*Article* **Effects of Soil Nutrients on Plant Nutrient Traits in Natural** *Pinus tabuliformis* **Forests**

**Jie Gao 1,2,\*, Jiangfeng Wang <sup>1</sup> and Yanhong Li 1,\***


**Abstract:** In light of global warming, the interaction between plant nutrient traits and soil nutrients is still unclear. Plant nutrient traits (e.g., N and P) and their stoichiometric relationships (N/P ratio) are essential for plant growth and reproduction. However, the specific role of soil nutrients in driving variation in plant nutrient traits remains poorly understood. Fifty natural *Pinus tabuliformis* forests were used as the research object to clarify the interaction between plant nutrient traits and soil nutrients. We show that: (1) The Nmass, Pmass and N/P ratios of leaves were significantly higher than those of roots. The N/P ratio of both leaves and roots was less than 14. (2) Leaf nutrient traits showed diverse relationship patterns with root nutrient traits throughout the growing period. Significant changes were found in root nutrient PC2 (the second principal component of root nutrient traits) and leaf nutrient PC1 (the first principal component of leaf traits), and non-significant changes were found in other relationships between leaf and root traits (*p* > 0.05). Root nutrient traits explained 36.4% of the variance in leaf nutrient traits. (3) With the increase in soil nutrient PC2 (related to N), leaf PC2 (related to N) showed a significant trend of first decreasing and then increasing (*p* < 0.05). Only the soil Nmass was significantly correlated with the leaf Nmass (*p* < 0.05), which demonstrated that the growth and survival of *Pinus tabuliformis* forests were mainly affected by N-limitation.

**Keywords:** plant–soil interaction; leaf nutrient; N-limitation; *Pinus tabuliformis*

### **1. Introduction**

Nutrient traits refer to traits related to nutrient characteristics (e.g., Nmass and Pmass), reflecting the survival strategies of plants in response to global warming, and are widely used in ecology [1–3]. Nitrogen (N) and phosphorus (P) are basic components of plant genetic material and nutrients, and their stoichiometric relationships significantly influence the process of plant growth and reproduction [4,5]. As a major limiting element, N is a fundamental component of enzymes [4]. Meanwhile, phosphorus drives the generation and maintenance of proteins and is also limiting in most environments [6]. The absence of nitrogen and phosphorus in leaves will affect the formation of chlorophyll, further reduce the productivity of forest communities and regulate carbon cycling [3]. The ratio of nitrogen to phosphorus (N/P) in plants reflects environmental factors, especially the nutrient supply of soil-to-plant growth [7,8]. It can clarify which elements restrict the plant's productivity. In other words, in a habitat where P is scarce and N is relatively abundant, plant N/P is relatively high, while in the habitat where N is scarce and P is relatively rich, plant N/P is relatively low and plant P content is significantly increased [3]. Soil nutrient limitation not only affects the nutrient structure of species but also affects the composition of community species and the direction of community succession [9].

Some studies have found that climatic factors may have a certain impact on plant nutrient traits [10]. However, as the direct living environment of plants, soil provides the necessary water and nutrients for plants to survive [11]. Therefore, soil nutrient factors may

**Citation:** Gao, J.; Wang, J.; Li, Y. Effects of Soil Nutrients on Plant Nutrient Traits in Natural *Pinus tabuliformis* Forests. *Plants* **2023**, *12*, 735. https://doi.org/10.3390/ plants12040735

Academic Editor: Yasutomo Hoshika

Received: 4 January 2023 Revised: 2 February 2023 Accepted: 4 February 2023 Published: 7 February 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

play a more critical role in shaping plant nutrient trait differences. However, the specific interaction between soil nutrients and plant nutrients remains unclear.

Complex feedback regulation mechanisms exist between plant nutrients and soil nutrients [12]. For example, litter in nutrient-rich soils will introduce higher nutrients, which release large amounts of nutrients after decay, thus maintaining a higher soil fertility level. In nutrient-poor soils, plants naturally produce less litter, and their decay progresses very slowly, which further leads to soil barrenness [4,11]. N and P are important components of soil nutrients, and it is unclear whether their performance is consistent with that of plant nutrient feedback and which nutrient trait plays a more important role in plant–soil nutrient feedback.

Plants with different life forms occupy different plant–soil nutrient feedback [13]. The nutrient profiles of leaves vary significantly between different life forms due to differences in their survival strategies [2]. This plant response feedback on soil nutrient supply reflects a nutrient trade-off in plant growth and development and reflects the survival strategies adopted by plants in coping with survival pressure [14]. Based on global data, Wright et al. [15] found that the leaf nitrogen and phosphorus contents of shrubs were significantly higher than those of trees. Plants with long-living leaves have low N and P contents [2] and, thus, tree species can adapt to a living environment with low nutritional status.

In recent years, an increasing number of studies have attempted to explore the correlations between traits of different organs from the perspective of plant functional traits. Relevant studies not only help to understand the mechanisms of interaction between plant traits [4] and the utilization and allocation of resources during plant growth [16] but also have important significance in further predicting the response of plants to environmental changes. Previous studies on plant nutrient traits (e.g., N, P) often focused on aboveground organs, and few studies were conducted on roots [17]. Exploring the difference in nutrient traits between aboveground and underground organs can help us to better understand the nutrient allocation strategies of plants as well as the plant–soil nutrient feedback [18].

Songshan Nature Reserve preserves the only natural *Pinus tabuliformis* forest in North China. *Pinus tabuliformis* plays an extremely important role in resisting wind and sand, conserving water sources and purifying air, etc. The shrub species are *Syinga reticulata* var. *Mandshurica*, *Corylus mandshurica* and *Euonymus verrucosus*. *Pinus tabuliformis* is the constructive species in Songshan Nature Reserve. We aim to explore the relative effects of soil nutrients on plant nutrient traits based on the plant nutrient trait data (e.g., Nmass, Pmass) of roots and leaves and soil nutrient data collected from 50 natural *Pinus tabuliformis* forests. We proposed the following hypotheses: (1) There exists a significant difference between roots and leaves in nutrient traits (e.g., Nmass, Pmass). (2) Soil nutrient factors are better at explaining the variation in root nutrient traits than leaf nutrient traits.

### **2. Results**

The Nmass (Figure 1A), Pmass (Figure 1B) and N/P ratios (Figure 1C) of leaves were significantly higher than those of roots (Table 1). We also found that the phosphorus content of trees was significantly higher than that of shrubs. However, there was no significant difference (*p* > 0.05) in nitrogen content between trees and shrubs (Figure S1).

The first two principal components (PC1 = 56.97%; PC2 = 41.54%) can explain 98.51% of the soil nutrient variation. The N/P ratio and PC1 showed a positive correlation. However, the Nmass, Pmass and PC1 showed a negative correlation (Figure 2A). The first principal component mainly represents the components related to nutrient restriction. The second principal component mainly represents the components related to nitrogen.

The first two principal components (PC1 = 53.61%; PC2 = 44.22%) can explain 97.83% of the plant nutrient variation. Both the nutrient function traits of roots and the nutrient traits of leaves were positively correlated with the second principal component (Figure 2B). The first principal component mainly represents the components related to nutrient restriction. The second principal component mainly represents the components related to nitrogen.

