# Scaling Relationships between Leaf Shape and Area of 12 Rosaceae Species

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{b}, where a is the normalization constant and b is the scaling exponent [17]. When b > 1, larger leaves have higher LMAs, whereas b < 1 indicates the opposite. If b = 1, changes in leaf size have no effect on LMA. A higher LMA indicates a higher energy investment in supporting leaf structure and function, and it also reflects leaf longevity [18,19,20]. Pan et al. [21] analyzed the scaling relationship between leaf dry weight and area of 121 species along an altitudinal gradient in a subtropical forest. They found that there was a significant power-law relationship between leaf weight and area, and reported that the scaling exponent b increased from 0.859 to 1.299 with an increase in altitude. Thus, leaves manifest different scaling relationships across environmental gradients. Huang et al. [22] tested whether there were scaling relationships between leaf fresh weight and leaf surface area using 12 species within two genera in Bambusoideae, and they found that the scaling relationships of leaf fresh weight versus area also held and the scaling relationship of leaf fresh weight versus area was stronger than that of leaf dry weight versus area for each species investigated.

## 2. Materials and Methods

#### 2.1. Plants, Sampling, and Image Processing

#### 2.2. Leaf Data Acquisition

#### 2.3. Models and Data Analysis

#### 2.3.1. The Relationship between Leaf Dry Weight and Leaf Surface Area

^{2}) conformed with a power function [17,33]:

^{b}

^{b−}

^{1}

#### 2.3.2. The Relationships among Lamina Area, Length, and Width

^{2}= kw

^{2}/λ

#### 2.3.3. Leaf-Shape Indices and the Scaling Relationships with Leaf Area

^{θ}

^{θ−}

^{1}

#### 2.3.4. Statistical Analysis

## 3. Results

^{2}(P. indica) to 93.15 cm

^{2}(P. serratifolia), blade dry weight ranged from 0.0059 g (P. indica) to 1.4330 g (P. serratifolia), and LMA ranged from 0.0015 g/cm

^{2}(R. hirsutus) to 0.0189 g/cm

^{2}(P. serratifolia) (Figure 3).

^{2}) of individual species equaled or exceeded 0.6, with the exception of M. halliana and R. hirsutus. The coefficients of determination of seven species even exceeded 0.8 (Figure 4).

## 4. Discussion

^{2}> 0.98), indicated that the proportionality k can be regarded as species-specific constant and independent from leaf area. Since leaf area was proportional to the product of leaf length and width [34,39], we have A = kλl

