How to Define, Use, and Interpret Pagel's λ$$ \lambda $$ (Lambda) in Ecology and Evolution
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.032 | 0.122 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.010 | 0.011 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.004 | 0.007 |
| Insufficient payload (model declined to judge) | 0.016 | 0.014 |
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 source (direct Gemma or distilled Codex), 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".