Chance of extinction of populations in food chain model under demographic stochasticity

Bapi Saha; Bapi Saha

doi:10.3934/mbe.2019177

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 3537-3560. doi: 10.3934/mbe.2019177

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Research article Special Issues

Chance of extinction of populations in food chain model under demographic stochasticity

Bapi Saha ^,

Dept. of Mathematics, Govt. College of Engg. & Textile Technology, Berhampore, Murshidabad, West Bengal, PIN-742101 MO +919339831862, India

Received: 28 December 2018 Accepted: 17 March 2019 Published: 19 April 2019

The extinction of different species from the earth is increasing at an alarming rate. So, assessment of probability of extinction of different important species in our ecosystem could help us to take proper conservation policy for those population whose chance of extinction is high. In this paper a method is developed to find the probability of extinction of populations in a general n-trophic food chain model under demographic stochasticity. The birth-death process is used to incorporate the demographic stochasticity and the necessary mathematical expressions are obtained. The theoretical finding is validated by numerical simulation for a two dimensional predator-prey system.
- extinction probability,
- food chain,
- prey-predator model,
- population size,
- random variable,
- birth-death process
Citation: Bapi Saha. Chance of extinction of populations in food chain model under demographic stochasticity[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3537-3560. doi: 10.3934/mbe.2019177

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Abstract

The extinction of different species from the earth is increasing at an alarming rate. So, assessment of probability of extinction of different important species in our ecosystem could help us to take proper conservation policy for those population whose chance of extinction is high. In this paper a method is developed to find the probability of extinction of populations in a general n-trophic food chain model under demographic stochasticity. The birth-death process is used to incorporate the demographic stochasticity and the necessary mathematical expressions are obtained. The theoretical finding is validated by numerical simulation for a two dimensional predator-prey system.

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