^{2}or A = kw

^{2}/λ. That is, the relationship between leaf area and leaf length (or leaf width) should theoretically hold, and leaf area can be conveniently estimated from length measures in the field.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Musarella, C.M.; Cano-Ortiz, A.; Pinar Fuentes, J.C.; Navas-Urena, J.; Pinto Gomes, C.J.; Quinto-Canas, R.; Cano, E.; Spampinato, G. Similarity analysis between species of the genus Quercus L. (Fagaceae) in southern Italy based on the fractal dimension. PhytoKeys
**2018**, 113, 79–95. [Google Scholar] [CrossRef] [PubMed] - De Araujo Mariath, J.E.; Pires Dos Santos, R.; Pires Dos Santos, R. Fractal dimension of the leaf vascular system of three Relbunium species (Rubiaceae). Braz. J. Biol. Sci.
**2010**, 8, 30–33. [Google Scholar] - Dengler, N.G.; Kang, J. Vascular patterning and leaf shape. Curr. Opin. Plant Biol.
**2001**, 4, 50–56. [Google Scholar] [CrossRef] - Runions, A.; Fuhrer, M.; Lane, B.; Federl, P.; Rolland-Lagan, A.-G.; Prusinkiewicz, P. Modeling and visualization of leaf venation patterns. ACM Trans. Graphics
**2005**, 24, 702–711. [Google Scholar] [CrossRef] [Green Version] - Roderick, M.L.; Berry, S.L.; Noble, I.R.; Farquhar, G.D. A theoretical approach to linking the composition and morphology with the function of leaves. Funct. Ecol.
**1999**, 13, 683–695. [Google Scholar] [CrossRef] - Brodribb, T.J.; Field, T.S.; Jordan, G.J. Leaf maximum photosynthetic rate and venation are linked by hydraulics. Plant Physiol.
**2007**, 144, 1890–1898. [Google Scholar] [CrossRef] - Nicotra, A.B.; Leigh, A.; Boyce, C.K.; Jones, C.S.; Niklas, K.J.; Royer, D.L.; Tsukaya, H. The evolution and functional significance of leaf shape in the angiosperms. Funct. Plant Biol.
**2011**, 38, 535–552. [Google Scholar] [CrossRef] [Green Version] - Niinemets, Ü.; Kull, K. Leaf weight per area and leaf size of 85 Estonian woody species in relation to shade tolerance and light availability. For. Ecol. Manag.
**1994**, 70, 1–10. [Google Scholar] [CrossRef] - Smith, W.K.; Vogelmann, T.C.; DeLucia, E.H.; Bell, D.T.; Shepherd, K.A. Leaf form and photosynthesis: Do leaf structure and orientation interact to regulate internal light and carbon dioxide? BioScience
**1997**, 47, 785–793. [Google Scholar] [CrossRef] - Niinemets, Ü. Research review: Components of leaf dry mass per area-thickness and density-alter leaf photosynthetic capacity in reverse directions in woody plants. New Phytol.
**1999**, 144, 35–47. [Google Scholar] [CrossRef] - Niinemets, Ü. Global-scale climatic controls of leaf dry mass per area, density, and thinness in trees and shrubs. Ecology
**2001**, 82, 453–469. [Google Scholar] [CrossRef] - Funk, J.L.; Cornwell, W.K. Leaf traits within communities: Context may affect the mapping of traits to function. Ecology
**2013**, 94, 1893–1897. [Google Scholar] [CrossRef] [PubMed] - Onoda, Y.; Saluñga, J.B.; Akutsu, K.; Aiba, S.; Yahara, T.; Anten, N.P.R. Trade-off between light interception efficiency and light use efficiency: Implications for species coexistence in one-sided light competition. J. Ecol.
**2014**, 102, 167–175. [Google Scholar] [CrossRef] - Puglielli, G.; Crescente, M.F.; Frattaroli, A.R.; Gratani, L. Leaf mass per area (LMA) as a possible predictor of adaptive strategies in two species of Sesleria (Poaceae): Analysis of morphological, anatomical and physiological leaf traits. Ann. Bot. Fenn.
**2015**, 52, 135–143. [Google Scholar] [CrossRef] - Yu, X.J.; Shi, P.J.; Hui, C.; Miao, L.F.; Liu, C.L.; Zhang, Q.Y.; Feng, C.N. Effects of salt stress on the seaf shape and scaling of Pyrus betulifolia Bunge. Symmetry
**2019**, 11, 991. [Google Scholar] [CrossRef] - Jurik, T.W. Temporal and spatial patterns of specific leaf weight in successional northern hardwood tree species. Am. J. Bot.
