 ).during development because it corresponds to the figure generated by an organ that grows from a fixed point of insertion [15]. Thus, plane figures of animal embryos, leaves, and seeds resemble the cardioid (Figure 2).

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Figure 2. (a) The cardioid visualized as the envelope of a pencil of circles formed in a way that their Figure 2. (a) The cardioid visualized as the envelope of a pencil of circles formed in a way that their midpoints lie on the perimeter of the fixed generator circle. The cardioid shape is common in embryos midpointsFigure lie 2. on(a) theThe perimeter cardioid ofvisualized the fixed as generator the envelope circle. of The a pencil cardioid of circles shape isformed common in a in way embryos that their (b) and leaves (c). (b) andmidpoints leaves (liec). on the perimeter of the fixed generator circle. The cardioid shape is common in embryos (b) and leaves (c). 2.2.2.2. Ellipse Ellipse 2.2.TheThe Ellipse ellipse ellipse is is defined defined as as a regulara regular oval oval shape, shape, traced traced by by a pointa point moving moving in in a planea plane so so that that the the sumsum of of its its distances distances from from two two fixed fixed points points (the (the foci) foci) is is constant, constant, or or resulting resulting when when a conea cone is is cut cut by by an an The ellipse is defined as a regular oval shape, traced by a point moving in a plane so that the obliqueoblique plane plane that that does does not not intersect intersect the the base base [16 [16].]. An An ellipse ellipse is is defined defined by by the the length length of of the the major major sum of its distances from two fixed points (the foci) is constant, or resulting when a cone is cut by an andand minor minor axes. axes. Changing Changing the the relations relations between between the the axes axes results results in in di differentfferent ellipses, ellipses, more more or or less less oblique plane that does not intersect the base [16]. An ellipse is defined by the length of the major elongated.elongated. Leaves Leaves of of many many species species tend tend to to an an elliptical elliptical shape, shape, which which is is also also common common among among diverse diverse and minor axes. Changing the relations between the axes results in different ellipses, more or less animalsanimals like like for for example exampleStylostomum Stylostomum ellipse ellipse, a, platelmyntha platelmynth (Figure (Figure3)[ 3)17 [17].]. elongated. Leaves of many species tend to an elliptical shape, which is also common among diverse animals like for example Stylostomum ellipse, a platelmynth (Figure 3) [17].

Figure 3. (a) The ellipse is a regular oval curve, traced by a point moving in a plane so that the sum of

its distances from two other points (the foci, F1 and F2) is constant. The ellipse is observed in the image ofFigure a platelmynth 3. (a) The (b )ellipse and in is leaves a regular of many oval speciescurve, traced (c). by a point moving in a plane so that the sum of its distances from two other points (the foci, F1 and F2) is constant. The ellipse is observed in the Figure 3. (a) The ellipse is a regular oval curve, traced by a point moving in a plane so that the sum image of a platelmynth (b) and in leaves of many species (c). of its distances from two other points (the foci, F1 and F2) is constant. The ellipse is observed in the image of a platelmynth (b) and in leaves of many species (c).

Horticulturae 2019, 5, x FOR PEER REVIEW 4 of 19 Horticulturae 2019, 5, 60 4 of 18 2.3. Oval 2.3. OvalAn oval is a curve resembling a squashed circle but, unlike the ellipse, without a precise mathematicalAn oval is definition. a curve resembling The word oval a squashed is derived circle from but, the unlikeLatin word the ellipse,“ovus” meaning without aegg. precise Unlike mathematicalellipses, ovals definition. have only The a word single oval axis is derivedof reflec fromtion symmetry the Latin word (instead “ovus” of two). meaning Theegg. oval Unlike may be ellipses,obtained ovals by have the combination only a single axisof four of reflection arcs of circle symmetry, one of (instead which ofis two).a semi-circle The oval (AB), may bethe obtained other two byhave the combination their centers ofin four the extreme arcs of circle, points one of ofthe which semicircle is a semi-circle (A, B), and (AB), the fourth the other arc twocloses have the their image centerswith ina quarter the extreme of circle points traced of the from semicircle the point (A, B), (C), and equidistant the fourth arcto closesA and the B [18]. image Typical with a quarterovals are ofobserved circle traced in eggs from and the pointin some (C), fruits equidistant such as toavocado A and B(Figure [18]. Typical 4). ovals are observed in eggs and in some fruits such as avocado (Figure4).

Figure 4. (a) The oval is a curve resembling a squashed circle but, unlike the ellipse, without a precise

mathematical definition. In the image, the oval is obtained as a combination of four arcs of circle. The ovalFigure is observed 4. (a) The in eggsoval (isb )a andcurve avocado resembling fruit a (c squashed). circle but, unlike the ellipse, without a precise mathematical definition. In the image, the oval is obtained as a combination of four arcs of circle. The 2.4. Contour of Fibonacci’s Spiral oval is observed in eggs (b) and avocado fruit (c). Successive points dividing a golden rectangle into squares lie on a logarithmic spiral, which is sometimes2.4. Contour known of Fibonacci’s as the golden Spiral spiral [19,20] (Figure5). The logarithmic spiral is a spiral whose polar equation is given by Successive points dividing a golden rectangle into squares lie on a logarithmic spiral, which is r = aeˆ(b θ) sometimes known as the golden spiral [19,20] (Figure 5). The logarithmic spiral is a spiral whose wherepolar r equation is the distance is given from by the origin, θ is the angle from the x-axis, and a and b are arbitrary constants [21]. r = ae^(b θ) 2.5.where Heart r Curve is the distance from the origin, θ is the angle from the x-axis, and a and b are arbitrary constants [21]. There are a number of mathematical curves that produced heart shapes, some of which are illustrated below (Figure6)[22].

