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	Author	Shi, P.; Gielis, J.; Niklas, K.J.
	Title	Comparison of a universal (but complex) model for avian egg shape with a simpler model			Type	Editorial
	Year	2022	Publication	Annals of the New York Academy of Sciences	Abbreviated Journal	Ann Ny Acad Sci
	Volume	1514	Issue	1	Pages	34-42
	Keywords	Editorial; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Recently, a universal equation by Narushin, Romanov, and Griffin (hereafter, the NRGE) was proposed to describe the shape of avian eggs. While NRGE can simulate the shape of spherical, ellipsoidal, ovoidal, and pyriform eggs, its predictions were not tested against actual data. Here, we tested the validity of the NRGE by fitting actual data of egg shapes and compared this with the predictions of our simpler model for egg shape (hereafter, the SGE). The eggs of nine bird species were sampled for this purpose. NRGE was found to fit the empirical data of egg shape well, but it did not define the egg length axis (i.e., the rotational symmetric axis), which significantly affected the prediction accuracy. The egg length axis under the NRGE is defined as the maximum distance between two points on the scanned perimeter of the egg's shape. In contrast, the SGE fitted the empirical data better, and had a smaller root-mean-square error than the NRGE for each of the nine eggs. Based on its mathematical simplicity and goodness-of-fit, the SGE appears to be a reliable and useful model for describing egg shape.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000803394100001	Publication Date	2022-06-01
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0077-8923; 1749-6632	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	5.2	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 5.2
	Call Number	UA @ admin @ c:irua:188470			Serial	7139
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	Author	Shi, P.; Yu, K.; Niinemets, Ü.; Gielis, J.
	Title	Can leaf shape be represented by the ratio of leaf width to length? Evidence from nine species of Magnolia and Michelia (Magnoliaceae)			Type	A1 Journal article
	Year	2021	Publication	Forests	Abbreviated Journal	Forests
	Volume	12	Issue	1	Pages	41
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Leaf shape is closely related to economics of leaf support and leaf functions, including light interception, water use, and CO2 uptake, so correct quantification of leaf shape is helpful for studies of leaf structure/function relationships. There are some extant indices for quantifying leaf shape, including the leaf width/length ratio (W/L), leaf shape fractal dimension (FD), leaf dissection index, leaf roundness index, standardized bilateral symmetrical index, etc. W/L ratio is the simplest to calculate, and recent studies have shown the importance of the W/L ratio in explaining the scaling exponent of leaf dry mass vs. leaf surface area and that of leaf surface area vs. leaf length. Nevertheless, whether the W/L ratio could reflect sufficient geometrical information of leaf shape has been not tested. The FD might be the most accurate measure for the complexity of leaf shape because it can characterize the extent of the self-similarity and other planar geometrical features of leaf shape. However, it is unknown how strongly different indices of leaf shape complexity correlate with each other, especially whether W/L ratio and FD are highly correlated. In this study, the leaves of nine Magnoliaceae species (>140 leaves for each species) were chosen for the study. We calculated the FD value for each leaf using the box-counting approach, and measured leaf fresh mass, surface area, perimeter, length, and width. We found that FD is significantly correlated to the W/L ratio and leaf length. However, the correlation between FD and the W/L ratio was far stronger than that between FD and leaf length for each of the nine species. There were no strong correlations between FD and other leaf characteristics, including leaf area, ratio of leaf perimeter to area, fresh mass, ratio of leaf fresh mass to area, and leaf roundness index. Given the strong correlation between FD and W/L, we suggest that the simpler index, W/L ratio, can provide sufficient information of leaf shape for similarly-shaped leaves. Future studies are needed to characterize the relationships among FD and W/L in leaves with strongly varying shape, e.g., in highly dissected leaves.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000611074700001	Publication Date	2020-12-31
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1999-4907	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	1.951	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 1.951
	Call Number	UA @ admin @ c:irua:174473			Serial	7572
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	Author	Tian, F.; Wang, Y.; Sandhu, H.S.; Gielis, J.; Shi, P.