Leaf

Root

*Plants* **2023**, *12*, x FOR PEER REVIEW 3 of 9

**Figure 1.** A comparison of the differences in the Nmass (**A**), Pmass (**B**), and N/P (**C**) of different organs (leaf and root). \* represents *p* < 0.05, \*\* represents *p* < 0.01, \*\*\*\* represents *p* < 0.0001. **Figure 1.** A comparison of the differences in the Nmass (**A**), Pmass (**B**), and N/P (**C**) of different organs (leaf and root). \* represents *p* < 0.05, \*\* represents *p* < 0.01, \*\*\*\* represents *p* < 0.0001. Pmass 0.32 6.02 0.56 N:P 7.38 10.59 5.82


N:P 8.46 20.05 6.4


**Figure 2.** Principal component analysis (PCA) of nutrient characteristics of (**A**) soil and (**B**) leaves and roots. Nutrient characteristics included the Nmass, Pmass and N/P ratio. **Figure 2.** Principal component analysis (PCA) of nutrient characteristics of (**A**) soil and (**B**) leaves and roots. Nutrient characteristics included the Nmass, Pmass and N/P ratio.

**Figure 2.** Principal component analysis (PCA) of nutrient characteristics of (**A**) soil and (**B**) leaves and roots. Nutrient characteristics included the Nmass, Pmass and N/P ratio. The first two principal components (PC1 = 53.61%; PC2 = 44.22%) can explain 97.83% of the plant nutrient variation. Both the nutrient function traits of roots and the nutrient traits of leaves were positively correlated with the second principal component (Figure From the results of the generalized additive models (GAMs), it is clear that the investigated leaf traits showed diverse relationship patterns with root nutrient traits throughout the growing period (Table 2; Figure 3). Significant dynamic changes were found in the root nutrient PC2 and leaf PC1, and non-significant dynamic changes were found in other relationships between the leaf and root traits. Root nutrient traits explained 36.4% of the variance in leaf nutrient traits (Table 2; Figure 4).

The first two principal components (PC1 = 53.61%; PC2 = 44.22%) can explain 97.83% of the plant nutrient variation. Both the nutrient function traits of roots and the nutrient traits of leaves were positively correlated with the second principal component (Figure The soil nutrient factors had non-significant effects on the root nutrient traits (Table 2; Figure 5). The soil nutrient factors had significant nonlinear effects on the leaf nutrient traits (*p* < 0.05). With the increase in soil nutrient PC2 (related to N), leaf PC2 (related to N)

nitrogen.

showed a significant trend of first decreasing and then increasing (*p* < 0.05). Generally speaking, soil nutrients explained 25% of the variance in the leaf nutrient traits. root nutrient PC2 and leaf PC1, and non-significant dynamic changes were found in other relationships between the leaf and root traits. Root nutrient traits explained 36.4% of the variance in leaf nutrient traits (Table 2; Figure 4).

2B). The first principal component mainly represents the components related to nutrient restriction. The second principal component mainly represents the components related to

From the results of the generalized additive models (GAMs), it is clear that the investigated leaf traits showed diverse relationship patterns with root nutrient traits throughout the growing period (Table 2; Figure 3). Significant dynamic changes were found in the

*Plants* **2023**, *12*, x FOR PEER REVIEW 4 of 9

**Figure 3.** The plots of the GAMs smooth function indicating the effects of root nutrient traits on leaf nutrient traits. **A**: root PC1 vs. leaf PC1; **B**: root PC2 vs. leaf PC1; **C**: root PC1 vs. leaf PC2; **D**: root PC2 vs. leaf PC2. **Figure 3.** The plots of the GAMs smooth function indicating the effects of root nutrient traits on leaf nutrient traits. (**A**): root PC1 vs. leaf PC1; (**B**): root PC2 vs. leaf PC1; (**C**): root PC1 vs. leaf PC2; (**D**): root PC2 vs. leaf PC2. traits (*p* < 0.05). With the increase in soil nutrient PC2 (related to N), leaf PC2 (related to N) showed a significant trend of first decreasing and then increasing (*p* < 0.05). Generally speaking, soil nutrients explained 25% of the variance in the leaf nutrient traits.

**Figure 4.** The plots of the GAMs smooth function indicating the effects of soil nutrient factors on leaf nutrient traits. **A**: soil nutrient PC1 vs. leaf PC1; **B**: soil nutrient PC2 vs. leaf PC1; **C**: soil nutrient PC1 vs. leaf PC2; **D**: soil nutrient PC2 vs. leaf PC2. **Figure 4.** The plots of the GAMs smooth function indicating the effects of soil nutrient factors on leaf nutrient traits. (**A**): soil nutrient PC1 vs. leaf PC1; (**B**): soil nutrient PC2 vs. leaf PC1; (**C**): soil nutrient PC1 vs. leaf PC2; (**D**): soil nutrient PC2 vs. leaf PC2.


PC1 vs. leaf PC2; **D**: soil nutrient PC2 vs. leaf PC2.

*Plants* **2023**, *12*, x FOR PEER REVIEW 5 of 9

**Table 2.** Results of the generalized additive models (GAMs) explaining the influence of soil nutrient and root nutrient traits on leaf and root nutrient traits. \* *p* < 0.05.

The soil nutrient factors had non-significant effects on the root nutrient traits (Table 2; Figure 5). The soil nutrient factors had significant nonlinear effects on the leaf nutrient traits (*p* < 0.05). With the increase in soil nutrient PC2 (related to N), leaf PC2 (related to N) showed a significant trend of first decreasing and then increasing (*p* < 0.05). Generally

speaking, soil nutrients explained 25% of the variance in the leaf nutrient traits.

**Figure 5.** The plots of the GAMs smooth function indicating the effects of soil nutrient factors on root nutrient traits. (**A**): soil nutrient PC1 vs. root PC1; (**B**): soil nutrient PC2 vs. root PC1; (**C**): soil nutrient PC1 vs. root PC2; (**D**): soil nutrient PC2 vs. root PC2.

### **3. Discussion**

We found that the Nmass and Pmass of leaves were significantly higher than those of roots. Leaves are the main organ for photosynthesis, and Nmass and Pmass are closely related to protein synthesis [2]. Plant roots cannot participate in photosynthesis due to lack of chlorophyll. Therefore the Nmass and Pmass of plant roots are significantly lower than those of leaves [19–25].

We also found that the Pmass of tree leaves was significantly higher than that of shrub leaves. Plants of different life forms have unique niches and different resource utilization strategies for light, temperature and water under environmental pressure [2,25–32]. However, there was no significant difference in Nmass between tree and shrub leaves. The "community construction theory" based on nutrient traits explains that, in a local community, competition may lead to divergence between traits, but habitat screening may lead to the convergence of traits [33]. Often, the habitat selection effect causes different species to form more consistent characteristics so as to adapt to the same environment [3].

There exists a tradeoff between the nutrient traits of different plant organs [15]. Nmass and Pmass, in plant leaves, are mainly used for photosynthesis, while those of roots are mainly used for underground ecological processes so as to adapt to adverse environments. Therefore, when plants absorb nutrients from the soil, they will balance the nutrients according to their environment [34]. When plants are in an environment with sufficient resources (sufficient light, water, and heat), they will use more nutrients for photosynthesis to maximize resource utilization and facilitate plant growth and reproduction [26]. When plants are affected by osmotic stress, they will use more nutrients in underground processes (e.g., rooting) to avoid the threat [9].

In the past century, aboveground ecology has attracted extensive attention. However, the ecological links between aboveground and underground components remain unclear [2,3]. This knowledge gap hampers our ability to understand and predict the comprehensive responses of an ecosystem to environmental stresses [2,3]. Increasing evidence emphasizes that the importance of strong interactions between aboveground and underground components in regulating ecosystem multifunctionality and responses to global change [19–26].