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Figure 5. (a) Construction of a Fibonacci spiral. The Fibonacci spiral is observed in sea shells of the species Argonauta argo (b) as well as in the growth of some species of ferns (c).

2.5. Heart Curve There are a number of mathematical curves that produced heart shapes, some of which are illustratedFigure 5. below(a) Construction (Figure 6) of [22]. a Fibonacci spiral. The Fibonacci spiral is observed in sea shells of the speciesFigureArgonauta 5. (a) Construction argo (b) as wellof a Fibonacci as in the growth spiral. ofThe some Fibona speciescci spiral of ferns is observed (c). in sea shells of the species Argonauta argo (b) as well as in the growth of some species of ferns (c).

2.5. Heart Curve There are a number of mathematical curves that produced heart shapes, some of which are illustrated below (Figure 6) [22].

Figure 6. (a) An example of heart-shaped curve (a) and similar images in sea snails of the species CorculumFigure cardissa6. (a) An(b )example and leaves of heart-shaped of alfalfa (Medicago curve sativa(a) and)(c ).similar images in sea snails of the species Corculum cardissa (b) and leaves of alfalfa (Medicago sativa) (c). 2.6. Lens 2.6.A Lens lens is a lamina formed by the intersection of two offset disks of unequal radii such that the intersectionA lens is notis a empty,lamina oneformed disk by does the not intersection completely of enclose two offset the other, disks andof unequal the centers radii of such curvatures that the areintersection on opposite is sides not ofempty, the lens. one Imagesdisk does of some not fishescompletely as well enclose as fruits the resemble other, and lenses the (Figure centers7). of If the centersFigure 6. of ( curvaturea) An example are onof theheart-shaped same side, curve the resulting(a) and similar figure images is called in se aa lune snails [23 of]. the species Corculum cardissa (b) and leaves of alfalfa (Medicago sativa) (c).

2.6. Lens A lens is a lamina formed by the intersection of two offset disks of unequal radii such that the intersection is not empty, one disk does not completely enclose the other, and the centers of

Horticulturae 2019, 5, x FOR PEER REVIEW 6 of 19 curvaturesHorticulturae are 2019 on, 5 ,opposite x FOR PEER sides REVIEW of the lens. Images of some fishes as well as fruits resemble lenses6 of 19 (Figure 7). If the centers of curvature are on the same side, the resulting figure is called a lune [23]. curvatures are on opposite sides of the lens. Images of some fishes as well as fruits resemble lenses (Figure 7). If the centers of curvature are on the same side, the resulting figure is called a lune [23].

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Figure 7. ((a)) The The lens lens is the the figure figure produced by the intersection of two circles. ( b) Solea solea sp., a fishfish

of the family Soleidaidae. ( c) A lemon fruit (Citrus sp. Rutaceae). Figure 7. (a) The lens is the figure produced by the intersection of two circles. (b) Solea solea sp., a fish 3. Models Predominant in Particular Species and Taxonomic Groups 3. Modelsof the Predominant family Soleidaidae. in Particular (c) A lemon Species fruit ( andCitrus Taxonomic sp. Rutaceae). Groups 3.1. Variations in Seed Shape 3.1.3. VariationsModels Predominant in Seed Shape in Particular Species and Taxonomic Groups In general, seed shape is conserved at the species level. Nevertheless, shape is the result of a In general, seed shape is conserved at the species level. Nevertheless, shape is the result of a growth3.1. Variations process andin Seed even Shape in the same plant, or also in the same fruit, there may be differences in the growth process and even in the same plant, or also in the same fruit, there may be differences in the shape of seeds depending on many factors such as the ongoing developmental status or the position of shape ofIn seedsgeneral, depending seed shape on many is conserved factors suchat the as specie the ongoings level. developmental Nevertheless, shapestatus isor thethe resultposition of a the seed in the plant, in the inflorescence or in the fruit, and depending as well on the type of fruit. ofgrowth the seed process in the plant, and even in the in inflorescencethe same plant, or inor thealso fruit, in the and same depending fruit, there as well may on be the differences type of fruit in the. In fruits forming aggregates of seeds, such as in some capsules, the shape of each individual seed Inshape fruits offorming seeds depending aggregates on of manyseeds, factors such as such in someas the capsules, ongoing developmentalthe shape of each status individual or the position seed depends upon its position. This occurs in species of the Meliaceae (for example Swietenia mahogany dependsof the seed upon in itsthe position. plant, in Thisthe inflorescence occurs in species or in ofthe the fruit, Meliaceae and depending (for example as well Swietenia on the type mahogany of fruit . Jacq.), Myrtaceae (Eucalyptus L’Hér.) [24], and Nitrariaceae (Peganum harmala L.) (Figure8), as well as Jacq.),In fruits Myrtaceae forming (Eucalyptus aggregates L’ Hér.)of seeds, [24], such and Nitrariaceaeas in some capsules, (Peganum the harmala shape L.) of (Figure each individual 8), as well seedas in Nictaginaceae and other families. in dependsNictaginaceae upon andits position. other families. This occurs in species of the Meliaceae (for example Swietenia mahogany Jacq.), Myrtaceae (Eucalyptus L’Hér.) [24], and Nitrariaceae (Peganum harmala L.) (Figure 8), as well as in Nictaginaceae and other families.

