Geometric Models for Seed Shape Description and Quantification in the Cactaceae
Abstract
:1. Introduction
2. Results
2.1. New Geometric Models Based on the Equation of an Ellipse
2.2. New Geometric Models Based on the Archimedean Spiral
2.3. Application of the Models to Seed Shape Quantification
2.3.1. Overview of Seed Size and Shape in Some Cactus Species
2.3.2. Hylocereus undatus
2.3.3. Pachycereus pringlei
2.3.4. Ferocactus herrerae
2.3.5. Echinocactus platyacanthus
2.3.6. Cardioid-Derived Models for Opuntia ficus-indica
2.3.7. Models for Species of Pereskia and Maihuenia
3. Discussion
3.1. The Relationship between Seed Shape and Taxonomy
3.2. Seed Geometry in the Cactaceae
4. Materials and Methods
4.1. Plant Material
4.2. Photography and Image Analysis
4.3. Obtention of an Average Silhouette for Each Group of Seeds
4.4. Geometric Models
4.4.1. Geometric Models for the Symmetric Seeds of Rebutia and Echinopsis
4.4.2. Geometric Models for the Asymmetric Seeds of Echinocactus, Ferocactus, Hylocereus, Opuntia ficus-indica, Pachycereus, and Pereskia
4.4.3. Drawing of the Models
4.5. Seed Shape Quantification and Testing of the Models: J Index
4.6. Statistical Analysis
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
References
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N | A (mm2) | P (mm) | L (mm) | W (mm) | AR | C | R | |
---|---|---|---|---|---|---|---|---|
Echinocactus platyacanthus | 153 | 2.97 a (0.15) 2.50/3.42 | 6.83 b (0.26) 6.29/8.05 | 2.23 a (0.09) 2.03/2.54 | 1.70 b (0.07) 1.50/1.87 | 1.32 b (0.08) 1.17/1.54 | 0.80 cd (0.04) 0.60/0.86 | 0.76 c (0.05) 0.65/0.86 |
Ferocactus herrerae | 121 | 2.54 a (0.20) 1.72/3.02 | 6.19 a (0.25) 5.09/6.73 | 2.16 a (0.09) 1.73/2.36 | 1.49 a (0.06) 1.27/1.63 | 1.45 c (0.04) 1.36/1.63 | 0.83 d (0.01) 0.77/0.86 | 0.69 b (0.02) 0.61/0.73 |
Hylocereus undatus | 121 | 3.04 a (0.18) 2.53/3.56 | 7.46 c (0.38) 6.75/9.55 | 2.69 b (0.12) 2.33/2.96 | 1.44 a (0.06) 1.30/1.59 | 1.87 d (0.11) 1.62/2.17 | 0.69 a (0.05) 0.43/0.75 | 0.54 a (0.03) 0.46/0.62 |
Opuntia ficus-indica | 117 | 12.34 c (1.41) 8.71/15.70 | 14.49 e (1.11) 12.34/19.92 | 4.57 d (0.37) 3.71/5.63 | 3.43 d (0.25) 2.82/4.00 | 1.34 b (0.14) 1.07/1.74 | 0.74 b (0.07) 0.41/0.84 | 0.76 c (0.08) 0.57/0.94 |
Pachycereus pringley | 151 | 5.95 b (0.49) 4.25/7.04 | 9.89 d (0.63) 8.37/12.82 | 3.37 c (0.15) 2.95/3.72 | 2.25 c (0.11) 1.83/2.46 | 1.50 c (0.07) 1.30/1.72 | 0.77 bc (0.06) 0.49/0.83 | 0.67 b (0.03) 0.58/0.77 |
Pereskia bleo | 13 | 39.61 d (3.83) 31.38/44.78 | 26.78 f (2.23) 22.38/29.93 | 7.81 e (0.51) 6.92/8.60 | 6.45 e (0.36) 5.77/7.05 | 1.21 a (0.08) 1.04/1.34 | 0.70 a (0.09) 0.53/0.83 | 0.83 d (0.06) 0.74/0.96 |
N | CV(A) | CV(P) | CV(L) | CV(W) | CV(AR) | CV(C) | CV(R) | |
---|---|---|---|---|---|---|---|---|
Echinocactus platyacanthus | 153 | 5.13 | 3.85 | 3.92 | 4.01 | 6.11 | 5.19 | 5.97 |
Ferocactus herrerae | 121 | 7.87 | 4.05 | 4.12 | 4.20 | 2.49 | 1.66 | 2.47 |
Hylocereus undatus | 121 | 5.84 | 5.14 | 4.43 | 3.87 | 5.80 | 7.41 | 6.06 |
Opuntia ficus-indica | 117 | 11.39 | 7.63 | 8.16 | 7.24 | 10.67 | 9.87 | 10.49 |
Pachycereus pringley | 151 | 8.22 | 6.42 | 4.42 | 4.97 | 4.44 | 7.30 | 4.48 |
Pereskia bleo | 13 | 9.67 | 8.33 | 6.47 | 5.59 | 6.64 | 12.84 | 6.97 |
N | Area | P | L | W | AR | C | R | J Index SM | J Index LM | |
---|---|---|---|---|---|---|---|---|---|---|
S | 20 | 2.94 a (0.15) 2.65/3.21 | 6.69 a (0.21) 6.34/7.07 | 2.15 a (0.06) 2.05/2.28 | 1.74 b (0.05) 1.62/1.80 | 1.24 a (0.04) 1.18/1.30 | 0.83 b (0.02) 0.80/0.86 | 0.81 b (0.02) 0.77/0.85 | 92.1 b (1.12) 88.9/93.6 | 87.5 a (1.36) 84.8/90.3 |
L | 20 | 2.99 a (0.14) 2.74/3.19 | 6.86 b (0.19) 6.56/7.25 | 2.36 b (0.07) 2.24/2.50 | 1.61 a (0.05) 1.48/1.69 | 1.46 b (0.06) 1.37/1.60 | 0.80 a (0.02) 0.75/0.83 | 0.68 a (0.03) 0.63/0.73 | 87.7 a (1.90) 83.7/90.6 | 91.7 b (1.49) 88.9/93.8 |
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Martín-Gómez, J.J.; del Pozo, D.G.; Tocino, Á.; Cervantes, E. Geometric Models for Seed Shape Description and Quantification in the Cactaceae. Plants 2021, 10, 2546. https://doi.org/10.3390/plants10112546
Martín-Gómez JJ, del Pozo DG, Tocino Á, Cervantes E. Geometric Models for Seed Shape Description and Quantification in the Cactaceae. Plants. 2021; 10(11):2546. https://doi.org/10.3390/plants10112546
Chicago/Turabian StyleMartín-Gómez, José Javier, Diego Gutiérrez del Pozo, Ángel Tocino, and Emilio Cervantes. 2021. "Geometric Models for Seed Shape Description and Quantification in the Cactaceae" Plants 10, no. 11: 2546. https://doi.org/10.3390/plants10112546