On the mathematical properties of spatial Rao’s Q to compute ecosystem heterogeneity

IF 1.2 4区 环境科学与生态学 Q4 ECOLOGY
Duccio Rocchini, Michele Torresani, Carlo Ricotta
{"title":"On the mathematical properties of spatial Rao’s Q to compute ecosystem heterogeneity","authors":"Duccio Rocchini, Michele Torresani, Carlo Ricotta","doi":"10.1007/s12080-024-00587-3","DOIUrl":null,"url":null,"abstract":"<p>Spatio-ecological heterogeneity has a significant impact on various ecosystem properties, such as biodiversity patterns, variability in ecosystem resources, and species distributions. Given this perspective, remote sensing has gained widespread recognition as a powerful tool for assessing the spatial heterogeneity of ecosystems by analyzing the variability among different pixel values in both space and, potentially, time. Several measures of spatial heterogeneity have been proposed, broadly categorized into abundance-related measures (e.g., Shannon’s H) and dispersion-related measures (e.g., Variance). A measure that integrates both abundance and distance information is the Rao’s quadratic entropy (Rao’s Q index), mainly used in ecology to measure plant diversity based on in-situ based functional traits. The question arises as to why one should use a complex measure that considers multiple dimensions and couples abundance and distance measurements instead of relying solely on simple dispersion-based measures of heterogeneity. This paper sheds light on the spatial version of the Rao’s Q index, based on moving windows for its calculation, with a particular emphasis on its mathematical and statistical properties. The main objective is to theoretically demonstrate the strength of Rao’s Q index in measuring heterogeneity, taking into account all its potential facets and applications, including (i) integrating multivariate data, (ii) applying differential weighting to pixels, and (iii) considering differential weighting of distances among pixel reflectance values in spectral space.</p>","PeriodicalId":51198,"journal":{"name":"Theoretical Ecology","volume":"1 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Ecology","FirstCategoryId":"93","ListUrlMain":"https://doi.org/10.1007/s12080-024-00587-3","RegionNum":4,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECOLOGY","Score":null,"Total":0}
引用次数: 0

Abstract

Spatio-ecological heterogeneity has a significant impact on various ecosystem properties, such as biodiversity patterns, variability in ecosystem resources, and species distributions. Given this perspective, remote sensing has gained widespread recognition as a powerful tool for assessing the spatial heterogeneity of ecosystems by analyzing the variability among different pixel values in both space and, potentially, time. Several measures of spatial heterogeneity have been proposed, broadly categorized into abundance-related measures (e.g., Shannon’s H) and dispersion-related measures (e.g., Variance). A measure that integrates both abundance and distance information is the Rao’s quadratic entropy (Rao’s Q index), mainly used in ecology to measure plant diversity based on in-situ based functional traits. The question arises as to why one should use a complex measure that considers multiple dimensions and couples abundance and distance measurements instead of relying solely on simple dispersion-based measures of heterogeneity. This paper sheds light on the spatial version of the Rao’s Q index, based on moving windows for its calculation, with a particular emphasis on its mathematical and statistical properties. The main objective is to theoretically demonstrate the strength of Rao’s Q index in measuring heterogeneity, taking into account all its potential facets and applications, including (i) integrating multivariate data, (ii) applying differential weighting to pixels, and (iii) considering differential weighting of distances among pixel reflectance values in spectral space.

Abstract Image

论计算生态系统异质性的空间拉奥 Q 的数学特性
空间-生态异质性对生物多样性模式、生态系统资源的变异性和物种分布等各种生态系统特性具有重大影响。有鉴于此,遥感技术通过分析不同像素值在空间和潜在时间上的变异性,已被广泛视为评估生态系统空间异质性的有力工具。目前已提出了几种空间异质性测量方法,大致可分为与丰度相关的测量方法(如香农 H)和与离散度相关的测量方法(如方差)。拉奥二次熵(Rao's Q 指数)是一种综合了丰度和距离信息的测量方法,主要用于生态学中基于原地功能特征的植物多样性测量。由此产生的问题是,为什么要使用一种考虑多个维度并将丰度和距离测量相结合的复杂测量方法,而不是仅仅依靠基于离散度的简单异质性测量方法呢?本文阐明了基于移动窗口计算的空间版拉奥 Q 指数,并特别强调了其数学和统计特性。主要目的是从理论上证明 Rao Q 指数在测量异质性方面的优势,同时考虑到其所有潜在的方面和应用,包括:(i) 整合多元数据,(ii) 对像素进行差分加权,以及 (iii) 考虑对光谱空间中像素反射率值之间的距离进行差分加权。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Theoretical Ecology
Theoretical Ecology 环境科学-生态学
CiteScore
3.30
自引率
6.20%
发文量
23
审稿时长
>12 weeks
期刊介绍: Theoretical Ecology publishes innovative research in theoretical ecology, broadly defined. Papers should use theoretical approaches to answer questions of ecological interest and appeal to and be readable by a broad audience of ecologists. Work that uses mathematical, statistical, computational, or conceptual approaches is all welcomed, provided that the goal is to increase ecological understanding. Papers that only use existing approaches to analyze data, or are only mathematical analyses that do not further ecological understanding, are not appropriate. Work that bridges disciplinary boundaries, such as the intersection between quantitative social sciences and ecology, or physical influences on ecological processes, will also be particularly welcome. All areas of theoretical ecology, including ecophysiology, population ecology, behavioral ecology, evolutionary ecology, ecosystem ecology, community ecology, and ecosystem and landscape ecology are all appropriate. Theoretical papers that focus on applied ecological questions are also of particular interest.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信