City Research Online

Abstract

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.

Publication Type:	Article
Additional Information:	This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00285-022-01750-2
Publisher Keywords:	Harvesting, Stochastic environment, Density-dependent price, Controlled diffusion, Switching environment, Seasonality
Subjects:	Q Science > QA Mathematics
Departments:	School of Policy & Global Affairs School of Policy & Global Affairs > Economics
SWORD Depositor:	Symplectic Administrator

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