Matrix methods for stochastic dynamic programming in ecology and evolutionary biology
Bibliographic record
Abstract
Abstract Organisms are constantly making tradeoffs. These tradeoffs may be behavioural (e.g. whether to focus on foraging or predator avoidance) or physiological (e.g. whether to allocate energy to reproduction or growth). Similarly, wildlife and fishery managers must make tradeoffs while striving for conservation or economic goals (e.g. costs vs. rewards). Stochastic dynamic programming (SDP) provides a powerful and flexible framework within which to explore these tradeoffs. A rich body of mathematical results on SDP exist but have received little attention in ecology and evolution. Using directed graphs – an intuitive visual model representation – we reformulated SDP models into matrix form. We synthesized relevant existing theoretical results which we then applied to two canonical SDP models in ecology and evolution. We applied these matrix methods to a simple illustrative patch choice example and an existing SDP model of parasitoid wasp behaviour. The proposed analytical matrix methods provide the same results as standard numerical methods as well as additional insights into the nature and quantity of other, nearly optimal, strategies, which we may also expect to observe in nature. The mathematical results highlighted in this work also explain qualitative aspects of model convergence. An added benefit of the proposed matrix notation is the resulting ease of implementation of Markov chain analysis (an exact solution for the realized states of an individual) rather than Monte Carlo simulations (the standard, approximate method). It also provides an independent validation method for other numerical methods, even in applications focused on short‐term, non‐stationary dynamics. These methods are useful for obtaining, interpreting, and further analysing model convergence to the optimal time‐independent (i.e. stationary) decisions predicted by an SDP model. SDP is a powerful tool both for theoretical and applied ecology, and an understanding of the mathematical structure underlying SDP models can increase our ability to apply and interpret these models.
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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 | 0.005 | 0.016 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 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".