Plants and soil participate in the global material cycle together, existing in a close relationship [27]. Plants absorb nitrogen and phosphorus from the soil through their roots and return them to the soil in the form of litter [20]. Therefore, there is a feedback relationship between soil and plant nutrients [3]. The aboveground element characteristics of plants are usually related to the soil nutrient content. As the main substrate for plant growth, soil contains organic matter, nitrate nitrogen and ammonium nitrogen, which are decomposed to continuously provide essential nutrients for the normal physiological activities of plants. This enables the soil and plant to achieve and maintain a balanced element ratio through the dynamic exchange of nutrient supply and demand [28–32]. We found that only soil Nmass was significantly correlated with leaf Nmass, offering evidence that the growth and development of *Pinus tabuliformis* forests were mainly limited by the supply of soil Nmass, and Pmass was not the key element limiting factor.

### **4. Materials and Methods**

### *4.1. Study Area*

The longitude and latitude range of Songshan Nature Reserve is 115◦4304400 E–115◦5002200 E, 40◦2909 00 N–40◦3303500 N. The annual average temperature is 8.5 ◦C, the highest temperature in the hottest month is 39 ◦C, and the lowest temperature in the coldest month is −27.3 ◦C. The annual average duration of sunshine is 2836.3 h, the annual average frost-free period is approximately 150 days, the annual average rainfall is 493 mm, and the annual average evaporation is 1770 mm. The reserve has the second highest peak in Beijing, with a maximum altitude of 2198.39 m. Most mountains measure between 600 and 1600 m. There are three types of soil connected with the elevation changes: brown forest soil, mountain brown soil and mountain meadow soil. Mountain meadow soil is mainly distributed under shrub vegetation above an altitude of 1800 m. The reserve is rich in animal and plant resources, including 713 species of higher wild vascular plants, more than 300 species of medicinal plants and 158 species (subspecies) of birds. Fifty representative plots (30 m × 30 m) were established in natural *Pinus tabuliformis* forests. The average elevation is 800 m. The maximum altitude is 875 m, and the minimum altitude is 770 m. The soil type is brown forest soil.

### *4.2. Nutrient Trait Data*

More than 10 mature and well-developed *Pinus tabuliformis* trees were selected from each plot to collect fresh (one-ye ar-old) needles and twigs. The collected samples were mixed evenly and placed into paper file bags. We selected roots with diameters greater than 2 mm for our research. The contents of N (%) and P (%) in the leaves were determined after sterilization at 105 ◦C, drying at 60 ◦C and mechanical grinding. The average value of each sample was taken to calculate the average contents of N (%) and P (%). Soil samples of the surface layer (0–20 cm) were collected under the selected tree. The soil samples were mixed fully and evenly. After air-drying in the laboratory, impurities were removed and the contents of N (g/kg) and P (g/kg) were determined after grinding and screening with 0.25 mm mesh. Roots of *Pinus tabuliformis* collection were carried out by a root-tracking method. The main roots of the sampled *Pinus tabuliformis* were found first, and the fine roots on the main roots were sequentially exposed by gradually removing sediment downward in the direction of the main roots. Roots containing at least five grades were cut off with pruning scissors, and these fine root samples were placed in selfsealing bags for preservation through temporary freezing. After taking the root samples back to the laboratory, the soil attached to the root samples was washed with water. The samples were graded according to the root order. The measured fine roots were placed in an oven at 60 ◦C for 72 h to maintain their weight. Root samples were kept for testing after crushing and screening with a 2 mm sieve. The total N content was determined by Kjeldahl determination, the leaf P content was determined by the molybdenum antimony anti-colorimetric method, and the soil total phosphorus was determined by the alkali fusion-Mo-Sb anti-spectrophotometric method [19–21,35]. The calculation method for the Nmass and Pmass of the leaves and roots of shrub species is the same as that for *Pinus tabuliformis.*

### *4.3. Data Analysis*

Principal component analysis (PCA) was used to reduce the dimensions of the plant nutrient traits, root nutrient and soil nutrient factors and was conducted within the R environment using the "vegan" package.

Generalized additive models (GAMs) were used to evaluate the effects of soil nutrient factors on leaf and root nutrient traits. This approach utilizes both parametric and nonparametric components to reduce the model risks inherent to linear models [22]. The model can be summarized as:

$$\mathbf{g}(E(\mathbf{Y}\mathbf{i})) = \beta\_0 + \mathbf{S}\_1(\mathbf{x}\_{\mathbf{i}}) + \mathbf{S}\_2(\mathbf{x}\_{\mathbf{i}}) + \mathbf{e}\_{\mathbf{i}} \tag{1}$$

where g is a link function, *E*(*Y*<sup>i</sup> ) is the estimate for the responsible variable *Y*<sup>i</sup> , S<sup>1</sup> is the smooth function of x<sup>i</sup> for different light treatments, and S<sup>2</sup> is the smooth function of x<sup>i</sup> throughout the investigation time. x<sup>i</sup> (i = 1, 2, 3, . . . , 12) are the explanatory variables, and they are the number of new rhizomes, new rhizome length, new rhizome diameter, etc. β<sup>0</sup> is the constant term and e<sup>i</sup> is the error term. All calculations were conducted within the R environment using the "mgcv" package.

**Supplementary Materials:** The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/plants12040735/s1, Figure S1: A comparison of the differences in the Nmass (A), Pmass (B), and N/P (C) at different life forms (Tree and Shrub), \*\*\*\* represents *p* < 0.0001.

**Author Contributions:** Conceptualization, J.G.; experiment implementation, J.G.; validation, J.G.; formal analysis, J.G.; writing—original draft preparation, J.G.; writing—review and editing, J.G., J.W. and Y.L.; visualization, J.G.; project administration, J.G. and Y.L.; funding acquisition, J.G. and Y.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** The study was supported by the Xinjiang Normal University Landmark Achievements Cultivation Project, China (grant number: no number), the Scientific Research Program of Colleges and Universities in Xinjiang (no. XJEDU2021I023) and the General Program in Xinjiang (no. 2022D01A213).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

### **References**


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## *Article* **Curvature Analysis of Seed Silhouettes in** *Silene* **L.**

**Emilio Cervantes 1,\*, José Luis Rodríguez-Lorenzo <sup>2</sup> , José Javier Martín-Gómez <sup>1</sup> and Ángel Tocino <sup>3</sup>**


**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.

**Keywords:** Bézier curve; complexity; curvature; development; Elliptic Fourier Transform; models; morphology; seed; systematics

### **1. Introduction**

The Caryophyllaceae Juss. comprises ca. 100 genera and 3000 species of herbs and small shrubs [1,2] of a cosmopolitan distribution and characterized by a peripheral position of the embryo in the developing seed [3], anatropous to campylotropous ovules [4], with an interesting diversity in seed shape [5–14].

Morphological analysis of seeds in the Caryophyllaceae focuses on two aspects: overall seed shape and detailed seed surface structure. Cardioid-derived models have been applied to the quantification of overall shape in lateral views of the seed [5–7], while ellipse-based models fit well to dorsal views of the seed in many species [8]. The application of models to seed shape quantification contributes to the identification of useful characters for taxonomy. Seeds of *Silene* L. subg. *Behenantha* conform better to a cardioid than those of *Silene* subg. *Silene* [5]. Seed images of species of sect. *Melandrium* fit better to models derived from a modified cardioid closed in the hilum region, whereas seeds of sect. *Silene* fit better to open models [9].

