Vol.5 , No. 3, Publication Date: Aug. 10, 2018, Page: 58-65

[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. |

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

[01] | Mwegoha, W. J. S, Kaseva, M. E and S. M. M. Sabai, S. M. M, (2010), Mathematical modelling of dissolved oxygen in fish Ponds, African Journal of Environmental Science and Technology Vol. 4 (9), pp. 625-638, DOI: 10.5897/AJEST10.206 |

[02] | Malthus, T. R. (1798). An essay on the principle of population and summary viewsof the principlepopulation. Penguin, Harmondsworth, England. |

[03] | Comprez, B. (1825). On the natura of the function expressive of the law of human mortality. Philosophical Transations. 115\513-585.s. |

[04] | Lotka, A. J. (1924). Elements PhysicalBiology. Williams and Wilkins, Baltimore. |

[05] | Volterra, V. (1926). Fluctuations in the abundance of a species considered Mathematically Nature. 118: 558-560. |

[06] | Hutchinson, G. E. (1978). An Introduction to Population Ecology. Yale University Press, New Haven. |

[07] | Verhulst, F. P. (1838). Notice sur la loique la population suite dand son Acroissment. Correspondance Mathathematiqueet Physique. 10: 113-121. |

[08] | Kingslad, S. (1985). Modeling Nature. University of Chicago Press, Chicago. |

[09] | Rescigno, A, and I. W. Rechardson (1967). On the competitive exclusing principle. Bulletin of Mathematical Biophysics. 27\85-90 |

[10] | May, R. M. (1972). Limit cycles in predator-prey communities. Science. 177\900-902. |

[11] | Albrsecht, F., H. Gatzke, haddad, and n. Wax (1974). The dynamics two Bartlett, M. S (1960). Stochastic models in ecology and epidemiology. Methuen London. |

[12] | Lefkovitch, L. P. (1965). The study of population growth in organism grouped by stages. Biometrics. 21\1-15. |

[13] | Sauer, J. P., and N. A. slade (1987). Underground demography \ is body mass a better categorical variable than age? Ecology. 68\624-650. |

[14] | Turchin, P. (1995). Population regulation\ old arguments and a new synthesis. Page 19-40 in N. cappuccino and P. W Price editors- population. |

[15] | May, R. M., and G. F. Oster (1976). Bifurcations and dynamic complexity in simply ecological models. American Naturalist. 110\573-599. |

[16] | Hastings, A., Hom, C. L, Ellner, S., Truchin, P. and Godfrey, H. C. J. (1993). Chaos in Ecology and Systematics. 34\1-33. |

[17] | Kerr, S. R. (1985). Niche theory and fisheries ecology. Trans. Am. Fish soc. 109\254-257. |

[18] | Werner, E. E. (1982). Niche theory in fisheries ecology. Trans. Am. Fish Soc. 109: 257-260. |

[19] | Pauly, D. (1980). On the relationship between natural mortality, growth parameters and means environmental temperature in 175 fish stock. Rapp. R. V. Reun. Cons. Int. Explore. Mer. 39\175-192 |

[20] | Strong, D. R, (1984). Density vagues ecology and liberal population regulation in insects, in A New ecology\ Novel Approaches to Interactive Systems, P. W. Price, G. N Slobodchikoff and W. S Caud (eds.). pp 313-329 Wiley, New York. |

[21] | Leslies, P. H. (1945). On the use of matrices in population mathematics. Biometrika. 35\213\235. |

[22] | Smith, P. E. (1981). Fisheries on coastal pelagic schoolingfish. In Marine fish Larvae\ Morphology Ecology, and Relation to Fisheries. R. Lasker (ed). Pp 1-32 University of Washington Press, Seattle. |

[23] | Gillian, J. F., and D. F. fraser (1987). Habital selection under predation hazard\ test of a model with foraging minnoows. Ecology 68\1856-62, |

[24] | Odondi, L. T. (1999). Optimal Fish Farming. M. Phil. Thesis submitted to Mathematics Department, Moi University, Kenya. |

[25] | Schnute, J. T., (1994). A general framework for developing sequential fisheries models. Can J. Fish Aquatic. Sci 51\1676-1688. |

[26] | Braverman. E and S. H. Saker. 2008. On the Cushing-Henson conjecture, delay difference equations and attenuant cycles. Journal of Difference Equations and Applications, vol. 14, no. 3, pp. 275–286. |

[27] | Lin. X., and N. E Breslow (1996). Bias correction in generalized linear mixed models with multiple components of dispersion. J. Amer. Stat. Assoc. 91/ 1007-1016. |

[28] | Baranov, F. I (1918), On the question of the biological basis of fisheries, Izvestiya, 1: 81–128 |

[29] | Idels, L. V. and Wang, M. 2008. Harvesting fisheries management strategies with modified effort function. International Journal Modelling, Identification and Control 3: 83-87. |

[30] | Agudze, G., (2013) Modelling Sustainable Harvesting, Strategies Of A Fish Pond, M.Sc Thesis in Industrial Mathematics, Department Of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, pp 74-75. |