Modelling the Migratory Population Dynamics of the Serengeti Ecosystem

Janeth James Ngana; Livingstone Serwadda Luboobi; Dmitry Kuznetsov

doi:doi:10.11648/j.acm.20140304.13

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Modelling the Migratory Population Dynamics of the Serengeti Ecosystem

Janeth James Ngana, Livingstone Serwadda Luboobi, Dmitry Kuznetsov

Published in Applied and Computational Mathematics (Volume 3, Issue 4)

Received: 7 July 2014 Accepted: 15 July 2014 Published: 30 July 2014

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Abstract

Many ecological studies have tried to explain the animal migrations, but none has embarked on modeling the Great Migration and its impact on the migratory animals’ population dynamics, in combination with food and the impact of predation. In this paper, we present a mathematical model of the four dynamic Ordinary Differential Equations of Grass, Herbivores, Lions and Crocodiles. Using secondary data covering ten years 1996-2006 we estimated the parameters in the model. The grass forage grew periodically, the herbivores population grew, the predation rate of lions grew and so did its population. But the crocodiles’ population grew less. The study has shown that there was no extinction and migration continued. Herbivores population grew provided that there was enough food.

Published in	Applied and Computational Mathematics (Volume 3, Issue 4)
DOI	10.11648/j.acm.20140304.13
Page(s)	125-129
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Great Migration, Grass, Herbivores, Lions, Crocodiles, Predation, Prey, Serengeti, Masai Mara

References

[1]	Fryxell, J. M., Greever, J., and Sinclair, A. R. E. (1988). Causes and consequences of migration in large herbivores. Trends in Ecology and Evolution 3: 237-241.
[2]	Holdo, R. M., Holt, R. D., Sinclair, A. R., Godley, B. J., & Thirgood, S. (2011). Migration impacts on communities and ecosystems: empirical evidence and theoretical insights. Animal Migration: A Synthesis, 131-143.
[3]	Holdo, R. M., Holt, R. D., and Fryxell, J.M. (2009). Opposing rainfall and pant nutritional grsdients best explain the wildebeest migration in the Serengeti. The American Naturalist, 173 (4), 431-445.
[4]	Maddock, L., Sinclair, A. R. E and Norton-Griffiths, M. (1979). The Migration and Grazzing succession in Serengeti: Dynamics of an Ecosystem. 104-29. Chicago: University of Chicago Press.
[5]	Mduma S.A.R, Sinclair A.R.E. AND Hiborn, R. (1999). Food regulates the Serengeti Wildbeest: a 40-year record. Journal of Animal Ecology, 68, 1101-1122
[6]	Musiega, D. E., and Kazadi, S.N. (2004). Simulating the East African Wildebeest Migration Patterns using GIS and remote sensing. African Journal of Ecology, 42 (4), 355-362.
[7]	Pennycuick, C.J. (1975). On the running of gnu (Connochaetes taurinus) and other animals. Journal of Experimental Biology. 63, p.775-799.
[8]	Stratton, D. (2010). Wildebeest in Serengeti: limits to exponential growth. University of Chicago Press.
[9]	Sinclair, A. R. E, Arcese, P. (1995). Serengeti II: Dynamics, management and conservation of an ecosystem. University of Chicago Press, Chicago.
[10]	Wilmhurst, J. F. Fryxell, J. M., Fram, B.P., Sinclair, A. R. E., Henschel, C. P. (1999). Spatial Distribution of Serengeti Wildebeest in relation to Resources. Can. J. Zool.77, 1223-1232.
[11]	Wolanski, E. & Gereta, E. (2001) .The water quality and quantity as the factors driving the Serengeti ecosystems, Tanzania. Hydrobiologia 458, 169–180.

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Janeth James Ngana, Livingstone Serwadda Luboobi, Dmitry Kuznetsov. (2014). Modelling the Migratory Population Dynamics of the Serengeti Ecosystem. Applied and Computational Mathematics, 3(4), 125-129. https://doi.org/10.11648/j.acm.20140304.13

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ACS Style

Janeth James Ngana; Livingstone Serwadda Luboobi; Dmitry Kuznetsov. Modelling the Migratory Population Dynamics of the Serengeti Ecosystem. Appl. Comput. Math. 2014, 3(4), 125-129. doi: 10.11648/j.acm.20140304.13

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AMA Style

Janeth James Ngana, Livingstone Serwadda Luboobi, Dmitry Kuznetsov. Modelling the Migratory Population Dynamics of the Serengeti Ecosystem. Appl Comput Math. 2014;3(4):125-129. doi: 10.11648/j.acm.20140304.13