**1986**, 73, 1083–1092. [Google Scholar] [CrossRef] - Niklas, K.J.; Cobb, E.D.; Niinemets, Ü.; Reich, P.B.; Sellin, A.; Shipley, B.; Wright, I.J. “Diminishing returns” in the scaling of functional leaf traits across and within species groups. Proc. Natl. Acad. Sci. USA
**2007**, 104, 8891–8896. [Google Scholar] [CrossRef] [PubMed] - Howland, H.C. Structural, Hydraulic, and ‘Economic’ Aspects of Leaf Venation and Shape. In Biological Prototypes and Synthetic Systems; Bernard, E.E., Kare, M.R., Eds.; Plenum Press: New York, NY, USA, 1962. [Google Scholar]
- Grubb, P.J. A reassessment of the strategies of plants which cope with shortages of resources. Perspect. Plant Ecol.
**1998**, 1, 3–31. [Google Scholar] [CrossRef] - Wright, I.J.; Reich, P.B.; Westoby, M.; Ackerly, D.D.; Baruch, Z.; Bongers, F.; Cavender-Bares, J.; Chapin, T.; Cornelissen, J.H.C.; Diemer, M.; et al. The worldwide leaf economics spectrum. Nature
**2004**, 428, 821–827. [Google Scholar] [CrossRef] - Pan, S.; Liu, C.; Zhang, W.P.; Xu, S.S.; Wang, N.; Lin, Y.; Gao, J.; Wang, Y. The scaling relationships between leaf mass and leaf area of vascular plant species change with altitude. PLoS ONE
**2013**, 8, e76872. [Google Scholar] [CrossRef] - Huang, W.W.; Su, X.F.; Ratkowsky, D.A.; Niklas, K.J.; Gielis, J.; Shi, P.J. The scaling relationships of leaf biomass vs. leaf surface area of 12 bamboo species. Glob. Ecol. Conserv.
**2019**, 20, e00793. [Google Scholar] [CrossRef] - Klingenberg, C.P.; Barluenga, M.; Meyer, A. Shape analysis of symmetric structures: Quantifying variation among individuals and asymmetry. Evolution
**2002**, 56, 1909–1920. [Google Scholar] [CrossRef] [PubMed] - Wang, P.; Ratkowsky, D.A.; Xiao, X.; Yu, X.J.; Su, J.L.; Zhang, L.F.; Shi, P.J. Taylor’s power law for leaf bilateral symmetry. Forests
**2018**, 9, 500. [Google Scholar] [CrossRef] - Leigh, A.; Zwieniecki, M.A.; Rockwell, F.E.; Boyce, C.K.; Nicotra, A.B.; Holbrook, N.M. Structural and hydraulic correlates of heterophylly in Ginkgo biloba. New Phytol.
**2011**, 189, 459–470. [Google Scholar] [CrossRef] [PubMed] - Editorial Board of Flora of China, Chinese Academy of Sciences. Flora of China; Science Press: Beijing, China, 1993. [Google Scholar]
- Niklas, K.J.; Christianson, M.L. Differences in the scaling of area and mass of Ginkgo biloba (Ginkgoaceae) leaves and their relevance to the study of specific leaf area. Am. J. Bot.
**2011**, 98, 1381–1386. [Google Scholar] [CrossRef] - Poorter, H.; Niinemets, Ü.; Poorter, L.; Wright, I.J.; Villar, R. Causes and consequences of variation in leaf mass per area (LMA): A meta-analysis. New Phytol.
**2009**, 182, 565–588. [Google Scholar] [CrossRef] [PubMed] - Shi, P.J.; Huang, J.G.; Hui, C.; Grissino-Mayer, H.D.; Tardif, J.C.; Zhai, L.H.; Wang, F.S.; Li, B.L. Capturing spiral radial growth of conifers using the superellipse to model tree-ring geometric shape. Front. Plant Sci.
**2015**, 6, 856. [Google Scholar] [CrossRef] [Green Version] - Shi, P.J.; Ratkowsky, D.A.; Li, Y.; Zhang, L.F.; Lin, S.Y.; Gielis, J. A general leaf area geometric formula exists for plants-evidence from the simplified Gielis equation. Forests
**2018**, 9, 714. [Google Scholar] [CrossRef] - R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2015; Available online: http://www.R-project.org (accessed on 17 April 2018).
- Su, J.L.; Niklas, K.J.; Huang, W.W.; Yu, X.J.; Yang, Y.Y.; Shi, P.J. Lamina shape does not correlate with lamina surface area: An analysis based on the simplified Gielis equation. Glob. Ecol. Conserv.
