An extended stochastic Allee model with harvesting and the risk of extinction of the herring population

Sau, Anurag; Saha, Bapi; Bhattacharya, Sabyasachi

doi:10.1016/j.jtbi.2020.110375

Cited by 14 publications

(13 citation statements)

References 43 publications

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“…This leads the species under consideration to stay in a stable and safe mode instead of the risk of extinction. Similar stochastic models were also analyzed in Sau et al [28]. The extract of the paper was mainly associated with the species' probability of extinction and the expected time to extinction.…”

Section: Introductionmentioning

confidence: 85%

“…where x(t) is the biomass at time t, r is called the intrinsic growth rate, K is the carrying capacity, θ is called the density regulation around carrying capacity. We call this model as Allee-Saha model (ASM) [28]. However, in reality, most of the species follow θ−logistic process [27], and hence we also consider the θlogistic growth process to encompass a large number of species.…”

Section: Model Formulation 21 the Deterministic Modelmentioning

confidence: 99%

“…When θ is equal to 1, the equation (2.2) become classical logistic model. The sustainability of different rare and endangered species may greatly depend on harvesting strategy [28]. We consider two types of harvesting strategies viz.…”

Section: Model Formulation 21 the Deterministic Modelmentioning

confidence: 99%

“…But this does not give us any clue about the possible regime shift to a lower stable equilibrium (may be an extinction state) if the system is perturbed by the noise of sufficiently large strength. This entire part was missing in the work of Sau et al [28].…”

Section: Introductionmentioning

confidence: 98%

“…The author introduced this model in studying the extinction status of one of the economically beneficial fishes, viz. Atlantic herring [28]. We believe that, exploring the harvesting issue in the theta-logistic and Allee model must be an exciting research area to be explored as it can cover the growth profile of a wide range of species.…”

Section: Introductionmentioning

confidence: 99%

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Recognizing and prevention of probable regime shift in density regulated and Allee type stochastic harvesting model with application to herring conservation

Sau,

Bhattacharya,

Saha

2021

Preprint

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An ecological system with multiple stable equilibria is prone to undergo catastrophic change or regime shift from one steady-state to another. It should be noted that, if one of the steady states is an extinction state, the catastrophic change may lead to extinction. A suitable manual measure may control the prevention of catastrophic changes of different species from one equilibrium to another. We consider two stochastic models with linear and nonlinear harvesting terms. We inspect either density regulation or Allee type density regulated models [Saha et al., Ecological Modelling, 2013], which have substantial applications in the herring fish population's viability study. Both the deterministic models we consider here contain bi-stability under certain restrictions, and in that case, one of the stable states is the extinction state. We assume that the dynamical system under consideration is closed, i.e., immigration and emigration are absent. The demographic noise is introduced in the system by substituting an ordinary differential equation with a stochastic differential equation model, where the birth and death rates of the deterministic process are used to obtain the instantaneous mean and variance in the stochastic differential equation. Our study reveals that, the catastrophic changes can be avoided manually by a suitable choice of handling time that will eventually help to prevent the sudden extinction of the harvested population. The entire study is illustrated through the herring population size data obtained from the Global Population Dynamics Database (GPDD) and simulation experiment.

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Section: Introductionmentioning

confidence: 85%

Section: Model Formulation 21 the Deterministic Modelmentioning

confidence: 99%

Section: Model Formulation 21 the Deterministic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Recognizing and prevention of probable regime shift in density regulated and Allee type stochastic harvesting model with application to herring conservation

Sau,

Bhattacharya,

Saha

2021

Preprint

Self Cite

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Global dynamics in stochastic n‐species food chain systems with white noise and Lévy jumps

Tuerxun

Teng

2022

Math Methods in App Sciences

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This paper is concerned with a n-species stochastic food chain model with white noise and Lévy jumps. The global stochastic dynamics are established, including the existence of the global and positive solutions, stochastic ultimate boundedness, extinction with probability one, and the permanence and global stability in the mean by developing a new research method, using the auxiliary functions and theory of stochastic differential equations. Furthermore, the numerical simulations are presented to verify the theoretical results and illustrate the proposed open problems.

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Revisiting and redefining return rate for determination of the precise growth status of a species

2023

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An extended stochastic Allee model with harvesting and the risk of extinction of the herring population

Cited by 14 publications

References 43 publications

Recognizing and prevention of probable regime shift in density regulated and Allee type stochastic harvesting model with application to herring conservation

Recognizing and prevention of probable regime shift in density regulated and Allee type stochastic harvesting model with application to herring conservation

Global dynamics in stochastic n‐species food chain systems with white noise and Lévy jumps

Revisiting and redefining return rate for determination of the precise growth status of a species

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