Reactivity, Attenuation, and Transients in Metapopulations
Bibliographic record
Abstract
Transient dynamics often differ drastically from the asymptotic dynamics of systems. In this paper we analyze transient dynamics in birth-jump metapopulations where dispersal occurs immediately after birth (e.g., via larval dispersal). We address the choice of appropriate norms as well as the effect of stage structure on transient dynamics. We advocate the use of the $\ell_1$ norm, because of its biological interpretation, and extend the transient metrics of reactivity and attenuation to birth-jump metapopulations in this norm. By way of examples we compare this norm to the more commonly used $\ell_2$ norm. Our focus is the case where transient dynamics are very different than asymptotic dynamics. We provide simple examples of metapopulations where this is the case and also show how increasing the number of habitat patches can increase this difference. We then connect the reactivity and attenuation of metapopulations to the source-sink classification of habitat patches and demonstrate how to meaningfully measure reactivity when metapopulations are stage-structured, with a focus on marine metapopulations. Our paper makes three primary contributions. First, it provides guidance to readers as to the appropriate norm and scalings for studying transients in birth-jump metapopulations. Second, it provides three examples of transient behavior in metapopulations involving slow-fast systems, crawl-bys, and high dimensionality. Third, it connects the concepts of reactivity and attenuation to the source-sink classification of habitat patches more commonly found in marine metapopulations.
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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 | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".