The weighted quadratic index of biodiversity for pairs of species: a generalization of Rao’s index
Bibliographic record
Abstract
The distribution of biodiversity at multiple sites of a region has been traditionally investigated through the additive partitioning of the regional biodiversity, called γ-diversity, into the average within-site biodiversity or α-diversity, and the biodiversity among sites, or β-diversity. The standard additive partitioning of diversity requires the use of a measure of diversity which is a concave function of the relative abundance of species, like the Shannon entropy or the Gini- Simpson index, for instance. When a phylogenetic distance between species is also taken into account, Rao’s quadratic index has been used as a measure of dissimilarity. Rao’s index, however, is not a concave function of the distribution of relative abundance of either individual species or pairs of species and, consequently, only some nonstandard additive partitionings of diversity have been given using this index. The objective of this paper is to show that the weighted quadratic index of biodiversity, a generalization of the weighted Gini-Simpson index to the pairs of species, is a concave function of the joint distribution of the relative abundance of pairs of species and, therefore, may be used in the standard additive partitioning of diversity instead of Rao’s index. The replication property of this new measure is also discussed.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".