**2019**, 19, e00666. [Google Scholar] [CrossRef] - Milla, R.; Reich, P.B. The scaling of leaf area and mass: The cost of light interception increases with leaf size. Proc. R. Soc. B Biol. Sci.
**2007**, 274, 2109–2114. [Google Scholar] [CrossRef] - Montgomery, E.G. Correlation Studies in Corn; Annual Report No. 24.; Agricultural Experimental Station: Lincoln, NB, USA, 1911. [Google Scholar]
- Shi, P.J.; Liu, M.D.; Yu, X.J.; Gielis, J.; Ratkowsky, D.A. Proportional relationship between leaf area and the product of leaf length and width of four types of special leaf shapes. Forests
**2019**, 10, 178. [Google Scholar] [CrossRef] - Smith, R.J. Used and misuse of the reduced major axis for line-fitting. Am. J. Phys. Anthropol.
**2009**, 140, 476–786. [Google Scholar] [CrossRef] [PubMed] - Hsu, J.C. Multiple Comparisons: Theory and Methods; Chapman and Hall/CRC: New York, NY, USA, 1996. [Google Scholar]
- Lin, S.Y.; Shao, L.J.; Hui, C.; Song, Y.; Reddy, G.V.P.; Gielis, J.; Li, F.; Ding, Y.L.; Wei, Q.; Shi, P.J. Why does not the leaf weight-area allometry of bamboos follow the 3/2-power law? Front. Plant Sci.
**2018**, 9, 583. [Google Scholar] [CrossRef] [PubMed] - Shi, P.J.; Liu, M.D.; Ratkowsky, D.A.; Gielis, J.; Su, J.L.; Yu, X.J.; Wang, P.; Zhang, L.F.; Lin, Z.Y.; Schrader, J. Leaf area-length allometry and its implications in leaf-shape evolution. Trees
**2019**, 33, 1073–1085. [Google Scholar] [CrossRef] - Hughes, A.P.; Cockshull, K.E.; Heath, O.V.S. Leaf area and absolute water content. Ann. Bot.
**1970**, 34, 259–266. [Google Scholar] [CrossRef] - Witkowski, E.T.F.; Lamont, B.B. Leaf specific mass confounds leaf density and thickness. Oecologia
**1991**, 88, 486–493. [Google Scholar] [CrossRef] [PubMed] - Boardman, N.K. Comparative photosynthesis of sun and shade plants. Annu. Rev. Plant Physiol.
**1977**, 28, 355–377. [Google Scholar] [CrossRef] - Ostman, N.L.; Weaver, G.T. Autumnal nutrient transfers by retranslocation, leaching, and litter fall in a chestnut oak forest in southern Illinois. Can. J. For. Res.
**1982**, 12, 40–51. [Google Scholar] [CrossRef] - Küppers, M. Ecological significance of above-ground architectural patterns in woody plants: A question of cost-benefit relationships. Trends Ecol. Evol.
**1989**, 4, 375–379. [Google Scholar] [CrossRef] - Sumida, A.; Komiyama, A. Crown spread patterns for five deciduous broad-leaved woody species ecological significance of the retention patterns of larger branches. Ann. Bot.
**1997**, 80, 759–766. [Google Scholar] [CrossRef] - Sumida, A.; Terazawa, I.; Togashi, A.; Komiyama, A. Spatial arrangement of branches in relation to slope and neighbourhood competition. Ann. Bot.
**2002**, 89, 301–310. [Google Scholar] [CrossRef] [PubMed] - Wierman, C.A.; Oliver, C.D. Crown stratification by species in even-aged mixed stands of Douglas-fir-western hemlock. Can. J. For. Res.
**1979**, 9, 1–9. [Google Scholar] [CrossRef] - Kuuluvainen, T. Tree architectures adapted to efficient light utilization: Is there a basis for latitudinal gradients? Oikos
**1992**, 65, 275–284. [Google Scholar] [CrossRef] - Clatterbuck, W.K.; Hodges, J.D. Development of cherrybark oak and sweet gum in mixed, even-aged bottomland stands in central Mississippi, U.S.A. Can. J. For. Res.
**1988**, 18, 12–18. [Google Scholar] [CrossRef] - Itô, H.; Sumida, A.; Isagi, Y.; Kamo, K. The crown shape of an evergreen oak, Quercus glauca, in a hardwood community. J. For. Res.
**1997**, 2, 85–88. [Google Scholar] [CrossRef] - Wu, J. Landscape Ecology: Pattern, Process, Scale and Hierarchy, 2nd ed.; Higher Education Press: Beijing, China, 2007. [Google Scholar]

