The effects of random and seasonal environmental fluctuations on optimal harvesting and stocking.
Controlled diffusion
Density-dependent price
Harvesting
Seasonality
Stochastic environment
Switching environment
Journal
Journal of mathematical biology
ISSN: 1432-1416
Titre abrégé: J Math Biol
Pays: Germany
ID NLM: 7502105
Informations de publication
Date de publication:
25 04 2022
25 04 2022
Historique:
received:
27
09
2021
accepted:
02
04
2022
revised:
02
04
2022
entrez:
25
4
2022
pubmed:
26
4
2022
medline:
28
4
2022
Statut:
epublish
Résumé
We analyze the harvesting and stocking of a population that is affected by random and seasonal environmental fluctuations. The main novelty comes from having three layers of environmental fluctuations. The first layer is due to the environment switching at random times between different environmental states. This is similar to having sudden environmental changes or catastrophes. The second layer is due to seasonal variation, where there is a significant change in the dynamics between seasons. Finally, the third layer is due to the constant presence of environmental stochasticity-between the seasonal or random regime switches, the species is affected by fluctuations which can be modelled by white noise. This framework is more realistic because it can capture both significant random and deterministic environmental shifts as well as small and frequent fluctuations in abiotic factors. Our framework also allows for the price or cost of harvesting to change deterministically and stochastically, something that is more realistic from an economic point of view. The combined effects of seasonal and random fluctuations make it impossible to find the optimal harvesting-stocking strategy analytically. We get around this roadblock by developing rigorous numerical approximations and proving that they converge to the optimal harvesting-stocking strategy. We apply our methods to multiple population models and explore how prices, or costs, and environmental fluctuations influence the optimal harvesting-stocking strategy. We show that in many situations the optimal way of harvesting and stocking is not of threshold type.
Identifiants
pubmed: 35467160
doi: 10.1007/s00285-022-01750-2
pii: 10.1007/s00285-022-01750-2
doi:
Types de publication
Journal Article
Research Support, U.S. Gov't, Non-P.H.S.
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
41Informations de copyright
© 2022. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
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