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Moments and probability density of threshold crossing times for populations in random environments under sustainable harvesting policies

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Abstract

Stochastic differential equations are used to model the dynamics of harvested populations in random environments. The main goal of this work is to compute, for a particular fish population under constant effort harvesting, the mean and standard deviation of first passage times by several lower and upper thresholds values. We apply logistic or logistic-like with Allee effects average growth dynamics. In addition, we present a method to obtain the probability density function of the first passage time by a threshold through the numerical inversion of its Laplace transform.

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Acknowledgements

The helpful comments from anonymous Referees and from the Editor are gratefully acknowledged. Nuno M. Brites was partially financed by Fundação para a Ciência e a Tecnologia (FCT), through national funds within the Projects CEMAPRE/REM - UIDB/05069/2020 and EXPL/EGE-IND/0351/2021. Carlos A. Braumann is member of Centro de Investigação em Matemática e Aplicações, Universidade de Évora, a research center supported by FCT, project UID/04674/2020.

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Authors and Affiliations

  1. ISEG – School of Economics and Management, REM - Research in Economics and Mathematics, CEMAPRE, Universidade de Lisboa, Rua do Quelhas, 6, Lisboa, Portugal

    Nuno M. Brites

  2. Departamento de Matemática, Escola de Ciências e Tecnologia, Universidade de Évora, Centro de Investigação em Matemática e Aplicações, Instituto de Investigação e Formação Avançada, Universidade de Évora, Rua Romão Ramalho, 59, Évora, Portugal

    Carlos A. Braumann

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  1. Nuno M. Brites
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  2. Carlos A. Braumann
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Correspondence to Nuno M. Brites.

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Brites, N.M., Braumann, C.A. Moments and probability density of threshold crossing times for populations in random environments under sustainable harvesting policies. Comput Stat (2022). https://doi.org/10.1007/s00180-022-01237-0

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