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	Author	Lian, M.; Shi, P.; Zhang, L.; Yao, W.; Gielis, J.; Niklas, K.J.
	Title	A generalized performance equation and its application in measuring the Gini index of leaf size inequality			Type	A1 Journal article
	Year	2023	Publication	Trees: structure and function	Abbreviated Journal
	Volume	37	Issue		Pages	1555-1565
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The goal of this study is to provide a rigorous tool to quantify the inequality of the leaf size distribution of an individual plant, thereby serving as a reference trait for quantifying plant adaptations to local environmental conditions. The tool to be presented and tested employs three components: (1) a performance equation (PE), which can produce flexible asymmetrical and symmetrical bell-shaped curves, (2) the Lorenz curve (i.e., the cumulative proportion of leaf size vs. the cumulative proportion of number of leaves), which is the basis for calculating, and (3) the Gini index, which measures the inequality of leaf size distribution. We sampled 12 individual plants of a dwarf bamboo and measured the area and dry mass of each leaf of each plant. We then developed a generalized performance equation (GPE) of which the PE is a special case and fitted the Lorenz curve to leaf size distribution using the GPE and PE. The GPE performed better than the PE in fitting the Lorenz curve. We compared the Gini index of leaf area distribution with that of leaf dry mass distribution and found that there was a significant difference between the two indices that might emerge from the scaling relationship between leaf dry mass and area. Nevertheless, there was a strong correlation between the two Gini indices (r2 = 0.9846). This study provides a promising tool based on the GPE for quantifying the inequality of leaf size distributions across individual plants and can be used to quantify plant adaptations to local environmental conditions.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	001069570200001	Publication Date	2023-08-26
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0931-1890; 1432-2285	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	2.3	Times cited		Open Access	Not_Open_Access: Available from 26.02.2024
	Notes				Approved	Most recent IF: 2.3; 2023 IF: 1.842
	Call Number	UA @ admin @ c:irua:199562			Serial	8874
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	Author	Wang, L.; Shi, P.; Chen, L.; Gielis, J.; Niklas, K.J.
	Title	Evidence that Chinese white olive (Canarium album(Lour.) DC.) fruits are solids of revolution			Type	A1 Journal article
	Year	2023	Publication	Botany letters	Abbreviated Journal
	Volume		Issue		Pages	1-7
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Although many fruit geometries resemble a solid of revolution, this assumption has rarely been rigorously examined. To test this assumption, 574 fruits of Canarium album (Lour.) DC. which appear to have an ellipsoidal shape, were examined to determine the validity of a general avian-based egg-shape equation, referred to as the explicit Preston equation (EPE). The assumption that the C. album fruit geometry is a solid of revolution is tested by applying the volume formula for a solid of revolution using the EPE. The goodness of fit of the EPE was assessed using the adjusted root-mean-square error (RMSEadj). The relationship between the observed volume (Vobs) of each fruit, as measured by water displacement in a graduated cylinder, and the predicted volumes (Vpre) based on the EPE was also evaluated using the equation Vpre = slope * Vobs. All the RMSEadj values were smaller than 0.05, which demonstrated the validity of the EPE based on C. album fruit profiles. The 95% confidence interval of the slope of Vpre vs. Vobs included 1.0, indicating that there was no significant difference between Vpre and Vobs. The data confirm that C. album fruits are solids of revolution. This study provides a new approach for calculating the volume and surface area of geometrically similar fruits, which can be extended to other species with similar fruit geometries to further explore the ontogeny and evolution of angiosperm reproductive organs.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	001033135400001	Publication Date	2023-07-25
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2381-8107; 2381-8115	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	1.5	Times cited		Open Access	Not_Open_Access: Available from 24.01.2024
	Notes				Approved	Most recent IF: 1.5; 2023 IF: NA
	Call Number	UA @ admin @ c:irua:198001			Serial	8864
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	Author	Li, Q.; Niklas, K.J.J.; Niinemets, U.; Zhang, L.; Yu, K.; Gielis, J.; Gao, J.; Shi, P.
	Title	Stomatal shape described by a superellipse in four Magnoliaceae species			Type	A1 Journal article
	Year	2023	Publication	Botany letters	Abbreviated Journal
	Volume		Issue		Pages	1-9
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Stomata are essential for the exchange of water vapour and atmospheric gases between vascular plants and their external environments. The stomatal geometries of many plants appear to be elliptical. However, prior studies have not tested whether this is a mathematical reality, particularly since many natural shapes that appear to be ellipses are superellipses with greater or smaller edge curvature than predicted for an ellipse. Compared with the ellipse equation, the superellipse equation includes an additional parameter that allows generation of a larger range of shapes. We randomly selected 240 stomata from each of four Magnoliaceae species to test whether the stomatal geometries are superellipses or ellipses. The stomatal geometries for most stomata (943/960) were found to be described better using the superellipse equation. The traditional “elliptical stomata hypothesis” resulted in an underestimation of the area of stomata, whereas the superellipse equation accurately predicted stomatal area. This finding has important implications for the estimation of stomatal area in studies looking at stomatal shape, geometry, and function.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	001024190300001	Publication Date	2023-07-12
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2381-8107; 2381-8115	ISBN		Additional Links	UA library record; WoS full record
	Impact Factor	1.5	Times cited		Open Access	Not_Open_Access: Available from 12.01.2024
	Notes				Approved	Most recent IF: 1.5; 2023 IF: NA
	Call Number	UA @ admin @ c:irua:197847			Serial	8935
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	Author	Shi, P.; Chen, L.; Quinn, B.K.; Yu, K.; Miao, Q.; Guo, X.; Lian, M.; Gielis, J.; Niklas, K.J.