Figure 8. In fruits forming aggregates of seeds, the position of a seed in the aggregate determines their Figure 8. In fruits forming aggregates of seeds, the position of a seed in the aggregate determines their shape. Examples: Peganum harmala L., (Nitrariaceae); Eucalyptus sp. L’Hér. (Myrtaceae); Swietenia shape. Examples: Peganum harmala L., (Nitrariaceae); Eucalyptus sp. L’Hér. (Myrtaceae); Swietenia mahogany Jacq. (Meliaceae). mahoganyFigure 8. Jacq. In fruits (Meliaceae). forming aggregates of seeds, the position of a seed in the aggregate determines their Intra-specificshape. Examples: variability Peganum in seedharmala shape L., may(Nitrariaceae); be due to Eucalyptus causes other sp. thanL’Hér. di ff(Myrtaceae);erences between Swietenia seeds of the samemahogany plant. Jacq. Di (Meliaceae).fferences between seeds may occur between wild-type and cultivated subspecies and varieties, as reported for Triticum aestivum L. [25]. In wheat, differences in shape have been reported between ancestral genotypes (ssp. spelta (L.) Thell., sive Triticum spelta L.) and modern bread subspecies and varieties (ssp. aestivum, cv. Torke or Zebra for example), the latter being more rounded [25,26]. Horticulturae 2019, 5, 60 7 of 18

Also, seed shape may vary in plants grown in different geographic regions or climatic conditions, as observed in Olea europaea L. [27], Jatropha curcas L. [28], and Ricinus communis L. [29,30]. Finally, quantitative differences in seed shape between wild-type seeds and mutants have been also reported for Arabidopsis thaliana, Medicago truncatula, and Lotus japonicus [31–33]. Nevertheless, and taking into account all these cases of variation, seed shape may be considered relatively constant for the majority of species under normal growth conditions. In contrast, there may be large differences in seed shape between species of the same family, but, also in some families, a model may be predominant. Even in some orders, most of the genera and species may have their seeds resembling a few particular models. In the following sections, we review the cases where particular geometric figures have been used for the description and quantification of seed shape in some species and higher taxonomic groups, allowing the analysis of seed shape with practical applications. Cardioid-derived figures were used in the model plant Arabidopsis thaliana (L.), Heynh. (Brassicaceae) [32], as well as in the model legume Medicago truncatula Gaertn. (Fabaceae) [33,34]. The cardioid was also the figure used in the model legume Lotus japonicus L. (Fabaceae) [33], and in Capparis spinosa L. (Capparaceae) [35]. The ellipse was the model in Jatropha curcas L. and Ricinus communis L. (Euphorbiaceae) [28–30], and in Quercus species (Fagaceae) [36]. We also review the cases of some families that have seeds resembling a predominant model or in which the application of a model has allowed a new point of view on taxonomic relationships. Finally, we discuss the cases where a given morphotype is abundant in an order. The oval and the ellipse are the predominant types in the Cucurbitales and the heart-shaped curve the predominant type in the Vitales.

3.2. The Cardioid as a Tool for Seed Shape Quantification in Model Species The magnitude used to describe the similarity between the geometric model (cardioid) and the seed image is called J index. J index is the percent of similarity between both images, geometric model (cardioid), and seed image. It is the percent of the total surface of both images that is shared (ratio shared/not shared 100; see, for example, [32–35,37]). Arabidopsis seeds resemble cardioids elongated × in the direction of the symmetry axis by a factor of Phi (the Golden Proportion). Their values of J index are over 90 and increase in the course of imbibition before germination, reaching maximum values of 95 and over at 20 h imbibition [38]. Differences in seed shape revealed as differences in J index were described with reduced values respect to the wild type for mutants in both the ethylene signal transduction [32] and cellulose biosynthesis [38] pathways in Arabidopsis thaliana. Similarly, seeds of the model legumes Lotus japonicus and Medicago truncatula were found to resemble, respectively, the cardioid and the cardioid elongated by a factor of Phi. Values of J index increase in the course of imbibition [34] and differences were found between wild-type seeds and ethylene pathway mutants in both species [33].

3.3. The Cardioid Applies also to Capparis Seeds Allowing Description of Intra-Specific Variability Capparis spinosa L. belongs to the family Capparaceae, related to the Brassicaceae in the order Brassicales. Two subspecies are described of Capparis spinosa in Tunisia: ssp. spinosa and ssp. rupestris [39,40]. C. spinosa subsp. rupestris is more creeping and smaller, and adapted to a variety of diverse conditions including drought and arid conditions in southern regions, where mean annual precipitation is under 100 mm. In addition, seeds are smaller in subsp. rupestris. Based on seed shape quantification with the cardiod model, results showed a larger diversity in seed shape in populations of C. spinosa subsp. rupestris than in ssp. spinosa [35].