	Title	Comparison of seed morphology of two ginkgo cultivars			Type	A1 Journal article
	Year	2020	Publication	Journal Of Forestry Research	Abbreviated Journal	J Forestry Res
	Volume	31	Issue	3	Pages	751-758
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Ginkgo biloba L. is a precious relic tree species with important economic value. Seeds, as a vital reproductive organ of plants, can be used to distinguish cultivars of the species. We chose 400 seeds from two cultivars of ginkgo (Fozhi and Maling; 200 seeds for each cultivar) as the study material and used the Gielis equation to fit the projected shape of these seeds. The coefficients of variation (CV) in root mean squared errors (RMSE) obtained from the fitted data were used to compare the level of inter-cultivar variations in seed shape. We also used the covariance analysis to compare the allometric relationships between seed weights and projected areas of these two cultivars. The Gielis equation fitted well the seed shapes of two ginkgo cultivars. The lower CV in RMSE of cultivar Fozhi than Maling indicated a less symmetrical seed shape in the latter than the former. The bootstrap percentile method showed that the seed shape differences between the two cultivars were significant. However, there was no significant difference in the exponents between the seed weights and the projected areas of these two cultivars. Overall, the significant differences in shapes between the seeds of two ginkgo cultivars were well explained by the Gielis equation; this model can be further extended to compare morphological differences in other ginkgo cultivars, and even for plant seeds or animal eggs that have similar oval shapes.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000529367600005	Publication Date	2018-07-28
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1007-662x	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	3	Times cited	3	Open Access
	Notes	; ;			Approved	Most recent IF: 3; 2020 IF: 0.774
	Call Number	UA @ admin @ c:irua:154987			Serial	6474
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	Author	Li, Y.; Niklas, K.J.; Gielis, J.; Niinemets, Ü.; Schrader, J.; Wang, R.; Shi, P.
	Title	An elliptical blade is not a true ellipse, but a superellipse : evidence from two Michelia species			Type	A1 Journal article
	Year	2022	Publication	Journal of forestry research	Abbreviated Journal	J Forestry Res
	Volume	33	Issue	4	Pages	1341-1348
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The shape of leaf laminae exhibits considerable diversity and complexity that reflects adaptations to environmental factors such as ambient light and precipitation as well as phyletic legacy. Many leaves appear to be elliptical which may represent a ‘default’ developmental condition. However, whether their geometry truly conforms to the ellipse equation (EE), i.e., (x/a)2 + (y/b)2 = 1, remains conjectural. One alternative is described by the superellipse equation (SE), a generalized version of EE, i.e., \|x/a\|n +\|y/b\|n = 1. To test the efficacy of EE versus SE to describe leaf geometry, the leaf shapes of two Michelia species (i.e., M. cavaleriei var. platypetala, and M. maudiae), were investigated using 60 leaves from each species. Analysis shows that the majority of leaves (118 out of 120) had adjusted root-mean-square errors of < 0.05 for the nonlinear fitting of SE to leaf geometry, i.e., the mean absolute deviation from the polar point to leaf marginal points was smaller than 5% of the radius of a hypothesized circle with its area equaling leaf area. The estimates of n for the two species were ˂ 2, indicating that all sampled leaves conformed to SE and not to EE. This study confirms the existence of SE in leaves, linking this to its potential functional advantages, particularly the possible influence of leaf shape on hydraulic conductance.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000695118600001	Publication Date	2021-09-12
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1007-662x; 1993-0607	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	3	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 3
	Call Number	UA @ admin @ c:irua:180967			Serial	7152
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	Author	Li, Y.; Quinn, B.K.; Niinemets, Ü.; Schrader, J.; Gielis, J.; Liu, M.; Shi, P.
