Meng Lian, Peijian Shi, Liuyue Zhang, Weihao Yao, Johan Gielis, Karl J. Niklas
{"title":"A generalized performance equation and its application in measuring the Gini index of leaf size inequality","authors":"Meng Lian, Peijian Shi, Liuyue Zhang, Weihao Yao, Johan Gielis, Karl J. Niklas","doi":"10.1007/s00468-023-02448-8","DOIUrl":null,"url":null,"abstract":"<div><h3>Key message</h3><p>A generalized performance equation is proposed to fit the Lorenz curve of the leaf size distribution of an individual plant and is validated using 12 individual bamboo plants.</p><h3>Abstract</h3><p>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 (<i>r</i><sup>2</sup> = 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.</p></div>","PeriodicalId":805,"journal":{"name":"Trees","volume":"37 5","pages":"1555 - 1565"},"PeriodicalIF":2.1000,"publicationDate":"2023-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Trees","FirstCategoryId":"2","ListUrlMain":"https://link.springer.com/article/10.1007/s00468-023-02448-8","RegionNum":3,"RegionCategory":"农林科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"FORESTRY","Score":null,"Total":0}
引用次数: 2
Key message
A generalized performance equation is proposed to fit the Lorenz curve of the leaf size distribution of an individual plant and is validated using 12 individual bamboo plants.
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.
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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