Several ecological studies have tried to model the population dynamics of the ungulate migratory animals individually without including the food and predation factors in the models. In this paper, we analyze the population dynamics for herbivores, carnivores and the grass volume using the secondary data from the years 1996-2006. The lions’ data didn’t correlate with the model. Due to that, the sensitivity analysis was carried out for the parameters. The herbivores predation on grass reduces the volume of grass. The crocodile predation on herbivores decreases the population of herbivores. Then the crocodile population increases, when its’ natural death rate in the absence of prey decreases. The herbivores population increases as its’ intrinsic logistic rate increases. There is a trend of Grass periodic increase and decrease as the rainfall constant value changes periodically. The herbivores population decreases as the lion predation on them increases. And lastly, the lions’ population decreases as the natural death rate of lion in the absence of prey increased.
| Published in | Applied and Computational Mathematics (Volume 3, Issue 4) |
| DOI | 10.11648/j.acm.20140304.18 |
| Page(s) | 171-176 |
| 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 |
Carnivores, Herbivores, Grass, Population Dynamics, Migration, Ecosystem, Wildebeest
| [1] | Borner, M., FitzGibbon, C. D., Borner, Mo., Caro, T. M., Lindsay, W. K., Collins, D. A., Holt, M. E., (1987). "The decline of the Serengeti Thomson's gazelle population." Oecologia 73 (1): 32-40. |
| [2] | 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. |
| [3] | Dublin, H.T., Sinclair, A.R.E., Boutin, S., Anderson, E., Jago, M. & Arcese, P. (1990) Does competition regulate ungulate populations? Further evidence from Serengeti, Tanzania. Oecologia, 82, 283–288. |
| [4] | Dublin, H. T. (1995). Vegetation dynamics in the Serengeti- Mara ecosystem: The role of elephants, fi re, and other factors. In Serengeti II, ed. A. R. E. Sinclair and P. Arcese, 71–90. Chicago: University of Chicago Press. |
| [5] | 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. |
| [6] | Holdo, R. M., Holt, R. D., and Fryxell, J.M. (2009). Opposing rainfall and pant nutritional gradients best explain the wildebeest migration in the Serengeti. The American Naturalist, 173 (4), 431-445. |
| [7] | King, A. A. and Schaffer. W. M. (1999). The rainbow bridge: Hamiltonian limits and reso-nance in predator-prey dynamics. J. Math. Biol. 39: 439-469. |
| [8] | 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. |
| [9] | 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 |
| [10] | 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. |
| [11] | Ngana, J. J., Luboobi, L.S, Kuznetsov, D. (2014). Modelling the Migratory Population Dynamics of the Serengeti Ecosystem. Applied and Computational Mathematics. Vol. 3, No. 4, 2014, pp. 125-129. |
| [12] | Onyeanusi, A.E. (1989). Large herbivore grass take-off in Masai-Mara National Reserve:Implications for the Serengeti-Mara migrants. J. Arid Environ. 16, 203-209. |
| [13] | Pennycuick, C.J. (1975). On the running of gnu (Connochaetes taurinus) and other animals. Journal of Experimental Biology. 63, p.775-799. |
| [14] | Sinclair, A. (2003). Patterns of predation in a diverse predator- prey system. Nature, 425, 288-290. |
| [15] | Sinclair, A.R.E. and Norton-Griffiths, M. (1979). Serengeti: Dynamics of an Ecosystem. Univ. Chicago Press, Chicago, USA. |
| [16] | 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. |
| [17] | Wolanski, E.J and Gereta, E (2001) Water quantity and quality as the factors driving the Serengeti ecosystem, Tanzania. Hydrobiologia. 458: 169-180. |
APA Style
Janeth James Ngana, Livingstone Serwadda Luboobi, Dmitry Kuznetsov. (2014). Mathematical Model for the Population Dynamics of the Serengeti Ecosystem. Applied and Computational Mathematics, 3(4), 171-176. https://doi.org/10.11648/j.acm.20140304.18
ACS Style
Janeth James Ngana; Livingstone Serwadda Luboobi; Dmitry Kuznetsov. Mathematical Model for the Population Dynamics of the Serengeti Ecosystem. Appl. Comput. Math. 2014, 3(4), 171-176. doi: 10.11648/j.acm.20140304.18
AMA Style
Janeth James Ngana, Livingstone Serwadda Luboobi, Dmitry Kuznetsov. Mathematical Model for the Population Dynamics of the Serengeti Ecosystem. Appl Comput Math. 2014;3(4):171-176. doi: 10.11648/j.acm.20140304.18
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.acm.20140304.18,
author = {Janeth James Ngana and Livingstone Serwadda Luboobi and Dmitry Kuznetsov},
title = {Mathematical Model for the Population Dynamics of the Serengeti Ecosystem},
journal = {Applied and Computational Mathematics},
volume = {3},
number = {4},
pages = {171-176},
doi = {10.11648/j.acm.20140304.18},
url = {https://doi.org/10.11648/j.acm.20140304.18},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140304.18},
abstract = {Several ecological studies have tried to model the population dynamics of the ungulate migratory animals individually without including the food and predation factors in the models. In this paper, we analyze the population dynamics for herbivores, carnivores and the grass volume using the secondary data from the years 1996-2006. The lions’ data didn’t correlate with the model. Due to that, the sensitivity analysis was carried out for the parameters. The herbivores predation on grass reduces the volume of grass. The crocodile predation on herbivores decreases the population of herbivores. Then the crocodile population increases, when its’ natural death rate in the absence of prey decreases. The herbivores population increases as its’ intrinsic logistic rate increases. There is a trend of Grass periodic increase and decrease as the rainfall constant value changes periodically. The herbivores population decreases as the lion predation on them increases. And lastly, the lions’ population decreases as the natural death rate of lion in the absence of prey increased.},
year = {2014}
}
TY - JOUR T1 - Mathematical Model for the Population Dynamics of the Serengeti Ecosystem AU - Janeth James Ngana AU - Livingstone Serwadda Luboobi AU - Dmitry Kuznetsov Y1 - 2014/08/30 PY - 2014 N1 - https://doi.org/10.11648/j.acm.20140304.18 DO - 10.11648/j.acm.20140304.18 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 171 EP - 176 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20140304.18 AB - Several ecological studies have tried to model the population dynamics of the ungulate migratory animals individually without including the food and predation factors in the models. In this paper, we analyze the population dynamics for herbivores, carnivores and the grass volume using the secondary data from the years 1996-2006. The lions’ data didn’t correlate with the model. Due to that, the sensitivity analysis was carried out for the parameters. The herbivores predation on grass reduces the volume of grass. The crocodile predation on herbivores decreases the population of herbivores. Then the crocodile population increases, when its’ natural death rate in the absence of prey decreases. The herbivores population increases as its’ intrinsic logistic rate increases. There is a trend of Grass periodic increase and decrease as the rainfall constant value changes periodically. The herbivores population decreases as the lion predation on them increases. And lastly, the lions’ population decreases as the natural death rate of lion in the absence of prey increased. VL - 3 IS - 4 ER -
Email: