Resolving a sorites paradox: how large is a small population?
Bibliographic record
Abstract
Theoretically, small, isolated populations should not persist. Empirically, this predication appears to be supported in some cases and contradicted in others. Although small population size is a central concept in conservation biology, it is not defined consistently in a biologically meaningful way. Its definition can be arbitrary (e.g., population sizes associated with quasi-extinction risk), driven by Allee thresholds, or assumed tied to minimum viable population size. Published values of small populations range from 20 to 100 000 individuals. Here, we review the concept of small population size, including how one might identify it using risk-based and recovery-based approaches, both of which define smallness functionally. Ideally, we want an approach that is both predictive and practical, but it is not clear that both can be had. We emphasize the important effects of density and dispersion on the risk and performance of populations, effects that tend to be ignored. We suggest that small applied to biological populations is a multifaceted concept, and that no single definition is likely to capture all the complexity. In which case, neither risk-based methods of identifying small populations nor recovery-based methods alone will suffice. We propose a framework that offers several definitions of small population size based on function (i.e., behavior of the population), each of which is sufficient for defining a small population. From expected smallest to largest estimated threshold population size: (1) The population’s behavior is dominated by demographic stochasticity. (2) The population has crossed an Allee threshold, exhibiting negative growth because of a behavioral mechanism inherent in the species. (3) The population has declined to the minimum persistent population size as revealed by a stochastic, simulation model, omitting threats and mitigation. (4) The population is unresponsive to threat mitigation. Although this method results in a designation of small populations that is both functional and biologically meaningful, the systematic study of the dynamics of small populations across taxa, and across density and dispersion within taxa, will create a more nuanced understanding of extinction risk. Ultimately, developing a predictive, recovery-based understanding of small-population dynamics will help link the small-population and declining-population paradigms, and improve species management planning.
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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 | 0.022 | 0.087 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.003 | 0.025 |
| Scholarly communication | 0.006 | 0.020 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.006 | 0.009 |
| Insufficient payload (model declined to judge) | 0.003 | 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".