In relation to the seed surface, and based on their geometric properties, *Silene* seeds were divided into four groups: smooth, rugose, echinate and papillose [10,11]. Smooth seeds are defined by the absence of visible protuberances and this type was already described by other authors working with *Silene* [12–14] or related genera, such as *Arenaria* L. [15–17], *Minuartia* L. [18] and *Moehringia* L. [19]. In *Silene*, species with smooth

**Citation:** Cervantes, E.; Rodríguez-Lorenzo, J.L.; Martín-Gómez, J.J.; Tocino, Á. Curvature Analysis of Seed Silhouettes in *Silene* L. *Plants* **2023**, *12*, 2439. https://doi.org/ 10.3390/plants12132439

Academic Editors: Jie Gao, Weiwei Huang, Johan Gielis and Peijian Shi

Received: 17 May 2023 Revised: 13 June 2023 Accepted: 23 June 2023 Published: 25 June 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

seeds belong to *S.* subg. *Silene* sec. *Silene* such as *S. apetala* Willd., *S. borderei* Jord., *S. colorata* Poir., *S. damascena* Boiss. and Gaill., *S. diversifolia* Ott, *S. legionensis* Lag., *S. micropetala* Lag., *S. nicaeensis* All., *S. pomelii* Batt. subsp. *adusta* (Ball) Maire, *S. secundiflora* Ott, *S. vivianii* Steud.), other sections in *S.* subg. *Silene* such as *S. crassipes* Fenzl (sec. *Lasiocalycinae*), *S. colpophylla* Wrigley and *S. ramosissima* Desf. (sec. *Siphonomorpha*), and more rarely to *S.* subg. *Behenantha,* such as *S. baccifera* Roth (sec. *Cuccubalus*) and *S. littorea* Brot. (Sec. *Psammophilae*) [10,11].

Smooth seeds are characterized by high values of circularity and solidity in their lateral views, while, in dorsal views, higher values of circularity are shared by echinate and rugose seeds [10]. Papillose seeds are characterized by the lowest values of circularity and solidity in both lateral and dorsal views. Species included in this group are *S. holzmani* Heldr. ex Boiss. (sec. *Behenantha*), *S. laciniata* Cav. (sec. *Physolychnis*), *S. magellanica* (Desr.) Bocquet (sec. *Physolychnis*) and *S. perlmanii* W.L.Wagner, D.R.Herbst and Sohmer (sec. *Sclerophyllae*) [10].

Due to the large number of species, as well as infraspecific variation, it is important to quantitatively define seed surface structure properties and tubercle curvature in species of *Silene* and other genera in the Caryophyllaceae. The application of the Elliptic Fourier Transform (EFT) to seed images can provide new methods and models for seed shape description and quantification [20–22]. Once the seed silhouettes are represented by elemental functions, it is possible to calculate the corresponding curvature values. Curvature of a plane curve is a descriptive measure of shape that measures the rate at which the tangent line turns per unit distance moved along the curve. Departing from Bézier curves representing the root silhouettes, curvature was measured in *Arabidopsis* Heinh in Hall and Heinh (Brassicaceae) roots showing reduced values in ethylene-insensitive mutants (*etr1-1* and *ein2-1*) [23], as well as under hydrogen peroxide treatment [24]. In addition, curvature analysis allowed researchers to differentiate morphotypes in wheat kernels [25] and to define three groups of seeds in cultivated grapevine (*Vitis vinifera* L., Vitaceae) [26].

Closed plane curves based on EFT reproduced the seed silhouettes of representative *Silene* species [20]. The number of harmonics required to obtain curves reproducing the silhouettes provides an idea of the complexity of the seed surface and can be related to the four described types [10,11]. Curvature analysis based on EFT curves provides information about the geometry of the tubercles [20]. The analysis of seed surface structure has been applied to seeds of four *Silene* species: *S. colorata* Poir., *S. chlorifolia* Sm., *S. latifolia* Poir. and *S. perlmanii* W.L.Wagner, D.R.Herbst and Sohmer, representative of smooth, rugose, echinate and papillose seeds, respectively [10,11]. First, EFT curves are described for the lateral and dorsal views of seeds, and curvature analysis is performed on the EFT curves. Curvature analysis based on Bézier curves is also applied to the individual tubercles in the seeds of *S. chlorifolia* and *S. latifolia* providing an example for comparison of tubercle shape between seeds, populations or species. The analysis of curvature based on the combination of both EFT and Bézier curves provides a solid basis for the description and comparison of seed surface structure in *Silene*.

### **2. Results**

### *2.1. General Morphological Aspects of the Seeds*

Table 1 contains a summary of the morphological characteristics for the lateral and dorsal views of the seeds used in this work. In the lateral view, the seeds of *S. perlmanii* had the smallest area and lowest values of circularity and solidity, as was reported for the papillose-type seeds [10,11]. In the dorsal view, the highest values of solidity corresponded to the seeds of *S chlorifolia* and *S. latifolia*, representing the groups of rugose and echinate seeds, respectively. The high values of solidity and relatively low coefficients of variation are indicative of relatively stable morphological conditions in the seed populations.

**Table 1.** Morphological characteristics of the lateral and dorsal views of the seed populations subject of this work. A = area (mm<sup>2</sup> ); P = perimeter (mm); L = length (mm); W = width (mm); AR = aspect ratio; C = circularity; R = roundness; S = solidity. Different superscript letters indicate significant differences between files for the measurement indicated. The coefficients of variation are indicated between parentheses.


### *2.2. Elliptic Fourier Transform and Curvature: General Aspects*

Closed curves resulting from EFT analysis of seed contours reproduced the lateral and dorsal views of seed silhouettes [20]. The EFT curves for eight images representing the lateral and dorsal views of *Silene* seeds are presented. Similarity between the curve and the image silhouette is recognized by the coincidence between seed surface and EFT curve. Once a similarity was reached, Fourier curves representing the seed images were the subject for curvature analysis (Method 1: curvature based on EFT [20]; see supplementary data). In the case of seeds with tubercles, these and the protuberances of the EFT curve coincide. Curvature values were estimated for each EFT curve—including all the tubercles in a single analysis, and, later, individually for representative tubercles (Method 2: Curvature on individual tubercles, based on Bézier curves [23–26]). Both methods of curvature measurement, based, respectively, on EFT and Bézier curves, were applied to seed images of the three tuberculate species (*S. chlorifolia*, *S. latifolia* and *S. perlmanii*), while Method 1 alone was enough to describe the surface of *S. colorata* seeds. Notice the qualitative difference between the two methods: a study of the global form provided by Method 1 *versus* a local analysis obtained from Method 2.

### *2.3. Smooth Seeds Are Represented by Curves with a Low Number of Harmonics*

Figures 1 and 2 show the original seed images and the EFT closed curves for the lateral and dorsal views of *S. colorata*, together with their corresponding curvature values along the curves. To obtain the EFT curves, 40 points were taken from the surface of the seed images, and the EFT images represented equations with 20 harmonics. In the lateral view, maximum curvature values correspond to the micropile region (Figure 1) and, in the dorsal view, to the two concave regions in the upper and lower sides of the seed image (Figure 2). The other peaks of curvature correspond to irregularities of the seed surface.