	Title	Ellipticalness index : a simple measure of the complexity of oval leaf shape			Type	A1 Journal article
	Year	2022	Publication	Pakistan journal of botany : An official publication of pakistan botanical society	Abbreviated Journal	Pak J Bot
	Volume	54	Issue	6	Pages	1-8
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Plants have diverse leaf shapes that have evolved to adapt to the environments they have experienced over their evolutionary history. Leaf shape and leaf size can greatly influence the growth rate, competitive ability, and productivity of plants. However, researchers have long struggled to decide how to properly quantify the complexity of leaf shape. Prior studies recommended the leaf roundness index (RI = 4πA/P2) or dissection index (DI = ), where P is leaf perimeter and A is leaf area. However, these two indices merely measure the extent of the deviation of leaf shape from a circle, which is usually invalid as leaves are seldom circular. In this study, we proposed a simple measure, named the ellipticalness index (EI), for quantifying the complexity of leaf shape based on the hypothesis that the shape of any oval leaf can be regarded as a variation from a standard ellipse. 2220 leaves from nine species of Magnoliaceae were sampled to check the validity of the EI. We also tested the validity of the Montgomery equation (ME), which assumes a proportional relationship between leaf area and the product of leaf length and width, because the EI actually comes from the proportionality coefficient of the ME. We also compared the ME with five other models of leaf area. The ME was found to be the best model for calculating leaf area based on consideration of the trade-off between model fit vs. complexity, which strongly supported the robustness of the EI for describing oval leaf shape. The new index can account for both leaf shape and size, and we conclude that it is a promising method for quantifying and comparing oval leaf shapes across species in future studies.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000814279700028	Publication Date	2022-05-23
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0556-3321	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	1.2	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 1.2
	Call Number	UA @ admin @ c:irua:188469			Serial	7153
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	Author	Gielis, J.
	Title	Double helix of phyllotaxis : analysis of the geometric model of plant morphogenesis, by Boris Rozin			Type	Review
	Year	2021	Publication	Quarterly Review Of Biology	Abbreviated Journal	Q Rev Biol
	Volume	96	Issue	2	Pages	139-140
	Keywords	Review; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2021-05-19
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0033-5770; 1539-7718	ISBN		Additional Links	UA library record
	Impact Factor	4.25	Times cited		Open Access	Not_Open_Access
	Notes				Approved	Most recent IF: 4.25
	Call Number	UA @ admin @ c:irua:178829			Serial	7824
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	Author	Shi, P.; Ratkowsky, D.A.; Gielis, J.
	Title	The generalized Gielis geometric equation and its application			Type	A1 Journal article
	Year	2020	Publication	Symmetry-Basel	Abbreviated Journal	Symmetry-Basel
	Volume	12	Issue	4	Pages	645-10
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Many natural shapes exhibit surprising symmetry and can be described by the Gielis equation, which has several classical geometric equations (for example, the circle, ellipse and superellipse) as special cases. However, the original Gielis equation cannot reflect some diverse shapes due to limitations of its power-law hypothesis. In the present study, we propose a generalized version by introducing a link function. Thus, the original Gielis equation can be deemed to be a special case of the generalized Gielis equation (GGE) with a power-law link function. The link function can be based on the morphological features of different objects so that the GGE is more flexible in fitting the data of the shape than its original version. The GGE is shown to be valid in depicting the shapes of some starfish and plant leaves.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000540222200156	Publication Date	2020-04-21
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2073-8994	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	2.7	Times cited	4	Open Access
	Notes	; This research was funded by the Jiangsu Government Scholarship for Overseas Studies (grant number: JS-2018-038). ;			Approved	Most recent IF: 2.7; 2020 IF: 1.457
	Call Number	UA @ admin @ c:irua:168141			Serial	6526
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	Author	Li, Y.; Quinn, B.K.; Gielis, J.; Li, Y.; Shi, P.
