How to Define, Use, and Interpret Pagel's λ $$ \lambda $$ (Lambda) in Ecology and Evolution

IF 6.3 1区 环境科学与生态学 Q1 ECOLOGY
William D. Pearse, T. Jonathan Davies, E. M. Wolkovich
{"title":"How to Define, Use, and Interpret Pagel's \n \n \n λ\n \n $$ \\lambda $$\n (Lambda) in Ecology and Evolution","authors":"William D. Pearse,&nbsp;T. Jonathan Davies,&nbsp;E. M. Wolkovich","doi":"10.1111/geb.70012","DOIUrl":null,"url":null,"abstract":"<div>\n \n \n <section>\n \n <h3> Aim</h3>\n \n <p>Pagel's <span></span><math>\n <semantics>\n <mrow>\n <mi>λ</mi>\n </mrow>\n <annotation>$$ \\lambda $$</annotation>\n </semantics></math> (lambda) is a useful tool in ecology and evolution for describing trait evolution, imputing missing species' data, and generalising ecological relationships beyond their study system. Here, we review the various applications and interpretations of <span></span><math>\n <semantics>\n <mrow>\n <mi>λ</mi>\n </mrow>\n <annotation>$$ \\lambda $$</annotation>\n </semantics></math>, highlight common misconceptions, and show how confusion in defining and using <span></span><math>\n <semantics>\n <mrow>\n <mi>λ</mi>\n </mrow>\n <annotation>$$ \\lambda $$</annotation>\n </semantics></math> can mislead our interpretation of ecological and evolutionary processes.</p>\n </section>\n \n <section>\n \n <h3> Innovation</h3>\n \n <p>We highlight that: (1) as an index of phylogenetic signal applied to continuous traits, <span></span><math>\n <semantics>\n <mrow>\n <mi>λ</mi>\n </mrow>\n <annotation>$$ \\lambda $$</annotation>\n </semantics></math> typically (but not always) ranges between 0 and 1, and is a rate-independent measure of the degree to which closely-related species resemble one-another relative to a Brownian motion expectation. (2) <span></span><math>\n <semantics>\n <mrow>\n <mi>λ</mi>\n </mrow>\n <annotation>$$ \\lambda $$</annotation>\n </semantics></math> estimated on incompletely sampled clades assumes random species sampling, which is rarely the case in ecological data sets, and likely has large uncertainty. (3) High <span></span><math>\n <semantics>\n <mrow>\n <mi>λ</mi>\n </mrow>\n <annotation>$$ \\lambda $$</annotation>\n </semantics></math> is a necessary but not sufficient prerequisite for phylogenetic imputation. (4) <span></span><math>\n <semantics>\n <mrow>\n <mi>λ</mi>\n </mrow>\n <annotation>$$ \\lambda $$</annotation>\n </semantics></math> in Phylogenetic Generalised Least Squares (PGLS) models is estimated using model residuals and is not (in most cases) an index of phylogenetic signal of measured traits. (5) New hierarchical methods including intra-specific variation return metrics such as <span></span><math>\n <semantics>\n <mrow>\n <msup>\n <mi>h</mi>\n <mn>2</mn>\n </msup>\n </mrow>\n <annotation>$$ {h}^2 $$</annotation>\n </semantics></math> that are similar but not identical to <span></span><math>\n <semantics>\n <mrow>\n <mi>λ</mi>\n </mrow>\n <annotation>$$ \\lambda $$</annotation>\n </semantics></math>; we show how these disparate approaches can be unified within a single framework.</p>\n </section>\n \n <section>\n \n <h3> Main Conclusions</h3>\n \n <p>Phylogenetic methods are increasingly integrated into ecological and evolutionary analyses. Pagel's <span></span><math>\n <semantics>\n <mrow>\n <mi>λ</mi>\n </mrow>\n <annotation>$$ \\lambda $$</annotation>\n </semantics></math>, a phylogenetic scaling parameter that describes how shared evolutionary history structures species similarities and differences, is commonly used as both a metric of ‘phylogenetic signal’ and as a statistical correction for the evolutionary non-independence of species in phylogenetic comparative analysis. We show how to use <span></span><math>\n <semantics>\n <mrow>\n <mi>λ</mi>\n </mrow>\n <annotation>$$ \\lambda $$</annotation>\n </semantics></math> to resolve these conceptual and statistical discrepancies.</p>\n </section>\n </div>","PeriodicalId":176,"journal":{"name":"Global Ecology and Biogeography","volume":"34 4","pages":""},"PeriodicalIF":6.3000,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/geb.70012","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Global Ecology and Biogeography","FirstCategoryId":"93","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/geb.70012","RegionNum":1,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ECOLOGY","Score":null,"Total":0}
引用次数: 0

Abstract

Aim

Pagel's λ $$ \lambda $$ (lambda) is a useful tool in ecology and evolution for describing trait evolution, imputing missing species' data, and generalising ecological relationships beyond their study system. Here, we review the various applications and interpretations of λ $$ \lambda $$ , highlight common misconceptions, and show how confusion in defining and using λ $$ \lambda $$ can mislead our interpretation of ecological and evolutionary processes.