*Plants* **2023**, *12*, x FOR PEER REVIEW 4 of 14

**Figure 1.** EFT and curvature analysis in a smooth seed. Lateral view of a seed of *S. colorata* with the EFT curve superimposed in green and the corresponding curvature values plotted. This is a smoothtype seed, lacking tubercles, and the maximum and minimum curvature values correspond to the micropilar region The EFT curve resulted from 43 points taken equidistantly along the seed silhouette and 20 harmonics, following the protocol published [20]. The program that provides the EFT curve contains the algorithm to plot the curvature values along it (see Supplementary Materials). Bar represents 1 mm. **Figure 1.** EFT and curvature analysis in a smooth seed. Lateral view of a seed of *S. colorata* with the EFT curve superimposed in green and the corresponding curvature values plotted. This is a smooth-type seed, lacking tubercles, and the maximum and minimum curvature values correspond to the micropilar region The EFT curve resulted from 43 points taken equidistantly along the seed silhouette and 20 harmonics, following the protocol published [20]. The program that provides the EFT curve contains the algorithm to plot the curvature values along it (see Supplementary Materials). Bar represents 1 mm. micropilar region The EFT curve resulted from 43 points taken equidistantly along the seed silhouette and 20 harmonics, following the protocol published [20]. The program that provides the EFT curve contains the algorithm to plot the curvature values along it (see Supplementary Materials). Bar represents 1 mm.

**Figure 2.** EFT and curvature analysis in a smooth seed. Dorsal view of a seed of *S. colorata* with the EFT curve superimposed in green and the corresponding curvature values plotted. This is a smooth-**Figure 2.** EFT and curvature analysis in a smooth seed. Dorsal view of a seed of *S. colorata* with the EFT curve superimposed in green and the corresponding curvature values plotted. This is a smoothtype seed, lacking tubercles and the maximum and minimum curvature values correspond to the upper and lower concavities. The EFT curve resulted from 38 points taken at regular distances along the silhouette and 20 harmonics, following the protocol published [20]. The program that provides **Figure 2.** EFT and curvature analysis in a smooth seed. Dorsal view of a seed of *S. colorata* with the EFT curve superimposed in green and the corresponding curvature values plotted. This is a smooth-type seed, lacking tubercles and the maximum and minimum curvature values correspond to the upper and lower concavities. The EFT curve resulted from 38 points taken at regular distances along the silhouette and 20 harmonics, following the protocol published [20]. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Bar represents 1 mm.

type seed, lacking tubercles and the maximum and minimum curvature values correspond to the upper and lower concavities. The EFT curve resulted from 38 points taken at regular distances along the silhouette and 20 harmonics, following the protocol published [20]. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Bar represents 1 mm. Lateral and dorsal views of *Silene colorata* seeds were accurately represented by 40 point-derived curves with 20 to 30 harmonics. In contrast, for tuberculate seeds, models the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Bar represents 1 mm. Lateral and dorsal views of *Silene colorata* seeds were accurately represented by 40 point-derived curves with 20 to 30 harmonics. In contrast, for tuberculate seeds, models derived from 40-point curves resemble the general shape, without considering the tubercles. These models are easy to develop and can be useful to obtain visual information on Lateral and dorsal views of *Silene colorata* seeds were accurately represented by 40-pointderived curves with 20 to 30 harmonics. In contrast, for tuberculate seeds, models derived from 40-point curves resemble the general shape, without considering the tubercles. These models are easy to develop and can be useful to obtain visual information on the general seed shape (Figure 3) for characteristics such as solidity and roundness (or aspect ratio). However, adjusting the surface contour to include the tubercles requires models obtained with more points.

#### derived from 40-point curves resemble the general shape, without considering the tuberaspect ratio). However, adjusting the surface contour to include the tubercles requires *2.4. Seeds with Tubercles Require a Higher Number of Harmonics*

cles. These models are easy to develop and can be useful to obtain visual information on the general seed shape (Figure 3) for characteristics such as solidity and roundness (or aspect ratio). However, adjusting the surface contour to include the tubercles requires models obtained with more points. The curves resulting from the application of the EFT with 100–250 points and 40–80 harmonics to the lateral and dorsal views of *S. chlorifolia*, *S. latifolia* and *S. perlmanii* are shown together with their corresponding curvature values (Figures 4–9).

the general seed shape (Figure 3) for characteristics such as solidity and roundness (or

models obtained with more points. In the lateral view of *S. chlorifolia* and *S. latifolia* seeds, there are less tubercles and with lower curvature values in the regions around the micropile. Curvature values in the tubercles comprise between −4 and 1 in *S. chlorifolia* and −8 and 5 in *S. latifolia*. Nevertheless, the highest values are due to small irregularities in the process of generation of the curve, and real tubercle curvature comprises between −2 and 1 *S. chlorifolia* and between −5 and 4 for *S. latifolia*. Tubercle number and absolute curvature values are higher in *S. latifolia*. In the seeds analyzed, in both species, the tubercles are of regular size and shape.

*Plants* **2023**, *12*, x FOR PEER REVIEW 5 of 14

In the dorsal view of seeds from both species, the tubercles were concentrated in the seed poles, being more pronounced and with higher curvature values than in the lateral sides (Figures 6 and 7).

Curves reproducing the silhouette of the lateral view of *S. perlmanii* were derived from the selection of 180–200 points in the application of EFT (Figure 8). The tubercles were larger than in *S. chlorifolia* and *S. latifolia* in relation to seed size. Estimated curvature values were between −3 and 1. *Plants* **2023**, *12*, x FOR PEER REVIEW 5 of 14

The curve representing the dorsal view of *S. perlmanii* reproduced 23 individual tubercles of curvature values between 1 and 35 (Figure 9).

**Figure 3.** EFT curves with a low number of harmonics. EFT curves representing the silhouettes corresponding to seeds of *Silene colorata*, *S. chlorifolia*, *S. latifolia* and *S. perlmanii* (left to right). Above: lateral views. Below: dorsal views. Fourier analysis [20] was performed taking 40 points from the seed surface, and the resulting EFT curves obtained from 20 harmonics. **Figure 3.** EFT curves with a low number of harmonics. EFT curves representing the silhouettes corresponding to seeds of *Silene colorata*, *S. chlorifolia*, *S. latifolia* and *S. perlmanii* (left to right). Above: lateral views. Below: dorsal views. Fourier analysis [20] was performed taking 40 points from the seed surface, and the resulting EFT curves obtained from 20 harmonics. less, the highest values are due to small irregularities in the process of generation of the curve, and real tubercle curvature comprises between −2 and 1 *S. chlorifolia* and between −5 and 4 for *S. latifolia*. Tubercle number and absolute curvature values are higher in *S. latifolia*. In the seeds analyzed, in both species, the tubercles are of regular size and shape.

**Figure 4.** EFT and curvature analysis in a rugose seed. Lateral view of a seed of *S. colorata* with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve resulted from 193 points taken along the silhouette and 96 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Rounded tubercles are disposed regularly and the maximum and minimum curvature values correspond to individual tubercles. Bar **Figure 4.** EFT and curvature analysis in a rugose seed. Lateral view of a seed of *S. colorata* with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve resulted from 193 points taken along the silhouette and 96 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Rounded tubercles are disposed regularly and the maximum and minimum curvature values correspond to individual tubercles. Bar represents 1 mm.

**Figure 4.** EFT and curvature analysis in a rugose seed. Lateral view of a seed of *S. colorata* with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve resulted from 193 points taken along the silhouette and 96 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Rounded tubercles are disposed regularly and the maximum and minimum curvature values correspond to individual tubercles. Bar

represents 1 mm.

represents 1 mm.