3.4. The Cardioid as a Tool for Seed Shape Quantification in Other Species of Brassicaceae and Legumes The cardioid or modified cardioid may be useful for seed quantification in many members of the families Brassicaceae and Fabaceae (Figures9–11). Many species give J index values over 90 with these Horticulturae 2019, 5, x FOR PEER REVIEW 8 of 19 Horticulturae 2019, 5, x FOR PEER REVIEW 8 of 19 3.4. The Cardioid as a Tool for Seed Shape Quantification in Other Species of Brassicaceae and Legumes Horticulturae3.4. The Cardioid2019, 5 ,as 60 a Tool for Seed Shape Quantification in Other Species of Brassicaceae and Legumes 8 of 18 The cardioid or modified cardioid may be useful for seed quantification in many members of The cardioid or modified cardioid may be useful for seed quantification in many members of the families Brassicaceae and Fabaceae (Figures 9–11). Many species give J index values over 90 with the families Brassicaceae and Fabaceae (Figures 9–11). Many species give J index values over 90 with thesemodels, models, and in and some in genera some suchgenera as suchMedicago as Medicago, different, different models can models be applied can be with applied species with resembling species these models, and in some genera such as Medicago, different models can be applied with species resemblingthe cardioid the (Figure cardioid 10) and(Figure others 10) elongatedand others cardioids elongated (Figure cardioids 11)[ (Figure34]. 11) [34]. resembling the cardioid (Figure 10) and others elongated cardioids (Figure 11) [34].

Figure 9. The cardioid and modified cardioid (elongated in the horizontal direction) can be used for Figure 9. The cardioid and modified modified cardioid (elongated in the horizontal direction) can be used for seed shape quantification in the Brassicaceae. The values indicated correspond to J index in the images seed shape quantification quantification in the Brassicaceae. The values indicated correspond to J index in the images shown and do not represent mean values for each particular species. Bar equals 0.5 mm. shown and do not represent mean values forfor each particularparticular species.species. Bar equals 0.5 mm.

Figure 10. The cardioid can be used for seed shape quantification in many species of legumes, including Figure 10. The cardioid can be used for seed shape quantification in many species of legumes, Figurethe model 10. speciesThe cardioidLotus japonicus can be. Theused values for seed indicated shape correspond quantification to J indexin many in the species images of shown legumes, and including the model species Lotus japonicus. The values indicated correspond to J index in the images includingdo not represent the model mean species values Lotus for eachjaponicus particular. The values species. indicated Bar equals correspond 0.5 mm. to J index in the images shown and do not represent mean values for each particular species. Bar equals 0.5 mm. shown and do not represent mean values for each particular species. Bar equals 0.5 mm. Horticulturae 2019, 5, 60 9 of 18 Horticulturae 2019, 5, x FOR PEER REVIEW 9 of 19

Figure 11. The cardioid elongated by a factor of Phi (The Golden Ratio) either in the horizontal axis (top), or in the vertical axis (bottom) is the figurefigure for seed shape quantificationquantification in many species of legumes, including the model species Medicago truncatula. The The values values indicated indicated correspond correspond to J J index index in the images shown and do not repr representesent mean values for each particularparticular species. Bar equals 0.5 mm. 3.5. The Cardioid as a Model in Seeds of Other Families 3.5. The Cardioid as a Model in Seeds of Other Families In addition to the observed cases in the Brassicaceae or Capparaceae (Brassicales), and the Fabaceae In addition to the observed cases in the Brassicaceae or Capparaceae (Brassicales), and the (Fabales), seeds resembling the cardioid occur in the Aizoaceae and are common in the Papaveraceae Fabaceae (Fabales), seeds resembling the cardioid occur in the Aizoaceae and are common in the (Ranunculales), Malvaceae (Malvales), Caryophyllaceae (Caryophyllales), as well as in other families. Papaveraceae (Ranunculales), Malvaceae (Malvales), Caryophyllaceae (Caryophyllales), as well as in other3.5.1. families. Papaveraceae

3.5.1.The Papaveraceae Papaveraceae contain 44 genera with about 770 species, mostly herbs, with only one tree, Bocconia, and several shrubs. Seeds of species in the Papaveraceae adjust well to a cardioid (FigureThe 12 Papaveraceae)[41]. contain 44 genera with about 770 species, mostly herbs, with only one tree, Bocconia, and several shrubs. Seeds of species in the Papaveraceae adjust well to a cardioid (Figure 12)3.5.2. [41]. Malvaceae In contrast to the Papaveraceae, the family Malvaceae contains herbs, shrubs, and trees. The diverse life forms in the family allow testing our hypothesis of a relationship between life form and similarity to the cardioid in the seeds. In the Malvaceae, seed shape was investigated in a total of 53 genera (118 species) [42]. The greatest resemblance of seeds to a cardioid was found in seeds of herbs (Figure 13, Table1), whereas less cases of similarity to the cardioid and reduced values of the J index were found in trees. Among the subfamilies of the Malvaceae, the Malvoideae presented most herbaceous species. Out of 77 species analyzed in this subfamily, 53 were herbs and 24 shrubs or trees. The seeds of woody species in this family presented reduced similarity to the cardioid and lower values of the J index than in herbaceous species [42].

