How to define, use, and interpret Pagel’s λ (lambda) in ecology and evolution
Bibliographic record
Abstract
1 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 h 2 . 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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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".