*Plants* **2023**, *12*, x FOR PEER REVIEW 6 of 14

*Plants* **2023**, *12*, x FOR PEER REVIEW 6 of 14

**Figure 5.** EFT and curvature analysis in an echinate-type seed. Lateral view of a seed of *S. latifolia* with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve resulted from 228 points taken along the silhouette and 74 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). This is an echinate-type seed, with acute tubercles disposed regularly and the maximum and minimum curvature values correspond to individual tubercles. Bar represents 1 mm. In the dorsal view of seeds from both species, the tubercles were concentrated in the seed poles, being more pronounced and with higher curvature values than in the lateral sides (Figures 6 and 7). **Figure 5.** EFT and curvature analysis in an echinate-type seed. Lateral view of a seed of *S. latifolia* with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve resulted from 228 points taken along the silhouette and 74 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). This is an echinate-type seed, with acute tubercles disposed regularly and the maximum and minimum curvature values correspond to individual tubercles. Bar represents 1 mm. tocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). This is an echinate-type seed, with acute tubercles disposed regularly and the maximum and minimum curvature values correspond to individual tubercles. Bar represents 1 mm. In the dorsal view of seeds from both species, the tubercles were concentrated in the seed poles, being more pronounced and with higher curvature values than in the lateral sides (Figures 6 and 7).

**Figure 6.** EFT and curvature analysis in a rugose seed. Dorsal view of a seed of with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve resulted from 102 points taken along the silhouette and 40 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Maximum curvature values correspond to individual tubercles in the poles. Bar represents 1 mm. **Figure 6.** EFT and curvature analysis in a rugose seed. Dorsal view of a seed of with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve resulted from 102 points taken along the silhouette and 40 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Maximum curvature values correspond to individual tubercles in the poles. Bar represents 1 mm. **Figure 6.** EFT and curvature analysis in a rugose seed. Dorsal view of a seed of with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve resulted from 102 points taken along the silhouette and 40 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Maximum curvature values correspond to individual tubercles in the poles. Bar represents 1 mm. *Plants* **2023**, *12*, x FOR PEER REVIEW 7 of 14

**Figure 7.** EFT and curvature analysis in an echinate-type seed. Dorsal view of a seed of *S. latifolia* with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve results from 98 points taken along the silhouette and 74 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Maximum curvature values correspond to individual tubercles. Bar represents 1 mm. Curves reproducing the silhouette of the lateral view of *S. perlmanii* were derived **Figure 7.** EFT and curvature analysis in an echinate-type seed. Dorsal view of a seed of *S. latifolia* with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve results from 98 points taken along the silhouette and 74 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Maximum curvature values correspond to individual tubercles. Bar represents 1 mm.

values were between −3 and 1.

from the selection of 180–200 points in the application of EFT (Figure 8). The tubercles were larger than in *S. chlorifolia* and *S. latifolia* in relation to seed size. Estimated curvature

**Figure 8.** EFT and curvature analysis in a papillose-type seed. Lateral view of a seed of *S. perlmanni* with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve shown resulted from 189 points taken along the silhouette and 74 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). This is a papillosetype seed, with tubercles of varied shape disposed unevenly at the seed surface. The maximum and

minimum curvature values correspond to particular tubercles. Bar represents 1 mm.

correspond to individual tubercles. Bar represents 1 mm.

values were between −3 and 1.

**Figure 7.** EFT and curvature analysis in an echinate-type seed. Dorsal view of a seed of *S. latifolia* with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve results from 98 points taken along the silhouette and 74 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Maximum curvature values

Curves reproducing the silhouette of the lateral view of *S. perlmanii* were derived from the selection of 180–200 points in the application of EFT (Figure 8). The tubercles were larger than in *S. chlorifolia* and *S. latifolia* in relation to seed size. Estimated curvature

**Figure 8.** EFT and curvature analysis in a papillose-type seed. Lateral view of a seed of *S. perlmanni* with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve shown resulted from 189 points taken along the silhouette and 74 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). This is a papillosetype seed, with tubercles of varied shape disposed unevenly at the seed surface. The maximum and minimum curvature values correspond to particular tubercles. Bar represents 1 mm. **Figure 8.** EFT and curvature analysis in a papillose-type seed. Lateral view of a seed of *S. perlmanni* with the EFT curve superimposed in green and the corresponding curvature values plotted. The EFT curve shown resulted from 189 points taken along the silhouette and 74 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). This is a papillose-type seed, with tubercles of varied shape disposed unevenly at the seed surface. The maximum and minimum curvature values correspond to particular tubercles. Bar represents 1 mm. *Plants* **2023**, *12*, x FOR PEER REVIEW 8 of 14 The curve representing the dorsal view of *S. perlmanii* reproduced 23 individual tubercles of curvature values between 1 and 35 (Figure 9).

**Figure 9.** EFT and curvature analysis in a papillose-type seed. Dorsal view of a seed of *S. perlmanii* with the EFT curve superimposed in green and the corresponding curvature values plotted. The maximum and minimum curvature values correspond to individual tubercles. The EFT curve shown results from 184 points taken along the silhouette and 60 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. Bar represents 1 mm. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Bar represents 1 mm. **Figure 9.** EFT and curvature analysis in a papillose-type seed. Dorsal view of a seed of *S. perlmanii* with the EFT curve superimposed in green and the corresponding curvature values plotted. The maximum and minimum curvature values correspond to individual tubercles. The EFT curve shown results from 184 points taken along the silhouette and 60 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. Bar represents 1 mm. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Bar represents 1 mm.

### *2.5. Curvature Analysis on Individual Tubercles 2.5. Curvature Analysis on Individual Tubercles*

tively.

Figure 10 shows the curvature analysis of individual tubercles, numbers 23, 1, 2 and 3, from the dorsal view of *S. perlmanii* represented in Figure 9. Curvature values are of 1.2 for tubercles 23, 1 and 2, and 2.1 for tubercle number 3. In contrast with *S. chlorifolia* and *S. latifolia*, the tubercles of *S. perlmanii* present great diversity in size and shape. Figure 10 shows the curvature analysis of individual tubercles, numbers 23, 1, 2 and 3, from the dorsal view of *S. perlmanii* represented in Figure 9. Curvature values are of 1.2 for tubercles 23, 1 and 2, and 2.1 for tubercle number 3. In contrast with *S. chlorifolia* and *S. latifolia*, the tubercles of *S. perlmanii* present great diversity in size and shape.

**Figure 10.** Curvature analysis of individual tubercles in *S. perlmanii.* Right: Four tubercles of *S. perlmanii*, numbers 23, 1, 2 and 3, from Figure 9 were selected to measure curvature individually. The corresponding Bézier curve (middle) and curvature plot (right) are shown in blue and green, respec-

The results of Fourier analysis indicated differences in curvature values between species*.* To investigate this in more detail, curvature analysis was performed in *S. chlorifolia*  and *S. perlmanii*, two species that have regular tubercles. Figure 11 shows representative samples of a tubercle of each species with their Bézier curve and corresponding curvature analysis. Table 2 presents the comparison of means (ANOVA) for maximum and average curvature values in six tubercles of each species. The differences were significant (*p* < 0.05)

*2.5. Curvature Analysis on Individual Tubercles* 

resents 1 mm.

