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, T. Jonathan Davies, 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 (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 , highlight common misconceptions, and show how confusion in defining and using can mislead our interpretation of ecological and evolutionary processes.
Innovation
We highlight that: (1) as an index of phylogenetic signal applied to continuous traits, 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) 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 is a necessary but not sufficient prerequisite for phylogenetic imputation. (4) 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 that are similar but not identical to ; 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 , 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 to resolve these conceptual and statistical discrepancies.
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.