A geometric approach to beta diversity
Bibliographic record
Abstract
Abstract Beta diversity—the variation among community compositions in a region—is a fundamental measure of biodiversity. Most classic measures have posited that beta diversity is maximized when each community has a distinct, nonoverlapping set of species. However, this assumption overlooks the ecological significance of species interactions and non‐additivity in ecological systems, where the function and behavior of species depend on other species in a community. Here, we introduce a geometric approach to measure beta diversity as the hypervolume of the geometric embedding of a metacommunity. Besides considering compositional distinctiveness as in classic metrics, this geometric measure explicitly incorporates species associations and captures the idea that adding a unique, species‐rich community to a metacommunity increases beta diversity. We show that our geometric measure is closely linked to and naturally extends previous information‐ and variation‐based measures. Additionally, we provide a unifying geometric framework for widely adopted extensions of beta diversity. Applying our geometric measures to empirical data, we address two long‐standing questions in beta diversity research—the latitudinal pattern of beta diversity and the effect of sampling effort—and present novel ecological insights that were previously obscured by the limitations of classic approaches. In sum, our geometric approach offers a new and complementary perspective on beta diversity, is immediately applicable to existing data, and holds promise for advancing our understanding of the complex relationships between species composition, ecosystem functioning, and stability.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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".