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

William D. Pearse,T. J. Davies,E. Wolkovich

Published 2023 in bioRxiv

ABSTRACT

Pagel’s λ (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 λ depends on context, and there are many misconceptions about metrics that are similar but not identical to λ. As an index of phylogenetic signal applied to continuous traits, λ 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 λ 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, λ is frequently confused with distinct metrics such as h2. We show how confusion in defining and using λ can mislead our interpretation of ecological and evolutionary processes. Open research statement No data were used or collected as part of this work.

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