**Figure 10.** Curvature analysis of individual tubercles in *S. perlmanii.* Right: Four tubercles of *S. perlmanii*, numbers 23, 1, 2 and 3, from Figure 9 were selected to measure curvature individually. The corresponding Bézier curve (middle) and curvature plot (right) are shown in blue and green, respectively. **Figure 10.** Curvature analysis of individual tubercles in *S. perlmanii.* Right: Four tubercles of *S. perlmanii*, numbers 23, 1, 2 and 3, from Figure 9 were selected to measure curvature individually. The corresponding Bézier curve (middle) and curvature plot (right) are shown in blue and green, respectively.

The curve representing the dorsal view of *S. perlmanii* reproduced 23 individual tu-

**Figure 9.** EFT and curvature analysis in a papillose-type seed. Dorsal view of a seed of *S. perlmanii* with the EFT curve superimposed in green and the corresponding curvature values plotted. The maximum and minimum curvature values correspond to individual tubercles. The EFT curve shown results from 184 points taken along the silhouette and 60 harmonics, following the protocol published [20]. The numbers indicate the correspondence between individual tubercles and their curvature values. Bar represents 1 mm. The program that provides the EFT curve contains the algorithm to obtain and represent the curvature values along it (see Supplementary Materials). Bar rep-

Figure 10 shows the curvature analysis of individual tubercles, numbers 23, 1, 2 and 3, from the dorsal view of *S. perlmanii* represented in Figure 9. Curvature values are of 1.2 for tubercles 23, 1 and 2, and 2.1 for tubercle number 3. In contrast with *S. chlorifolia* and

*S. latifolia*, the tubercles of *S. perlmanii* present great diversity in size and shape.

bercles of curvature values between 1 and 35 (Figure 9).

The results of Fourier analysis indicated differences in curvature values between species*.* To investigate this in more detail, curvature analysis was performed in *S. chlorifolia*  and *S. perlmanii*, two species that have regular tubercles. Figure 11 shows representative samples of a tubercle of each species with their Bézier curve and corresponding curvature analysis. Table 2 presents the comparison of means (ANOVA) for maximum and average curvature values in six tubercles of each species. The differences were significant (*p* < 0.05) The results of Fourier analysis indicated differences in curvature values between species. To investigate this in more detail, curvature analysis was performed in *S. chlorifolia* and *S. perlmanii*, two species that have regular tubercles. Figure 11 shows representative samples of a tubercle of each species with their Bézier curve and corresponding curvature analysis. Table 2 presents the comparison of means (ANOVA) for maximum and average curvature values in six tubercles of each species. The differences were significant (*p* < 0.05) both for maximum and mean values in the comparison between *S. chlorifolia* and *S. perlmanii*. *Plants* **2023**, *12*, x FOR PEER REVIEW 9 of 14 both for maximum and mean values in the comparison between *S. chlorifolia* and *S. perlmanii*.

**Figure 11.** Curvature analysis for individual tubercles of *S. chlorifolia* and *S. latifolia.* Above: representative individual tubercles with points taken. Middle: curves and curvature plots. Below: plot of **Figure 11.** Curvature analysis for individual tubercles of *S. chlorifolia* and *S. latifolia.* Above: representative individual tubercles with points taken. Middle: curves and curvature plots. Below: plot of curvatures corresponding to five tubercles for each species. Green: *S. chlorifolia*; Red: *S. latifolia*.

**Table 2.** Summary of curvature results for the comparison between *S. chlorifolia* and *S. latifolia*. ANOVA for six individual tubercles of each species*.* Different letters in superscript indicate signifi-

**Species** *S. chlorifolia S. latifolia*

The curvature was also measured in six tubercles of each of three seeds (eighteen tubercles total) of *S. chlorifolia* and *S. latifolia* and the mean values were compared. The

in six tubercles (mean) 40.7 a 55.5 b

curvatures corresponding to five tubercles for each species. Green: *S. chlorifolia*; Red: *S. latifolia*.

cant differences between species.

Maximum curvature values

results are shown in Table 3.

**Table 2.** Summary of curvature results for the comparison between *S. chlorifolia* and *S. latifolia*. ANOVA for six individual tubercles of each species. Different letters in superscript indicate significant differences between species.


The curvature was also measured in six tubercles of each of three seeds (eighteen tubercles total) of *S. chlorifolia* and *S. latifolia* and the mean values were compared. The results are shown in Table 3.

**Table 3.** Summary of curvature results for the comparison between *S. chlorifolia* and *S. latifolia*. ANOVA for 18 individual tubercles corresponding to three seeds of each species. Different letters in superscript indicate significant differences between species. Different superscript letters indicate significant differences between files for the measurement indicated. The coefficients of variation are indicated between parentheses.


### **3. Discussion**

The field of descriptive systematics aims at discovering the patterns in nature and how they vary between organisms, populations and species [27]. This requires the application of mathematical protocols to define, quantify and compare the shapes in the organisms [28].

The species of the genus *Silene* L. have a remarkable variation in geographical distribution, breeding systems and ecological relationships. Due to their short life-cycles, facility to breed and the growing availability of genetic resources, they can be considered as models for ecology and evolution [29]. In addition, *S. latifolia* has heteromorphic sex-determination with an evolving non-recombining y region rich in repetitive DNA that provides a unique system for the study of the origin and modification of sex chromosomes [30]. In addition, an interesting seed shape diversity makes *Silene* a useful model for studying variations in seed morphology [5–14].

In many species of *Silene*, as well as in other species of Caryophyllaceae, seeds have tubercles arranged along the seed surface. Typically, 20 to 60 tubercles are observed in the lateral view and a smaller number in the dorsal view. Size and shape of the tubercles, as well as the regularity of their distribution, vary among species and among populations of the same species, making it possible to search for associations between tubercle characteristics and genetic or environmental factors. Infraspecific variation concerning tubercle size and shape has been reported in other genus of the Caryophyllaceae, such as *Arenaria* L., *Acanthophyllum* L. as well as *Silene* [14,16,31], and the variations in tubercle shape have been attributed to geographical and ecological factors or, in contrast, to taxonomic differences [16]. The study of seed surface variation will benefit from new quantitative methods for the description of tubercle morphology and seed surface.

The observation by optical microscopy of seeds of 100 species of *Silene* allowed for their classification into four groups according to their silhouettes: smooth, rugose, echinate and papillose [10,11]. Accurate representation of the seed surface structure was obtained by the application of Fourier Transform to seed images [20]. Subsequently, in this article, we have investigated the differences between representative species of the four morphological types related to the representation of their seed silhouettes by EFT. The main geometric features of the silhouettes of smooth seeds are represented with EFT curves derived from 40 points selected in the seed surface and 20 harmonics. This result agrees with estimates of 10 harmonics for reproducing the shape of leaves [32] and makes EFT with low harmonic number

an interesting tool for the representation of general aspects of seed shape. Nevertheless, Fourier analysis applied to the species of tuberculate seeds (rugose, echinate and papillose), required a higher number of harmonics to define well the individual protuberances. Thus, although Fourier analysis with a low number of harmonics can discriminate successfully between various seed morphotypes, only with a higher number of harmonics can the morphological properties, size, shape and distribution of the tubercles can be analyzed.

To obtain curves adjusting to the protuberances at least 100 points are required, and the accuracy increases with higher numbers up to 250 or even more. Equations of 60 to 80 harmonics are sufficient in most cases, but more may be necessary to have detailed representation of the tubercles.

In addition to curvature analysis on curves derived from EFT, the analysis was focused (involving higher precision) on individual tubercles. The comparison revealed lower curvature values in *S. chlorifolia* (rugose seeds) and higher in *S. latifolia* (echinate). The application of the method to diverse populations of these species is required to confirm that a range of curvature values is a property of each species. In addition, the application to different species of each of the groups (rugose, echinate and papillose) will tell whether curvature values may be associated with the general morphology of the tubercles. A constant curvature value observed in the seeds of *S. chlorifolia* is related to lower curvature values and the proximity between mean and maximum values.