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Figure 12.12. The cardioid is a model for seed shape descriptiondescription and quantificationquantification in species of thethe Papaveraceae. The values indicated correspond to J index in the images shown and do not represent HorticulturaePapaveraceae. 2019, 5, x FORThe PEERvalues REVIEW indicated correspond to J index in the images shown and do not represent11 of 19 mean values forfor eacheach particularparticular species.species. Bar equals 0.5 mm.

3.5.2. Malvaceae In contrast to the Papaveraceae, the family Malvaceae contains herbs, shrubs, and trees. The diverse life forms in the family allow testing our hypothesis of a relationship between life form and similarity to the cardioid in the seeds. In the Malvaceae, seed shape was investigated in a total of 53 genera (118 species) [42]. The greatest resemblance of seeds to a cardioid was found in seeds of herbs (Figure 13, Table 1), whereas less cases of similarity to the cardioid and reduced values of the J index were found in trees. Among the subfamilies of the Malvaceae, the Malvoideae presented most herbaceous species. Out of 77 species analyzed in this subfamily, 53 were herbs and 24 shrubs or trees. The seeds of woody species in this family presented reduced similarity to the cardioid and lower values of the J index than in herbaceous species [42].

Table 1. Summary of J index values in the Malvaceae. Adapted from [42]. Mean values of the J index were compared by ANOVA (Scheffé’s test; IBM SPSS statistics v25) between three groups of species according to their life form (trees, shrubs, and herbs). Different letters indicate significant differences at p = 0.05.

Plant Number of Maximum Minimum Standard Mean Values of the Subsets Form Species Value Value Deviation Different for p = 0.05 Trees 20 87.6 50.0 10.0 70.1 (a) Shrubs 26 92.8 55.2 9.2 79.6 (b) Herbs 56 92.8 66.6 5.7 84.9 (c) Figure 13. The cardioid is a model for seed shape description and quantification in species in the Figure 13. The cardioid is a model for seed shape description and quantification in species in the Malvaceae. All the species represented are herbs, except Abutilon, which is a sub-shrub. The values Malvaceae. All the species represented are herbs, except Abutilon, which is a sub-shrub. The values indicated correspond to J index in the images shown and do not mean values for each particular species. indicated correspond to J index in the images shown and do not mean values for each particular Bar equals 0.5 mm. species. Bar equals 0.5 mm.

3.5.3. Caryophyllaceae The cardioid model applies also to species in the Caryophyllaceae, in particular to plant species of small size with short life cycles (Figure 14) [43].

Figure 14. The cardioid is a model for seed shape description and quantification in species of Caryophyllales (Caryophyllaceae). The values indicated correspond to J index in the images shown and do not represent mean values for each particular species. Bar equals 0.5 mm.

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Table 1. Summary of J index values in the Malvaceae. Adapted from [42]. Mean values of the J index were compared by ANOVA (Scheffé’s test; IBM SPSS statistics v25) between three groups of species according to their life form (trees, shrubs, and herbs). Different letters indicate significant differences at p = 0.05.

Plant Number Maximum Minimum Standard Mean Values of the Subsets Form of Species Value Value Deviation Different for p = 0.05 FigureTrees 13. The cardioid 20 is a model 87.6 for seed 50.0 shape descrip 10.0tion and 70.1quantification (a) in species in the Malvaceae.Shrubs All the 26 species represented 92.8 are herbs, 55.2 except Abutilon, 9.2 which is a sub-shrub. 79.6 (b) The values Herbs 56 92.8 66.6 5.7 84.9 (c) indicated correspond to J index in the images shown and do not mean values for each particular species. Bar equals 0.5 mm. 3.5.3. Caryophyllaceae 3.5.3. Caryophyllaceae The cardioid model applies also to species in the Caryophyllaceae, in particular to plant species of smallThe size cardioid with short model life cyclesapplies (Figure also to 14 species)[43]. in the Caryophyllaceae, in particular to plant species of small size with short life cycles (Figure 14) [43].

Figure 14. TheThe cardioid cardioid is is a a model model for for seed seed shape desc descriptionription and quantification quantification in species of Caryophyllales (Caryophyllaceae). The The values values indi indicatedcated correspond correspond to to J J index in the images shown and do not represent mean values for each particular species.species. Bar equals 0.5 mm.

3.6. The Ellipse Is a Model for Seed Morphology in Diverse Families

3.6.1. Euphorbiaceae Morphological seed description of Jatropha and Ricinus in the Euphorbiaceae allows the identification of variations in the comparison between intra-specific groups. Seeds of Jatropha curcas resemble an ellipse whose proportion between major and minor axes is equal to the Golden Ratio [20]. Comparison of seed shape between nine varieties of Jatropha curcas obtained from different origins and grown in Tunisia indicated a relationship between seed yield, size, and shape. Lowest yield was obtained in the accessions with smaller and more circular seeds, whose shape adjusted less well to an ellipse (lower J index values) [28]. Seeds of Ricinus communis L. also resemble an ellipse. J index was evaluated in populations of Ricinus cultivated in different geographic localizations and found to be lower in the populations grown in the desert [29,30]. Horticulturae 2019, 5, x FOR PEER REVIEW 12 of 19