	Title	Evidence that supertriangles exist in nature from the vertical projections of Koelreuteria paniculata fruit			Type	A1 Journal article
	Year	2022	Publication	Symmetry	Abbreviated Journal	Symmetry-Basel
	Volume	14	Issue	1	Pages	23
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Many natural radial symmetrical shapes (e.g., sea stars) follow the Gielis equation (GE) or its twin equation (TGE). A supertriangle (three triangles arranged around a central polygon) represents such a shape, but no study has tested whether natural shapes can be represented as/are supertriangles or whether the GE or TGE can describe their shape. We collected 100 pieces of Koelreuteria paniculata fruit, which have a supertriangular shape, extracted the boundary coordinates for their vertical projections, and then fitted them with the GE and TGE. The adjusted root mean square errors (RMSEadj) of the two equations were always less than 0.08, and >70% were less than 0.05. For 57/100 fruit projections, the GE had a lower RMSEadj than the TGE, although overall differences in the goodness of fit were non-significant. However, the TGE produces more symmetrical shapes than the GE as the two parameters controlling the extent of symmetry in it are approximately equal. This work demonstrates that natural supertriangles exist, validates the use of the GE and TGE to model their shapes, and suggests that different complex radially symmetrical shapes can be generated by the same equation, implying that different types of biological symmetry may result from the same biophysical mechanisms.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000746030100001	Publication Date	2021-12-27
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2073-8994	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	2.7	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 2.7
	Call Number	UA @ admin @ c:irua:186453			Serial	7158
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	Author	Shi, P.; Wang, L.; Quinn, B.K.K.; Gielis, J.
	Title	A new program to estimate the parameters of Preston's equation, a general formula for describing the egg shape of birds			Type	A1 Journal article
	Year	2023	Publication	Symmetry	Abbreviated Journal	Symmetry-Basel
	Volume	15	Issue	1	Pages	231-10
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Preston's equation is a general model describing the egg shape of birds. The parameters of Preston's equation are usually estimated after re-expressing it as the Todd-Smart equation and scaling the egg's actual length to two. This method assumes that the straight line through the two points on an egg's profile separated by the maximum distance (i.e., the longest axis of an egg's profile) is the mid-line. It hypothesizes that the photographed egg's profile is perfectly bilaterally symmetrical, which seldom holds true because of photographic errors and placement errors. The existing parameter estimation method for Preston's equation considers an angle of deviation for the longest axis of an egg's profile from the mid-line, which decreases prediction errors to a certain degree. Nevertheless, this method cannot provide an accurate estimate of the coordinates of the egg's center, and it leads to sub-optimal parameter estimation. Thus, it is better to account for the possible asymmetry between the two sides of an egg's profile along its mid-line when fitting egg-shape data. In this paper, we propose a method based on the optimization algorithm (optimPE) to fit egg-shape data and better estimate the parameters of Preston's equation by automatically searching for the optimal mid-line of an egg's profile and testing its validity using profiles of 59 bird eggs spanning a wide range of existing egg shapes. We further compared this method with the existing one based on multiple linear regression (lmPE). This study demonstrated the ability of the optimPE method to estimate numerical values of the parameters of Preston's equation and provide the theoretical egg length (i.e., the distance between two ends of the mid-line of an egg's profile) and the egg's maximum breadth. This provides a valuable approach for comparing egg shapes among conspecifics or across different species, or even different classes (e.g., birds and reptiles), in future investigations.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000927531000001	Publication Date	2023-01-13
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2073-8994	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	2.7	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 2.7; 2023 IF: 1.457
	Call Number	UA @ admin @ c:irua:195347			Serial	7279
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	Author	Wang, L.; Ratkowsky, D.A.; Gielis, J.; Ricci, P.E.; Shi, P.
