eCite Digital Repository

'biogeom': An R package for simulating and fitting natural shapes


Shi, P and Gielis, J and Quinn, BK and Niklas, KJ and Ratkowsky, DA and Schrader, J and Ruan, H and Wang, L and Niinemets, A, 'biogeom': An R package for simulating and fitting natural shapes, Annals of the New York Academy of Sciences pp. 1-12. ISSN 0077-8923 (2022) [Refereed Article]

PDF (Published version)

Copyright Statement

© 2022 The Authors This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY 4.0) License, ( which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

DOI: doi:10.1111/nyas.14862


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.

Item Details

Item Type:Refereed Article
Keywords:boundary coordinates, Gielis equation, ovate leaf shape, sigmoid curve, symmetry
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Biological mathematics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the biological sciences
UTAS Author:Ratkowsky, DA (Dr David Ratkowsky)
ID Code:151594
Year Published:2022
Web of Science® Times Cited:7
Deposited By:TIA - Research Institute
Deposited On:2022-08-02
Last Modified:2022-09-15
Downloads:3 View Download Statistics

Repository Staff Only: item control page