3.6. The Ellipse Is a Model for Seed Morphology in Diverse Families

3.6.1. Euphorbiaceae Morphological seed description of Jatropha and Ricinus in the Euphorbiaceae allows the identification of variations in the comparison between intra-specific groups. Seeds of Jatropha curcas resemble an ellipse whose proportion between major and minor axes is equal to the Golden Ratio [20]. Comparison of seed shape between nine varieties of Jatropha curcas obtained from different origins and grown in Tunisia indicated a relationship between seed yield, size, and shape. Lowest yield was obtained in the accessions with smaller and more circular seeds, whose shape adjusted less well to an ellipse (lower J index values) [28]. Seeds of Ricinus communis L. also resemble an ellipse. J index was evaluated in populations of RicinusHorticulturae cultivated2019, 5, 60 in different geographic localizations and found to be lower in the populations12 of 18 grown in the desert [29,30]. 3.6.2. Oleaceae 3.6.2. Oleaceae Seeds and fruits of species Olea europaea, in the Oleaceae, adjust well to an ellipse allowing the Seeds and fruits of species Olea europaea, in the Oleaceae, adjust well to an ellipse allowing the comparison between subspecies and varieties [27]. comparison between subspecies and varieties [27]. 3.6.3. Campanulaceae 3.6.3. Campanulaceae Seeds in the Campanulaceae and many genera of the Asteraceae (Asterales) resemble the ellipse Seeds in the Campanulaceae and many genera of the Asteraceae (Asterales) resemble the ellipse (Figure 15), but the oval is also frequent in the Asteraceae. (Figure 15), but the oval is also frequent in the Asteraceae.

Figure 15. Seeds resembling an ellipse (Campanulaceae). The values indicated correspond to J index in Figure 15. Seeds resembling an ellipse (Campanulaceae). The values indicated correspond to J index the images shown and do not represent mean values for each particular species. Bar equals 0.5 mm. in the images shown and do not represent mean values for each particular species. Bar equals 0.5 mm. 3.6.4. Fagaceae 3.6.4. Fagaceae The ellipse describes well the images of the glands of Quercus suber, as well as other species in the Fagales.The ellipse describes well the images of the glands of Quercus suber, as well as other species in the Fagales. 3.7. The Oval Describes the Bi-Dimensional Image of Seeds in the Cucurbitaceae Well as in Other Families Seed images of many species in order Cucurbitales adjust well to an oval (Figure 16)[44]. This figure is useful for seed quantification in other families, for example Apiaceae, and may also apply to species in the Amborellaceae (Amborellales), Apocynaceae (Gentianales), Caryophyllaceae (Caryophyllales), Rutaceae (Sapindales), as well as to genera and species in the Asteraceae.

3.8. Seed Images Resembling Lenses The lenses are figures similar to the ellipses but have higher curvature values in their poles [45,46]. Adjust to a lens is good in Stemonurus sp. (Stemonuraceae) and Ilex sp. (Aquifoliaceae), both in the order Aquifoliales), as well as in some species of the Arecaceae (Arecales) and Calycera (Calyceraceae, Asterales), as well as in the Celastrales.

3.9. Other Geometric Figures Useful in Seed Description and Quantification

3.9.1. Heart-Shaped Curves Diverse heart-shaped curves define morphological types in the Vitaceae (Vitales; Figure 17). Horticulturae 2019, 5, x FOR PEER REVIEW 13 of 19 Horticulturae 2019, 5, 60 13 of 18 3.7. The Oval Describes the Bi-Dimensional Image of Seeds in the Cucurbitaceae Well as in Other Families

Figure 16. Seed images resemble ovals in thethe Cucurbitaceae.Cucurbitaceae. The values indicated correspond to J index in the imagesimages shown andand dodo notnot representrepresent meanmean valuesvalues forfor eacheach particularparticular species.species. Bar equals Horticulturae0.5 mm. 2019 , 5, x FOR PEER REVIEW 14 of 19

Seed images of many species in order Cucurbitales adjust well to an oval (Figure 16) [44]. This figure is useful for seed quantification in other families, for example Apiaceae, and may also apply to species in the Amborellaceae (Amborellales), Apocynaceae (Gentianales), Caryophyllaceae (Caryophyllales), Rutaceae (Sapindales), as well as to genera and species in the Asteraceae.

3.8. Seed Images Resembling Lenses The lenses are figures similar to the ellipses but have higher curvature values in their poles [45,46]. Adjust to a lens is good in Stemonurus sp. (Stemonuraceae) and Ilex sp. (Aquifoliaceae), both in the order Aquifoliales), as well as in some species of the Arecaceae (Arecales) and Calycera (Calyceraceae, Asterales), as well as in the Celastrales.

3.9. Other Geometric Figures Useful in Seed Description and Quantification

3.9.1. Heart-Shaped Curves Diverse heart-shaped curves define morphological types in the Vitaceae (Vitales; Figure 17).

Figure 17.17. Heart-shapedHeart-shaped curves curves in in the the Vitales. Vitales. The The values valu indicatedes indicated correspond correspond to J index to J inindex the imagesin the imagesshown andshown do notand representdo not represen mean valuest meanfor values each for particular each particular species. species. Bar equals Bar 0.5equals mm. 0.5 mm.