	Title	Effects of the numerical values of the parameters in the Gielis equation on its geometries			Type	A1 Journal article
	Year	2022	Publication	Symmetry	Abbreviated Journal	Symmetry-Basel
	Volume	14	Issue	12	Pages	2475-12
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The Lamé curve is an extension of an ellipse, the latter being a special case. Dr. Johan Gielis further extended the Lamé curve in the polar coordinate system by introducing additional parameters (n1, n2, n3; m): rφ=1Acosm4φn2+1Bsinm4φn3−1/n1, which can be applied to model natural geometries. Here, r is the polar radius corresponding to the polar angle φ; A, B, n1, n2 and n3 are parameters to be estimated; m is the positive real number that determines the number of angles of the Gielis curve. Most prior studies on the Gielis equation focused mainly on its applications. However, the Gielis equation can also generate a large number of shapes that are rotationally symmetric and axisymmetric when A = B and n2 = n3, interrelated with the parameter m, with the parameters n1 and n2 determining the shapes of the curves. In this paper, we prove the relationship between m and the rotational symmetry and axial symmetry of the Gielis curve from a theoretical point of view with the condition A = B, n2 = n3. We also set n1 and n2 to take negative real numbers rather than only taking positive real numbers, then classify the curves based on extremal properties of r(φ) at φ = 0, π/m when n1 and n2 are in different intervals, and analyze how n1, n2 precisely affect the shapes of Gielis curves.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000904525700001	Publication Date	2022-11-23
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2073-8994	ISBN		Additional Links	UA library record; WoS full record
	Impact Factor	2.7	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 2.7
	Call Number	UA @ admin @ c:irua:191860			Serial	7301
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	Author	Huang, W.; Li, Y.; Niklas, K.J.; Gielis, J.; Ding, Y.; Cao, L.; Shi, P.
	Title	A superellipse with deformation and its application in describing the cross-sectional shapes of a square bamboo			Type	A1 Journal article
	Year	2020	Publication	Symmetry-Basel	Abbreviated Journal	Symmetry-Basel
	Volume	12	Issue	12	Pages	2073
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Many cross-sectional shapes of plants have been found to approximate a superellipse rather than an ellipse. Square bamboos, belonging to the genus Chimonobambusa (Poaceae), are a group of plants with round-edged square-like culm cross sections. The initial application of superellipses to model these culm cross sections has focused on Chimonobambusa quadrangularis (Franceschi) Makino. However, there is a need for large scale empirical data to confirm this hypothesis. In this study, approximately 750 cross sections from 30 culms of C. utilis were scanned to obtain cross-sectional boundary coordinates. A superellipse exhibits a centrosymmetry, but in nature the cross sections of culms usually deviate from a standard circle, ellipse, or superellipse because of the influences of the environment and terrain, resulting in different bending and torsion forces during growth. Thus, more natural cross-sectional shapes appear to have the form of a deformed superellipse. The superellipse equation with a deformation parameter (SEDP) was used to fit boundary data. We find that the cross-sectional shapes (including outer and inner rings) of C. utilis can be well described by SEDP. The adjusted root-mean-square error of SEDP is smaller than that of the superellipse equation without a deformation parameter. A major finding is that the cross-sectional shapes can be divided into two types of superellipse curves: hyperellipses and hypoellipses, even for cross sections from the same culm. There are two proportional relationships between ring area and the product of ring length and width for both the outer and inner rings. The proportionality coefficients are significantly different, as a consequence of the two different superellipse types (i.e., hyperellipses and hypoellipses). The difference in the proportionality coefficients between hyperellipses and hypoellipses for outer rings is greater than that for inner rings. This work informs our understanding and quantifying of the longitudinal deformation of plant stems for future studies to assess the influences of the environment on stem development. This work is also informative for understanding the deviation of natural shapes from a strict rotational symmetry.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000602546300001	Publication Date	2020-12-15
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2073-8994	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	2.7	Times cited		Open Access
	Notes				Approved	Most recent IF: 2.7; 2020 IF: 1.457
	Call Number	UA @ admin @ c:irua:174472			Serial	8622
Permanent link to this record