A Stage-Structured Predator-Prey Model in a Patchy Environment
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Bibliographic record
Abstract
In this paper, we propose a stage-structured predator-prey model with migrations among patches in an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>n</mml:mi></mml:math>-patch environment. The net reproduction number for each patch in isolation is obtained along with the net reproduction number of the system of patches, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msub><mml:mrow><mml:mi mathvariant="normal">ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math>. Inequalities describing the relationship among these numbers are also given. Furthermore, threshold dynamics determined by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:msub><mml:mrow><mml:mi mathvariant="normal">ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math> is established: the predator dies out if <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:msub><mml:mrow><mml:mi mathvariant="normal">ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo><</mml:mo><mml:mn>1</mml:mn></mml:math> while the predator persists if <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:msub><mml:mrow><mml:mi mathvariant="normal">ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>></mml:mo><mml:mn>1</mml:mn></mml:math>. Focusing on the case with two patches, we obtain that the dispersal decreases the net reproduction number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:msub><mml:mrow><mml:mi mathvariant="normal">ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math>. By numerical simulations, we find that the dispersal may be a good thing or a bad thing because the dispersal could make the predator population thrive or extinct, and hence we might seek steady state in the ecological environment by controlling parameters related to the prey and the predator.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 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 it