3.9.2. Seeds Seeds Resembling Resembling the the Contour Contour of Fibonacci’s Spiral We havehave found found seeds seeds resembling resembling the contour the contour of Fibonacci’s of Fibonacci’s spiral in the spiral Coriariaceae in the (Cucurbitales;Coriariaceae (Cucurbitales;Figure 18) as well Figure as in 18) the as Alismataceae well as in the (Alismatales; Alismataceae Figure (Alismatales; 19). Figure 19).

Figure 18. Seeds resembling the contour of Fibonacci’s spiral in species of Coriaria. The values indicated correspond to J index in the images shown and do not represent mean values for each particular species. Bar equals 0.5 mm.

Horticulturae 2019, 5, x FOR PEER REVIEW 14 of 19

Figure 17. Heart-shaped curves in the Vitales. The values indicated correspond to J index in the images shown and do not represent mean values for each particular species. Bar equals 0.5 mm.

3.9.2. Seeds Resembling the Contour of Fibonacci’s Spiral Horticulturae 2019, 5, 60 14 of 18 We have found seeds resembling the contour of Fibonacci’s spiral in the Coriariaceae (Cucurbitales; Figure 18) as well as in the Alismataceae (Alismatales; Figure 19).

Figure 18.18. SeedsSeeds resembling resembling the the contour contour of Fibonacci’s of Fibonacci’s spiral spiral in species in species of Coriaria of .Coriaria The values. The indicated values correspondindicated correspond to J index in to the J index images in shown the images and do sh notown represent and do mean not valuesrepresent for eachmean particular values for species. each Horticulturae 2019, 5, x FOR PEER REVIEW 15 of 19 Barparticular equals species. 0.5 mm. Bar equals 0.5 mm.

Figure 19. SeedsSeeds resembling the contour of Fibonacci’s spiral in speciesspecies ofof thethe Alismataceae.Alismataceae. The values indicatedindicated correspondcorrespond to to J indexJ index in in the the images images shown shown and and do notdo not represent represent mean mean values values for each for eachparticular particular species. species. Bar equals Bar equals 0.5 mm. 0.5 mm. 4. Discussion 4. Discussion The lack of methods to quantify seed shape results in a difficulty to define shape at the species The lack of methods to quantify seed shape results in a difficulty to define shape at the species level, and consequently, to describe with accuracy both intra- as well as inter-specific variations in level, and consequently, to describe with accuracy both intra- as well as inter-specific variations in seed shape. seed shape. Variations in seed shape may be due to many reasons, for example: (1) Adaptations for dispersal, Variations in seed shape may be due to many reasons, for example: (1) Adaptations for dispersal, (2) structural restrictions and conditions inside the ovary in which the seeds develop, such as in (2) structural restrictions and conditions inside the ovary in which the seeds develop, such as in the the Nictaginaceae and Nitrariaceae, and (3) other intra-specific variations are due to seed formation Nictaginaceae and Nitrariaceae, and (3) other intra-specific variations are due to seed formation in in different parts of the inflorescence, or seeds formed under different environmental conditions. different parts of the inflorescence, or seeds formed under different environmental conditions. Nevertheless, in general, seed shape is conserved at the species level. The description of shape variations requires a method to quantify seed shape. Seed shape quantification is more feasible in those cases where seeds resemble geometric figures and whose shape is relatively constant. We have seen many examples of the presence of such geometrically shaped seeds in different families. The seeds of the model species (Arabidopsis thaliana, in the Cruciferae; Lotus japonicus and Medicago truncatula, in the Fabaceae) resemble geometric figures, thus raising the possibility that the conditions of life shared by model species may be related to aspects of the geometry of their seeds. In fact, seeds resembling simple geometric shapes are common in fast-growing annual species in other taxonomic groups such as the Caryophyllales, the Malvales, and the Ranunculales. Among them, cardioid-shaped seeds are common in fast growing species, such as Silene, Spergula, Stellaria, and Saponaria in the Caryophyllaceae, as well as many species in the Papaveraceae (Ranunculales). The genetic control of seed shape is far from being resolved. Species from different taxonomic groups may have a similar seed shape in common, and on the contrary, close relatives in the same family may have different seed shapes. Seeds are forms specialized for survival during long periods of time under difficult conditions such as water and nutrient restrictions. Many metabolic pathways have to be coordinately regulated during seed formation. In their aspect of resistance forms, seeds resemble the pupal phase of insects [47]. In both cases, a complex genetic regulation must be set up involving the coordinated regulation of complex developmental pathways. Work with model systems may be of great help for the identification of the pathways and mechanisms responsible for each type of seed shape. In this context, it is interesting that the ats mutant described in Arabidopsis has cardioid-shaped seeds [31] instead of the normal shape of an elongated cardioid. However, shape is a complex character and most probably under the control of diverse pathways and it is possible

