Ecological and biogeographic null hypotheses for comparing rarefaction curves
Why this work is in the frame
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Bibliographic record
Abstract
The statistical framework of rarefaction curves and asymptotic estimators allows for an effective standardization of biodiversity measures. However, most statistical analyses still consist of point comparisons of diversity estimators for a particular sampling level. We introduce new randomization methods that incorporate sampling variability encompassing the entire length of the rarefaction curve and allow for statistical comparison of i ≥2 individual‐based, sample‐based, or coverage‐based rarefaction curves. These methods distinguish between two distinct null hypotheses: the ecological null hypothesis ( H 0eco ) and the biogeographical null hypothesis ( H 0biog ). H 0eco states that the i samples were drawn from a single assemblage, and any differences among them in species richness, composition, or relative abundance reflect only sampling effects. H 0biog states that the i samples were drawn from assemblages that differ in their species composition but share similar species richness and species abundance distributions. To test H 0eco , we created a composite rarefaction curve by summing the abundances of all species from the i samples. We then calculated a test statistic Z eco , the (cumulative) summed areas of difference between each of the i individual curves and the composite curve. For H 0biog , the test statistic Z biog was calculated by summing the area of difference between all possible pairs of the i individual curves. Bootstrap sampling from the composite curve ( H 0eco ) or random sampling from different simulated assemblages using alternative abundance distributions ( H 0biog ) was used to create the null distribution of Z , and to provide a frequentist test of Z | H 0 . Rejection of H 0eco does not pinpoint whether the samples differ in species richness, species composition, and/or relative abundance. In benchmark comparisons, both tests performed satisfactorily against artificial data sets randomly drawn from a single assemblage (low Type I error). In benchmark comparisons with different species abundance distributions and richness, the tests had adequate power to detect differences among curves (low Type II error), although power diminished at small sample sizes and for small differences among underlying species rank abundances.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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 it