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International Journal of Mathematical Analysis and Applications

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A Mathematical Model for Recruitment and Developmental Sustainability of Fish Population in the Pond

International Journal of Mathematical Analysis and Applications
Vol.5 , No. 3, Publication Date: Aug. 10, 2018, Page: 58-65

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Authors

[1]	Ogbaji Eka Oche, Department of Mathematics and Statistics, Federal University, Wukari, Nigeria.
[2]	Ben Obakpo Johnson, Department of Mathematics and Statistics, Federal University, Wukari, Nigeria.
[3]	James Emmanuel Friday, Department of Mathematics and Statistics, Federal University, Wukari, Nigeria.
[4]	Okorie Charity Ebelechuku, Department of Mathematics and Statistics, Federal University, Wukari, Nigeria.
[5]	Muhammad Nuhu Abdullahi, Department of Mathematics and Statistics, Federal University, Wukari, Nigeria.
[6]	Adiku Lydia, Department of Mathematics and Statistics, Federal University, Wukari, Nigeria.

Abstract

Recruitment and sustainability for fish population are renewable natural resources, if correctly managed. The basic purpose of fish recruitment and sustainability is to provide advice on the optimum exploitation level of aquatic living resources such as fish. We formulate a mathematical model for recruitment and developmental sustainability of fish population in the pond by modifying growth model of Verhuls where we incorporate catch equation of Baranov as a function of time in the model. Runge-Kutta scheme of fourth order was used to solve the modified model. Furthermore, we collected data from Federal University Wukari fish pond to validate our modified model. We coded the Runge-Kutta scheme for our modified model by using Octave programming language, results are shown on Table 2 and figure 1, 2, 3, 4 and 5. It was observed that at P=1, P=20, P=100 and P=300 the fish recruited started increasing from 1st month to 5th month and at 6th month the fish population decrease equally because at 6th month fishes are expected to be harvested and top up. The result show that fish population recruited started increasing from first month to fifth month of recruitment and started decreasing equally at sixth month. We conclude that fish reach its maturity age at fifth month and our modified model can be use to predict expected fish population recruitment and sustainability from its initial recruitments.

Keywords

Fish Population, Pond, Recruitment and Sustainability

Reference

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