The method presented here opens the way to the analysis of size, shape and distribution of tubercles along the seed surface. The reported results remark upon the difference among seed types based on cell surface, with smooth seeds being characterized by a profile represented by low number of points, and on the other side, papillose seeds with numerous large tubercles that can only be represented by EFT when a large number of points are considered. Both types are distinguished also by their extreme values of circularity (highest in smooth seeds, lowest in papillose seeds) [10]. In between these two types remain the other two groups, rugose and echinate, here represented by *S. chlorifolia* and *S. latifolia,* respectively. While the tubercles in both are distributed more regularly than in papillose seeds, the results show differences with increased curvature values in *S. latifolia*. The results with other species and populations will demonstrate whether this is a property of echinate seeds, in contrast with rugose seeds, or if these differences are due to the species or populations chosen.

### **4. Materials and Methods**

### *4.1. Silene Seeds*

The populations of seeds analyzed in this work are listed in Table 4.

**Table 4.** List of seed populations analyzed in this work. The populations JBUV 519, JBUV100 and JBUV 1444 were obtained from the carpoespermateca at the Botanical Garden of the University of Valencia and proceed from an exchange protocol between seed collections through the world.


\* JBUV = Jardín Botánico Universidad de Valencia. \*\* U stands for unknown.

1

### *4.2. Seed Images*

For the analysis of individual tubercles, photographs were taken with a Nikon Stereomicroscope Model SMZ1500 (Nikon, Tokio, Japan) equipped with a 5.24 megapixel Nikon DS-Fi1 of camera (Nikon, Tokio, Japan); lateral and dorsal views used in FET analysis were taken with a Nikon Z6 camera (Nikon, Tokio, Japan), equipped with an objective AF-S Micro NIKKOR 60 mm f/2.8G ED (Nikon, Tokio, Japan).

### *4.3. Elliptic Fourier Transform (EFT)*

The application of EFT to any closed plane figure results in a curve that mimics the silhouette of the original figure and is amenable to curvature analysis. For this, a series of points were selected at regular intervals on the seed silhouette (Figure 12). The function, whose graphic approximates the shape, is a combination of trigonometric expressions; then, its expression allows for calculating the curvature values along the curve [20]. The program to obtain an EFT curve from a series of points and the application to the four seed types was made available (see Supplementary Material). The points were taken starting from the right side of the seed image silhouette and moving clockwise. Different curves can result from the same image depending on the number and positions of the points taken, as well as the number of points selected in the curve construction process (number of harmonics). It is important to avoid the duplication of points and to take a similar number of points at equivalent distances in the different samples when a comparative analysis is sought.

**Figure 12.** Example of the method (Method 1) to obtain EFT curve and curvature values from a seed image. Seed of *S. colorata* (lateral view), set of points selected, curve and results of curvature analysis. The red dot marks the initial point; the series of points follow clockwise, and the results of curvature analysis are shown counterclockwise, starting from the last point.

The process was divided in two consecutive methods. First (Method 1), 40 to 50 points were taken at regular intervals from the seed silhouettes of all four types and 20 or 30 points were selected for the Fourier curves. Method 1 resolved the silhouettes for lateral and dorsal views of *S. colorata* (smooth seeds), as well as the overall shape for all four species. For the tuberculate species (*S. chlorifolia*, *S. latifolia* and *S. perlmanii*), more points were taken at regular intervals from the seed silhouettes and Fourier curves performed with 60 harmonics or more were needed to fit the curve and the seed silhouette (Method 2). The program to obtain an EFT curve also contains the code for the calculation of curvature values along the curve and their corresponding plot (Figure 12).

### *4.4. Curvature Analysis*

Curvature values were calculated either from the EFT curves (whole-seed images) or for individual tubercles (See Supplementary Materials). In the figures, the curvature values are represented in reverse sense to the direction of the curve (starting at the last point and moving counterclockwise; Figure 12). Curvature values below the horizontal axis belong to peaks pointing towards the center of the seed, while peaks with positive values correspond to protuberances. Curvature values were determined for individual tubercles of each species according to established procedures [23–26] (See Supplementary Materials). In the measurements of curvature for individual tubercles, the points were taken either

manually, as represented in Figures 11 and 12, or automatically with the function Analyze line graph of Image J. In the first case (points taken manually; Figure 11 and Table 2), six tubercles were selected from the lateral views of representative seeds of *S. chlorifolia* and *S. latifolia*, and their maximum and mean curvature values determined. In the case of points taken automatically (Table 3), six tubercles of three representative seeds for each species were analyzed.

### *4.5. Statistical Analysis*

ANOVA was used to show significant differences between populations for the measured variables. In the case of the comparison of morphological characters involving four populations, ANOVA was followed by Tukey test to provide specific information on which means were significantly different from one another. Statistical analyses (ANOVA) were carried out on IBM SPSS statistics v28 (SPSS 2021).

### **5. Conclusions**

Fourier analysis has been applied to four representative morphotypes of *Silene* seeds based on seed surface structure: smooth, rugose, echinate and papillose. The method can successfully discriminate between various seed groups. The surface of smooth seeds, with no visible tubercles and higher circularity values, is represented by EFT equations with 40 harmonics. EFT opens the way to the analysis of seed surface protuberances. Curvature analysis applied to individual tubercles revealed differences between representative seeds of rugose and echinate groups, with lower values in rugose seeds and higher in tubercles of echinate seeds.

**Supplementary Materials:** The Mathematica® files with Fourier analysis, points for curvature analysis and curvature analysis of individual tubercles are available at https://www.mdpi.com/article/ 10.3390/plants12132439/s1. The file entitled "EFT for Silene seeds four types.nb" contains the EFT curves and curvature analysis shown in Figures 1, 2 and 4–9.

**Author Contributions:** Conceptualization, E.C., J.L.R.-L. and Á.T.; methodology, E.C., J.L.R.-L., J.J.M.-G. and Á.T.; software, E.C. and Á.T.; validation, E.C., J.L.R.-L. and Á.T.; formal analysis, E.C., J.L.R.-L., J.J.M.-G. and Á.T.; investigation, E.C., J.L.R.-L., J.J.M.-G. and Á.T.; resources, E.C., J.L.R.-L., J.J.M.-G. and Á.T.; data curation, E.C., J.L.R.-L., J.J.M.-G. and Á.T.; writing—original draft preparation, E.C.; writing—review and editing, E.C., J.L.R.-L., J.J.M.-G. and Á.T.; visualization, E.C., J.L.R.-L., J.J.M.-G. and Á.T.; supervision, E.C., J.L.R.-L. and Á.T.; project administration, E.C., J.L.R.-L. and Á.T.; funding acquisition, E.C., J.L.R.-L. and Á.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** Project "CLU-2019-05-IRNASA/CSIC Unit of Excellence", funded by the Junta de Castilla y León and co-financed by the European Union (ERDF "Europe drives our growth").

**Data Availability Statement:** The data presented in this study are available in Supplementary Materials.

**Acknowledgments:** We thank Ana Juan of the University of Alicante and Bohuslav Janousek from IBP Brno for continuous collaboration and constructive criticism, and Ana Juan and Elena Estrelles and the Carpoespermateca of the Botanical Garden at the University of Valencia for providing the seeds used in this study.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


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