	Title	A simple way to calculate the volume and surface area of avian eggs			Type	A1 Journal article
	Year	2023	Publication	Annals of the New York Academy of Sciences	Abbreviated Journal
	Volume	1524	Issue	1	Pages	118-131
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Egg geometry can be described using Preston's equation, which has seldom been used to calculate egg volume (V) and surface area (S) to explore S versus V scaling relationships. Herein, we provide an explicit re-expression of Preston's equation (designated as EPE) to calculate V and S, assuming that an egg is a solid of revolution. The side (longitudinal) profiles of 2221 eggs of six avian species were digitized, and the EPE was used to describe each egg profile. The volumes of 486 eggs from two avian species predicted by the EPE were compared with those obtained using water displacement in graduated cylinders. There was no significant difference in V using the two methods, which verified the utility of the EPE and the hypothesis that eggs are solids of revolution. The data also indicated that V is proportional to the product of egg length (L) and maximum width (W) squared. A 2/3-power scaling relationship between S and V for each species was observed, that is, S is proportional to (LW2)(2/3). These results can be extended to describe the shapes of the eggs of other species to study the evolution of avian (and perhaps reptilian) eggs.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000975679400001	Publication Date	2023-04-28
	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; 2023 IF: 4.706
	Call Number	UA @ admin @ c:irua:196724			Serial	8827
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	Author	Shi, P.; Gielis, J.; Niklas, K.J.; Niinemets, Ü.; Schrader, J.
	Title	Leaf functional traits : ecological and evolutionary implications			Type	ME3 Book as editor
	Year	2023	Publication		Abbreviated Journal
	Volume		Issue		Pages	185 p.
	Keywords	ME3 Book as editor; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2023-04-14
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN	978-2-8325-2086-4; 1664-8714	Additional Links	UA library record
	Impact Factor		Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:198002			Serial	8894
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	Author	Niklas, K.J.; Shi, P.; Gielis, J.; Schrader, J.; Niinemets, U.
	Title	Editorial: leaf functional traits : ecological and evolutionary implications			Type	Editorial
	Year	2023	Publication	Frontiers in plant science	Abbreviated Journal
	Volume	14	Issue		Pages	1169558-5
	Keywords	Editorial; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000964122500001	Publication Date	2023-03-21
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1664-462x	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	5.6	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 5.6; 2023 IF: 4.298
	Call Number	UA @ admin @ c:irua:196076			Serial	7834
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	Author	Shi, P.; Gielis, J.; Quinn, B.K.; Niklas, K.J.; Ratkowsky, D.A.; Schrader, J.; Ruan, H.; Wang, L.; Niinemets, Ü.; Niinennets, U.
	Title	‘biogeom’ : an R package for simulating and fitting natural shapes			Type	A1 Journal article
	Year	2022	Publication	Annals of the New York Academy of Sciences	Abbreviated Journal	Ann Ny Acad Sci
	Volume	1516	Issue	1	Pages	123-134
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Many natural objects exhibit radial or axial symmetry in a single plane. However, a universal tool for simulating and fitting the shapes of such objects is lacking. Herein, we present an R package called 'biogeom' that simulates and fits many shapes found in nature. The package incorporates novel universal parametric equations that generate the profiles of bird eggs, flowers, linear and lanceolate leaves, seeds, starfish, and tree-rings, and three growth-rate equations that generate the profiles of ovate leaves and the ontogenetic growth curves of animals and plants. 'biogeom' includes several empirical datasets comprising the boundary coordinates of bird eggs, fruits, lanceolate and ovate leaves, tree rings, seeds, and sea stars. The package can also be applied to other kinds of natural shapes similar to those in the datasets. In addition, the package includes sigmoid curves derived from the three growth-rate equations, which can be used to model animal and plant growth trajectories and predict the times associated with maximum growth rate. 'biogeom' can quantify the intra- or interspecific similarity of natural outlines, and it provides quantitative information of shape and ontogenetic modification of shape with important ecological and evolutionary implications for the growth and form of the living world.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000829772300001	Publication Date	2022-07-26
	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:189314			Serial	7131
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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	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	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
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	Author	Huang, W.; Su, X.; Ratkowsky, D.A.; Niklas, K.J.; Gielis, J.; Shi, P.
	Title	The scaling relationships of leaf biomass vs. leaf surface area of 12 bamboo species			Type	A1 Journal article
	Year	2019	Publication	Global ecology and conservation	Abbreviated Journal
	Volume	20	Issue		Pages	e00793
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	There is convincing evidence for a scaling relationship between leaf dry weight (DW) and leaf surface area (A) for broad-leaved plants, and most estimates of the scaling exponent of DW vs. A are greater than unity. However, the scaling relationship of leaf fresh weight (FW) vs. A has been largely neglected. In the present study, we examined whether there is a statistically strong scaling relationship between FW and A and compared the goodness of fit to that of DW vs. A. Between 250 and 520 leaves from each of 12 bamboo species within 2 genera (Phyllostachys and Pleioblastus) were investigated. The reduced major axis regression protocols were used to determine scaling relationships. The fit for the linearized scaling relationship of FW vs. A was compared with that of DW vs. A using the coefficient of determination (i.e., r2). A stronger scaling relationship between FW and A than that between DW and A was observed for each of the 12 bamboo species investigated. Among the 12 species examined, five had significantly smaller scaling exponents of FW vs. A compared to those of DW vs. A; only one species had a scaling exponent of FW vs. A greater than that of DW vs. A. No significant difference between the two scaling exponents was observed for the remaining 6 species. Researchers conducting future studies might be well advised to consider the influence of leaf fresh weight when exploring the scaling relationships of foliar biomass allocation patterns.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000498226800095	Publication Date	2019-09-19
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2351-9894; 2351-9894	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:162954			Serial	8497
Permanent link to this record