How to define, use, and interpret Pagel's lambda (lambda) in ecology and evolution

Abstract

1Pagels {lambda} (lambda) is a critical tool in ecology and evolution for describing trait evolution, imputing missing species data, and generalising ecological relationships beyond their study system. Yet the interpretation of {lambda} depends on context, and there are many misconceptions about metrics that are similar but not identical to {lambda}. As an index of phylogenetic signal applied to continuous traits, {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. But this measure is biased by non-random species sampling--a common characteristic of ecological data--which also makes phylogenetic imputation of missing traits challenging. The {lambda} estimated in regression models has little to do with the phylogenetic signal of measured traits and is better considered as either a statistical correction or a measure of the impact of unmeasured (latent) traits in the model. In other contexts, such as hierarchical models including intra-specific variation, {lambda} is frequently confused with distinct metrics such as h2. We show how confusion in defining and using {lambda} can mislead our interpretation of ecological and evolutionary processes. Open research statementNo data were used or collected as part of this work.