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@article{10.11648/j.acm.20140304.13,
  author = {Janeth James Ngana and Livingstone Serwadda Luboobi and Dmitry Kuznetsov},
  title = {Modelling the Migratory Population Dynamics of the Serengeti Ecosystem},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {4},
  pages = {125-129},
  doi = {10.11648/j.acm.20140304.13},
  url = {https://doi.org/10.11648/j.acm.20140304.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140304.13},
  abstract = {Many ecological studies have tried to explain the animal migrations, but none has embarked on modeling the Great Migration and its impact on the migratory animals’ population dynamics, in combination with food and the impact of predation. In this paper, we present a mathematical model of the four dynamic Ordinary Differential Equations of Grass, Herbivores, Lions and Crocodiles. Using secondary data covering ten years 1996-2006 we estimated the parameters in the model. The grass forage grew periodically, the herbivores population grew, the predation rate of lions grew and so did its population. But the crocodiles’ population grew less. The study has shown that there was no extinction and migration continued. Herbivores population grew provided that there was enough food.},
 year = {2014}
}

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TY  - JOUR
T1  - Modelling the Migratory Population Dynamics of the Serengeti Ecosystem
AU  - Janeth James Ngana
AU  - Livingstone Serwadda Luboobi
AU  - Dmitry Kuznetsov
Y1  - 2014/07/30
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140304.13
DO  - 10.11648/j.acm.20140304.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 125
EP  - 129
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140304.13
AB  - Many ecological studies have tried to explain the animal migrations, but none has embarked on modeling the Great Migration and its impact on the migratory animals’ population dynamics, in combination with food and the impact of predation. In this paper, we present a mathematical model of the four dynamic Ordinary Differential Equations of Grass, Herbivores, Lions and Crocodiles. Using secondary data covering ten years 1996-2006 we estimated the parameters in the model. The grass forage grew periodically, the herbivores population grew, the predation rate of lions grew and so did its population. But the crocodiles’ population grew less. The study has shown that there was no extinction and migration continued. Herbivores population grew provided that there was enough food.
VL  - 3
IS  - 4
ER  -

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Author Information

Janeth James Ngana

Nelson Mandela African Institution of Science and Technology (NM-AIST), Arusha, Tanzania
Livingstone Serwadda Luboobi

Department of Mathematics, Makerere University, Kampala, Uganda
Dmitry Kuznetsov

Nelson Mandela African Institution of Science and Technology (NM-AIST), Arusha, Tanzania

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APA Style

Janeth James Ngana, Livingstone Serwadda Luboobi, Dmitry Kuznetsov. (2014). Modelling the Migratory Population Dynamics of the Serengeti Ecosystem. Applied and Computational Mathematics, 3(4), 125-129. https://doi.org/10.11648/j.acm.20140304.13

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ACS Style

Janeth James Ngana; Livingstone Serwadda Luboobi; Dmitry Kuznetsov. Modelling the Migratory Population Dynamics of the Serengeti Ecosystem. Appl. Comput. Math. 2014, 3(4), 125-129. doi: 10.11648/j.acm.20140304.13

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AMA Style

Janeth James Ngana, Livingstone Serwadda Luboobi, Dmitry Kuznetsov. Modelling the Migratory Population Dynamics of the Serengeti Ecosystem. Appl Comput Math. 2014;3(4):125-129. doi: 10.11648/j.acm.20140304.13

Copy | Download

@article{10.11648/j.acm.20140304.13,
  author = {Janeth James Ngana and Livingstone Serwadda Luboobi and Dmitry Kuznetsov},
  title = {Modelling the Migratory Population Dynamics of the Serengeti Ecosystem},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {4},
  pages = {125-129},
  doi = {10.11648/j.acm.20140304.13},
  url = {https://doi.org/10.11648/j.acm.20140304.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140304.13},
  abstract = {Many ecological studies have tried to explain the animal migrations, but none has embarked on modeling the Great Migration and its impact on the migratory animals’ population dynamics, in combination with food and the impact of predation. In this paper, we present a mathematical model of the four dynamic Ordinary Differential Equations of Grass, Herbivores, Lions and Crocodiles. Using secondary data covering ten years 1996-2006 we estimated the parameters in the model. The grass forage grew periodically, the herbivores population grew, the predation rate of lions grew and so did its population. But the crocodiles’ population grew less. The study has shown that there was no extinction and migration continued. Herbivores population grew provided that there was enough food.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Modelling the Migratory Population Dynamics of the Serengeti Ecosystem
AU  - Janeth James Ngana
AU  - Livingstone Serwadda Luboobi
AU  - Dmitry Kuznetsov
Y1  - 2014/07/30
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140304.13
DO  - 10.11648/j.acm.20140304.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 125
EP  - 129
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140304.13
AB  - Many ecological studies have tried to explain the animal migrations, but none has embarked on modeling the Great Migration and its impact on the migratory animals’ population dynamics, in combination with food and the impact of predation. In this paper, we present a mathematical model of the four dynamic Ordinary Differential Equations of Grass, Herbivores, Lions and Crocodiles. Using secondary data covering ten years 1996-2006 we estimated the parameters in the model. The grass forage grew periodically, the herbivores population grew, the predation rate of lions grew and so did its population. But the crocodiles’ population grew less. The study has shown that there was no extinction and migration continued. Herbivores population grew provided that there was enough food.
VL  - 3
IS  - 4
ER  -

Copy | Download