{"title":"Ellipse or superellipse for tree-ring geometries? evidence from six conifer species","authors":"Weiwei Huang, Kehang Ma, Daniel K. Gladish","doi":"10.1007/s00468-024-02561-2","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Key message</h3><p>Tree-ring shapes of the six studied coniferous species tend to be bilaterally symmetrical, and the superellipse equation is sufficient to describe the tree-ring boundaries and estimate the basal area increment.</p><h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In nature, under environmental pressures, such as wind, slope, water availability, etc., tree-ring shapes in most cases appear to be elliptical rather than circular. Compared with the ellipse equation, the superellipse equation includes an additional parameter that allows the generation of a larger range of geometries: hypoellipse, ellipse, and hyperellipse. The more complex Gielis equation can generate asymmetrical shapes. In the present study, we modeled the geometries of tree-rings for six coniferous species using the superellipse equation (i.e., the three-parameter model) and the more complex Gielis equation (i.e., the five-parameter model). The species-specific mean value of <i>n</i> approached 2 and the <i>k</i>-value was lower than 1, which confirmed that most tree-ring shapes of the studied coniferous species were closer to an ellipse rather than a circle. However, based on superellipse equation the <i>n</i>-value and <i>k</i>-value both showed an inter-annual fluctuation that ranged between 1.75–2.25 and 0.82–1.00, respectively. This suggests that most samples of tree-rings did not follow the typical ellipse equation, but the superellipse equation. Although the Gielis equation is slightly better in the goodness of fit than the superellipse equation, 86.67% of the percent errors (PEs) of RMSE<sub>adj</sub> between these two equations were smaller than 5%, which means that the superellipse equation is better given the trade-off between the model structural complexity and goodness of fit. Most tree-ring shapes tend to be bilaterally symmetrical, and the three-parameter superellipse equation was verified to fit the tree-ring boundaries and estimate the inter-annual increments of tree-ring area well.</p>","PeriodicalId":805,"journal":{"name":"Trees","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Trees","FirstCategoryId":"2","ListUrlMain":"https://doi.org/10.1007/s00468-024-02561-2","RegionNum":3,"RegionCategory":"农林科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"FORESTRY","Score":null,"Total":0}
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Key message
Tree-ring shapes of the six studied coniferous species tend to be bilaterally symmetrical, and the superellipse equation is sufficient to describe the tree-ring boundaries and estimate the basal area increment.
Abstract
In nature, under environmental pressures, such as wind, slope, water availability, etc., tree-ring shapes in most cases appear to be elliptical rather than circular. Compared with the ellipse equation, the superellipse equation includes an additional parameter that allows the generation of a larger range of geometries: hypoellipse, ellipse, and hyperellipse. The more complex Gielis equation can generate asymmetrical shapes. In the present study, we modeled the geometries of tree-rings for six coniferous species using the superellipse equation (i.e., the three-parameter model) and the more complex Gielis equation (i.e., the five-parameter model). The species-specific mean value of n approached 2 and the k-value was lower than 1, which confirmed that most tree-ring shapes of the studied coniferous species were closer to an ellipse rather than a circle. However, based on superellipse equation the n-value and k-value both showed an inter-annual fluctuation that ranged between 1.75–2.25 and 0.82–1.00, respectively. This suggests that most samples of tree-rings did not follow the typical ellipse equation, but the superellipse equation. Although the Gielis equation is slightly better in the goodness of fit than the superellipse equation, 86.67% of the percent errors (PEs) of RMSEadj between these two equations were smaller than 5%, which means that the superellipse equation is better given the trade-off between the model structural complexity and goodness of fit. Most tree-ring shapes tend to be bilaterally symmetrical, and the three-parameter superellipse equation was verified to fit the tree-ring boundaries and estimate the inter-annual increments of tree-ring area well.
期刊介绍：
Trees - Structure and Function publishes original articles on the physiology, biochemistry, functional anatomy, structure and ecology of trees and other woody plants. Also presented are articles concerned with pathology and technological problems, when they contribute to the basic understanding of structure and function of trees. In addition to original articles and short communications, the journal publishes reviews on selected topics concerning the structure and function of trees.
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