Re-examination of evidence for low-dimensional chaos in the Canadian Lynx data
Bibliographic record
Abstract
The time series of the annual number ofCanadian lynx caught by the Hudson Bay company be-tween 1821 and 1935 exhibits pseudo-cyclic behaviour andhas long been considered as an archetypal example of irreg-ularly fluctuating population dynamics. Recently proposedglobal polynomial models of this data have been found toexhibt chaotic dynamics and were therefore presented asdirect evidence of chaos in a real ecosystem. In this pa-per we re-examine that evidence by constructing global ra-dial basis models subject to information theoretic parame-ter constraints. We find that the models exhibit very goodagreement with the data and are able to accurately repro-duce the qualitative long term dynamical behaviour. Themodels also often exhibit “almost” chaotic dynamics, ei-ther: (a) very long period periodicity, (b) a periodic or-bit embedded in a dissipative mixing region, or (c) verylong time transient irregular aperiodic dynamics with anasymptotically periodic orbit. In each case the dynamicsexhibit a very rich range of behaviour and can also pro-vide a qualitatively accurate deterministic model of the ap-parently chaotic dynamics when subjected to a delay re-construction. We conclude that, while the data and thesemodels are consistent with the hypothesis of chaos in a realecosystem, the data may also be adequately explained byperiodic “almost chaotic” behaviour.
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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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".