**Figure 1.**Leaf examples of 12 Rosaceae species. The examples of Potentilla indica (Andrews) T. Wolf, Rosa multiflora Thunb., and Rubus hirsutus Thunb. are actually leaflets of the compound leaves.

**Figure 2.**Illustration of the measure of bilateral symmetry for a blade of P. lannesiana. The leaf base is on the left, and the leaf apex is on the right. The upper part above the symmetry axis is defined as the left side of the blade, and the lower part is defined as the right side of the blade.

**Figure 3.**Comparisons of leaf functional traits among the 12 Rosaceae species including (

**A**) leaf area, (

**B**) leaf dry weight, and (

**C**) leaf dry mass per unit area (LMA). In each panel, the same letters represent non-significant difference, whereas different letters represents significant difference.

**Figure 4.**Fitted allometric relationship between leaf dry weight and area for the 12 Rosaceae species. Panels

**A**to

**L**represent the studied 12 Rosaceae species. For each panel, y represents ln(leaf dry weight), x represents ln(leaf area), 95% CI represents the 95% confidence interval of the slope, R

^{2}is the coefficient of determination that is used to measure the goodness of fit of a linear fit. The open circles represent the observations, and the red straight line is the regression line.

**Figure 5.**Comparisons of three leaf measures among the 12 Rosaceae species including (

**A**) leaf width, (

**B**) leaf length, and (

**C**) ratio of leaf width to length. In each panel, the same letters represent non-significant difference, whereas different letters represents significant difference.

**Figure 6.**Comparison of areal ratio of the left to the right side for the 12 Rosaceae species. In the panel, the same letters represent non-significant difference.

**Figure 7.**Fitted scaling relationship between the ratios of leaf perimeter to area (RPA) and leaf area for the 12 Rosaceae species. Panels

**A**to

**L**represent the studied 12 Rosaceae species. For each panel, y represents ln(ratio of leaf perimeter to leaf area), x represents ln(leaf area), 95% CI represents the 95% confidence interval of the slope, R

^{2}is the coefficient of determination that is used to measure the goodness of fit of a linear fit. The open circles represent the observations, and the red straight line is the regression line.

**Table 1.**Leaf collection information (including the Latin names, sampling times, sampling locations, and numbers of leaves sampled of 12 Rosaceae species). All leaves were collected on the Nanjing Forestry University campus.

Species Code | Latin Name | Sampling Time | Sampling Location | Sample Size |
---|---|---|---|---|

1 | Prunus persica Stokes | 22 April, 2018 | (32°04′44″N, 118°48′25″ E) | 308 |

2 | Prunus lannesiana E.H. Wilson | 30 April, 2018 | (32°04′50″ N, 118°48′39″ E) | 326 |

3 | Prunus yedoensis Matsum. | 26 April, 2018 | (32°04′49″ N, 118°48′29″ E) | 320 |

4 | Pseudocydonia sinensis C.K. Schneid. | 11 May, 2018 | (32°04′46″ N, 118°48′25″ E) | 316 |

5 | Potentilla indica (Andrews) T. Wolf | 9 May, 2018 | (32°05′03″ N, 118°48′45″ E) | 324 |

6 | Kerria japonica (L.) DC. | 29 April, 2018 | (32°04′46″ N, 118°48′33″ E) | 323 |