Innovation

We highlight that: (1) as an index of phylogenetic signal applied to continuous traits, λ $$ \lambda $$ typically (but not always) ranges between 0 and 1, and is a rate-independent measure of the degree to which closely-related species resemble one-another relative to a Brownian motion expectation. (2) λ $$ \lambda $$ estimated on incompletely sampled clades assumes random species sampling, which is rarely the case in ecological data sets, and likely has large uncertainty. (3) High λ $$ \lambda $$ is a necessary but not sufficient prerequisite for phylogenetic imputation. (4) λ $$ \lambda $$ in Phylogenetic Generalised Least Squares (PGLS) models is estimated using model residuals and is not (in most cases) an index of phylogenetic signal of measured traits. (5) New hierarchical methods including intra-specific variation return metrics such as h 2 $$ {h}^2 $$ that are similar but not identical to λ $$ \lambda $$ ; we show how these disparate approaches can be unified within a single framework.

Main Conclusions

Phylogenetic methods are increasingly integrated into ecological and evolutionary analyses. Pagel's λ $$ \lambda $$ , a phylogenetic scaling parameter that describes how shared evolutionary history structures species similarities and differences, is commonly used as both a metric of ‘phylogenetic signal’ and as a statistical correction for the evolutionary non-independence of species in phylogenetic comparative analysis. We show how to use λ $$ \lambda $$ to resolve these conceptual and statistical discrepancies.

Abstract Image

如何在生态学和进化中定义、使用和解释Pagel λ $$ \lambda $$ (Lambda)
Aim Pagel的λ $$ \lambda $$ (lambda)在生态学和进化中是一个有用的工具,用于描述特征进化,输入缺失物种数据,以及概括其研究系统之外的生态关系。在这里,我们回顾了λ $$ \lambda $$的各种应用和解释,强调了常见的误解,并说明在定义和使用λ $$ \lambda $$时的困惑会如何误导我们对生态和进化过程的解释。我们强调:(1)作为应用于连续性状的系统发育信号的指数,λ $$ \lambda $$通常(但并不总是)范围在0到1之间,并且是一个相对于布朗运动期望的密切相关物种彼此相似程度的独立于率的度量。(2)在不完全采样的进化枝上估计的λ $$ \lambda $$假设物种随机采样,这在生态数据集中很少出现,并且可能具有很大的不确定性。(3)高λ $$ \lambda $$是系统发育归算的必要条件,但不是充分条件。(4)系统发育广义最小二乘(PGLS)模型中的λ $$ \lambda $$是使用模型残差估计的,在大多数情况下,λ 不是被测性状的系统发育信号指标。(5)新的分层方法,包括与λ相似但不相同的种内变异回报指标,如h2 $$ {h}^2 $$$$ \lambda $$;我们将展示如何在一个框架内统一这些不同的方法。系统发育方法越来越多地与生态学和进化分析相结合。Pagel的λ $$ \lambda $$是一个系统发育尺度参数,描述了共同的进化历史如何构成物种的相似性和差异,它通常被用作“系统发育信号”的度量标准,也被用作系统发育比较分析中物种进化非独立性的统计校正。我们将展示如何使用λ $$ \lambda $$来解决这些概念上和统计上的差异。
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
Global Ecology and Biogeography
Global Ecology and Biogeography 环境科学-生态学
CiteScore
12.10
自引率
3.10%
发文量
170
审稿时长
3 months
期刊介绍: Global Ecology and Biogeography (GEB) welcomes papers that investigate broad-scale (in space, time and/or taxonomy), general patterns in the organization of ecological systems and assemblages, and the processes that underlie them. In particular, GEB welcomes studies that use macroecological methods, comparative analyses, meta-analyses, reviews, spatial analyses and modelling to arrive at general, conceptual conclusions. Studies in GEB need not be global in spatial extent, but the conclusions and implications of the study must be relevant to ecologists and biogeographers globally, rather than being limited to local areas, or specific taxa. Similarly, GEB is not limited to spatial studies; we are equally interested in the general patterns of nature through time, among taxa (e.g., body sizes, dispersal abilities), through the course of evolution, etc. Further, GEB welcomes papers that investigate general impacts of human activities on ecological systems in accordance with the above criteria.
×
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:604180095
Book学术官方微信