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New indices to balanceα-diversity against tree size inequality

Journal of Forestry Research 2024年第1期35卷 229-237页

作者： Li Zhang Brady K.Quinn Cang Hui Meng Lian johan gielis Jie Gao Peijian Shi College of Ecology and Environment Bamboo Research InstituteNanjing Forestry University159 Longpan RoadNanjing 210037People’s Republic of China Fisheries and Oceans Canada Andrews Biological Station125 Marine Science DriveSt.AndrewsNB E5B 0E4Canada Department of Mathematical Sciences Centre for Invasion BiologyStellenbosch UniversityMatieland 7602South Africa Mathematical and Physical Biosciences African Institute for Mathematical SciencesCape Town 7945South Africa Department of Biosciences Engineering University of AntwerpB-2020 AntwerpBelgium College of Life Science Xinjiang Normal University102 Xinyi RoadUrumqi 830054People’s Republic of China

The number and composition of species in a community can be quantified withα-diversity indices,including species richness(R),Simpson’s index(D),and the Shannon-Wiener index(H΄).In forest communities,there are large variations in tree size among species and individu-als of the same species,which result in differences in eco-logical processes and ecosystem functions.However,tree size inequality(TSI)has been largely neglected in studies using the available diversity indices.The TSI in the diameter at breast height(DBH)data for each of 99920 m×20 m forest census quadrats was quantified using the Gini index(GI),a measure of the inequality of size distribution.The generalized performance equation was used to describe the rotated and right-shifted Lorenz curve of the cumulative proportion of DBH and the cumulative proportion of number of trees per quadrat.We also examined the relationships ofα-diversity indices with the GI using correlation tests.The generalized performance equation effectively described the rotated and right-shifted Lorenz curve of DBH distributions,with most root-mean-square errors(990 out of 999 quadrats)being<0.0030.There were significant positive correlations between each of threeα-diversity indices(i.e.,R,D,and H’)and the GI.Nevertheless,the total abundance of trees in each quadrat did not significantly influence the GI.This means that the TSI increased with increasing spe-cies diversity.Thus,two new indices are proposed that can balanceα-diversity against the extent of TSI in the com-munity:(1−GI)×D,and(1−GI)×H’.These new indices were significantly correlated with the original D and H΄,and did not increase the extent of variation within each group of indices.This study presents a useful tool for quantifying both species diversity and the variation in tree sizes in forest communities,especially in the face of cumulative species loss under global climate change.

关键词： Diameter at breast height(DBH) Gini index Shannon-Wiener index Simpson’s index Quadrat Tree size

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An elliptical blade is not a true ellipse,but a superellipse–Evidence from two Michelia species

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Journal of Forestry Research 2022年第4期33卷 1341-1348页

作者： Yuping Li Karl JNiklas johan gielis Ülo Niinemets Julian Schrader Rong Wang Peijian Shi College of Horticulture Jinling Institute of TechnologyNanjing 210038People’s Republic of China Bamboo Research Institute Nanjing Forestry UniversityNanjing 210037People’s Republic of China Plant Biology Section School of Integrative Plant ScienceCornell UniversityIthacaNY 14853USA Department of Biosciences Engineering University of AntwerpB-2020 AntwerpBelgium Institute of Agricultural and Environmental Sciences Estonian University of Life Sciences51006 TartuEstonia Estonian Academy of Sciences 10130 TallinnEstonia Department of Biological Sciences Macquarie UniversitySydneyNSW 2109Australia Biodiversity Macroecology and BiogeographyUniversity of Göttingen37077 GöttingenGermany

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.

关键词： Bilateral symmetry Leaf ellipticalness index Leaf laminae Leaf roundness index Magnoliaceae

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Comparison of seed morphology of two ginkgo cultivars

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Journal of Forestry Research 2020年第3期31卷 751-758页

作者： Fang Tian Yujun Wang Hardev S.Sandhu johan gielis Peijian Shi Co-Innovation Centre for Sustainable Forestry in Southern China Nanjing Forestry UniversityNanjing 210037JiangsuPeople’s Republic of China Everglades Research and Education Center University of Florida3200 E.Palm Beach RoadBelle GladeFL 33430USA Department of Biosciences Engineering University of Antwerp2020 AntwerpBelgium

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 seedshapes 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.

关键词： Allometry Coefficient of variation Curve fitting gielis equation Root mean squared errors

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Spherical Harmonic Solution of the Robin Problem for the Helmholtz Equation in a Supershaped Shell

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Applied Mathematics 2013年第1期4卷 263-270页

作者： Diego Caratelli johan gielis Ilia Tavkhelidze Paolo Emilio Ricci Department of Bioscience Engineering University of Antwerp Antwerp Belgium Faculty of Engineering Campus Bio-Medico University Rome Italy Faculty of Exact and Natural Sciences Tbilisi State University Tbilisi Georgia Microwave Sensing Signals and Systems Delft University of Technology Delft The Netherlands

The Robin problem for the Helmholtz equation in normal-polar shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by a generalized version of the so-called “superformula” introduced by gielis. A dedicated numerical procedure based on the computer algebra system Mathematica? is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.

关键词： Robin Problem Helmholtz Equation Spherical Harmonic Expansion gielis Formula Supershaped Shell

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