Horticulturae 2019, 5, 60 15 of 18

Nevertheless, in general, seed shape is conserved at the species level. The description of shape variations requires a method to quantify seed shape. Seed shape quantification is more feasible in those cases where seeds resemble geometric figures and whose shape is relatively constant. We have seen many examples of the presence of such geometrically shaped seeds in different families. The seeds of the model species (Arabidopsis thaliana, in the Cruciferae; Lotus japonicus and Medicago truncatula, in the Fabaceae) resemble geometric figures, thus raising the possibility that the conditions of life shared by model species may be related to aspects of the geometry of their seeds. In fact, seeds resembling simple geometric shapes are common in fast-growing annual species in other taxonomic groups such as the Caryophyllales, the Malvales, and the Ranunculales. Among them, cardioid-shaped seeds are common in fast growing species, such as Silene, Spergula, Stellaria, and Saponaria in the Caryophyllaceae, as well as many species in the Papaveraceae (Ranunculales). The genetic control of seed shape is far from being resolved. Species from different taxonomic groups may have a similar seed shape in common, and on the contrary, close relatives in the same family may have different seed shapes. Seeds are forms specialized for survival during long periods of time under difficult conditions such as water and nutrient restrictions. Many metabolic pathways have to be coordinately regulated during seed formation. In their aspect of resistance forms, seeds resemble the pupal phase of insects [47]. In both cases, a complex genetic regulation must be set up involving the coordinated regulation of complex developmental pathways. Work with model systems may be of great help for the identification of the pathways and mechanisms responsible for each type of seed shape. In this context, it is interesting that the ats mutant described in Arabidopsis has cardioid-shaped seeds [31] instead of the normal shape of an elongated cardioid. However, shape is a complex character and most probably under the control of diverse pathways and it is possible that this phenotype change in ats mutants may be obtained by other genetic alterations. For example, mutants in brassinolide pathway also have shortened seeds [48]. Quantitative trait loci analysis is a powerful method to identify genomic components involved in seed shape [49]. The application of this and other modern methods requires the identification of morphological characters independent of size. The work presented here for the description of seed shape opens the way to combine seed morphology with other methods such as visible and near-infrared hyperspectral imaging [50] that may result in the discovery of new relationships in taxonomy and phylogeny.

5. Conclusions (1) A method to define and quantify seed shape is described based on the comparison with geometric models. (2) Geometric models include the cardioid, ellipse, oval, contour of Fibonacci’s spiral, lens, and diverse heart-shaped curves. (3) The combination of geometric models with statistical methods allows the quantitative analysis of seed shapes and opens the way to shape description and quantification in seeds of diverse plant families. (4) The method may be useful to discover new relationships in taxonomy and phylogeny as well as in the description of mutants and shape modifications in diverse growth conditions.

Author Contributions: Conceptualization, E.C.; methodology, J.J.M.G.; software, J.J.M.G.; formal analysis, J.J.M.G.; investigation, E.C. and J.J.M.G.; data curation, E.C. and J.J.M.G.; writing—original draft preparation, E.C.; writing—review and editing, E.C. Funding: This research received no external funding Acknowledgments: Seeds of the Campanulaceae in Figure 15 were kindly provided by Juan José Aldasoro and Marisa Alarcón. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A. Origin of the Images Used in the Figures The images whose precedence is not mentioned belong to our image collection at IRNASA-CSIC. Horticulturae 2019, 5, 60 16 of 18

Figure2: Cardioid: like2do.com Cyclamen: https://wildflowerfinder.org.uk/Flowers/S/Sowbread(Eastern)/Sowbread(Eastern).htm. Photo: © Angela Stephens. Embryo: http://www.meihsieh.com/meid2go/hereissomething-globalsoftpirka, https: //creepypasta.fandom.com/wiki/Creepypasta_Wiki:Creepy_Images/Page_52 Figure3: Paramecium: https://www.asturnatura.com/especie/stylostomum-ellipse.html Figure4: Argonaute: https://www.3djuegos.com/comunidad-foros/tema/6199248/0/argonauta-argonauta- argo/ Figure7: Sole from: https: //conxemar.com/es/lenguado-europeo Figure9: Diplotaxis erucoides, Cardamine cordifolia, Lunaria annua from USDA. Iodanthus pinnatifidus from University of Minnesota (TMI). Figure 10: Genista tinctoria, Derris robusta from USDA. Ononis repens, Astragalus bhotanensis from herbarium (PE). Figure 11: Adesmia muricata, Adenocarpus viscosum, Medicago hispida from herbarium (PE). Daviesia pubigera from RBG Kew. Figure 12: Dicentra chrysantha from USDA. Figure 13: Malvastrum hispidum, Lavatera thuringiaca, Abelmoschus esculentus, Abutilon lignosum, Hibiscus trionum, from USDA. Figure 14: Silene coronaria, Silene noctifolia from USDA. Stellaria media, Agrostemma ghithago, Cucubalus baccifer, Arenaria serpyllifolia from herbarium (PE). Figure 16: Cucurbita maxima from the Department of Horticulture and Crop Science (The Ohio State University); Bryonia alba, Citrullus lanatus, Scyos angulatus, Trichosanthes subvelutina, Coccinia eglandulosa from USDA. Figure 17: Ampelopsis arborea, Vitis cinerea, Parthenocissus tricuspidata, Parthenocissus quinquefolia from USDA. Figure 18: Sagitaria longiloba (Alismataceae) and Echinodorus tenellus (Alismataceae) from USDA; Coriaria arborea and Coriaria japonica from herbarium (PE).

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