7 | Malus halliana Koehne | 26 April, 2018 | (32°05′03″ N, 118°48′47″ E) | 326 |

8 | Photinia serratifolia (Desf.) Kalkman | 2 May, 2018 | (32°04′49″ N, 118°48′40″ E) | 320 |

9 | Prunus cerasifera Ehrhar f. atropurpurea (Jacq.) Rehd. | 28 April, 2018 | (32°04′44″ N, 118°48′26″ E) | 323 |

10 | Pyrus calleryana Decne. | 3 July, 2018 | (32°04′44″ N, 118°48′26″ E) | 320 |

11 | Rosa multiflora Thunb. | 27 April, 2018 | (32°04′50″ N, 118°48′50″ E) | 327 |

12 | Rubus hirsutus Thunb. | 4 May, 2018 | (32°05′03″ N, 118°48′45″ E) | 324 |

**Table 2.**Estimates and standard deviations (SD) of proportionality, as well as the goodness-of-fit (R

^{2}), for the proportional (i.e., isometric) relationship between leaf length and width for 12 Rosaceae species.

Data Set | Estimate | SD | R^{2} |
---|---|---|---|

1 | 0.4012 | 0.0022 | 0.9907 |

2 | 0.5548 | 0.0033 | 0.9884 |

3 | 0.5995 | 0.0043 | 0.9836 |

4 | 0.6505 | 0.0053 | 0.9796 |

5 | 0.6332 | 0.0032 | 0.9920 |

6 | 0.5261 | 0.0039 | 0.9825 |

7 | 0.4638 | 0.0028 | 0.9885 |

8 | 0.3800 | 0.0022 | 0.9897 |

9 | 0.5724 | 0.0030 | 0.9912 |

10 | 0.6623 | 0.0044 | 0.9861 |

11 | 0.6940 | 0.0042 | 0.9884 |

12 | 0.5165 | 0.0029 | 0.9898 |

**Table 3.**Correlation coefficient (r) between the left to right side leaf surface area ratio (AR), leaf surface area of 12 Rosaceae species, and the coefficients of variation (CV) in leaf area for these species (%). Notes: P > 0.05 indicates that the correlation coefficient between AR and leaf surface area is not significantly different from 0; P < 0.05 indicates that the correlation coefficient between the two variables is significantly different from 0.

Data Set | r | P | CV in Leaf Area (%) |
---|---|---|---|

1 | −0.0166 | 0.7718 | 36.13 |

2 | −0.0344 | 0.5365 | 30.54 |

3 | 0.0765 | 0.1722 | 34.68 |

4 | 0.1171 | 0.0376 | 44.93 |

5 | 0.0495 | 0.3742 | 30.35 |

6 | 0.0786 | 0.1586 | 26.51 |

7 | −0.0617 | 0.2662 | 30.69 |

8 | 0.0702 | 0.2102 | 32.73 |

9 | −0.0133 | 0.8116 | 29.14 |

10 | 0.0404 | 0.4718 | 50.51 |

11 | 0.0508 | 0.3601 | 28.45 |

12 | 0.0254 | 0.6480 | 29.62 |

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**MDPI and ACS Style**

Yu, X.; Hui, C.; Sandhu, H.S.; Lin, Z.; Shi, P.
Scaling Relationships between Leaf Shape and Area of 12 Rosaceae Species. *Symmetry* **2019**, *11*, 1255.
https://doi.org/10.3390/sym11101255

**AMA Style**

Yu X, Hui C, Sandhu HS, Lin Z, Shi P.
Scaling Relationships between Leaf Shape and Area of 12 Rosaceae Species. *Symmetry*. 2019; 11(10):1255.
https://doi.org/10.3390/sym11101255

**Chicago/Turabian Style**

Yu, Xiaojing, Cang Hui, Hardev S. Sandhu, Zhiyi Lin, and Peijian Shi.
2019. "Scaling Relationships between Leaf Shape and Area of 12 Rosaceae Species" *Symmetry* 11, no. 10: 1255.
https://doi.org/10.3390/sym11101255