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Modeling on Ratio-Dependent Three-Trophic Population Dynamics Responding to Environmental Impacts  

Lee, Sang-Hee (Department of Physics, Pusan National University)
Choi, Kyung-Hee (Division of Biological Sciences, Pusan National University)
Chon, Tae-Soo (Division of Biological Sciences, Pusan National University)
Publication Information
Korean Journal of Ecology and Environment / v.37, no.3, 2004 , pp. 304-312 More about this Journal
Abstract
The transient dynamics of three-trophic populations (prey, predator, and super predator) using ratio-dependent models responding to environmental impacts is analyzed. Environmental factors were divided into two parts: periodic factor (e.g., temperature) and general noise. Periodic factor was addressed as a frequency and bias, while general noise was expressed as a Gaussian distribution. Temperature bias ${\varepsilon}$, temperature frequency ${\Omega}$, and Gaussian noise amplitude ${\`{O}}$ accordingly revealed diverse status of population dynamics in three-trophic food chain, including extinction of species. The model showed stable limit cycles and strange attractors in the long-time behavior depending upon various values of the parameters. The dynamic behavior of the system appeared to be sensitive to changes in environmental input. The parameters of environmental input play an important role in determining extinction time of super predator and predator populations.
Keywords
Lotka-Volterra equations; population dynamics; stable limit cycle;
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  • Reference
1 Arditi, R. and L.R. Ginzburg. 1989. Coupling in predatorprey dynamics: ratio-dependent. J. Theor. Biol. 139: 311-326
2 La Barbera, A. and B. Spagnolo. 2002. Spatio-temporal patterns in population dynamics. Physica A, 120-124
3 Leslie, P.H. 1948. Some furthers notes on the use of matrices in population mathematics. Biometrica 35: 213-45
4 Wildhaber, M.L. 2001. The trade-off between food and temperature in the habitat choice of bluegill sunfish. J. Fish Biol. 58: 1476-1478
5 Ellner, E. McCauley, R.M. Nisbet and S.N. Wood. 1999. Why do population cycle? A synthesis of statistical and mechanistic modeling approaches. Ecology 80: 1789-1805
6 Gutierrez, A.P. 1992. Physiological basis of ratio-dependent predator-prey theory: the metabolic pool model as a paradigm. Ecology 73: 1552-1563
7 Freund, J.A. and T. Poschel (Eds.). 2000. Stochastic processes in physics, chemistry, and biology, Lecture Notes in Physics, Vol. 557, Springer, Berlin. Gakkhar, S. and R.K. Naji. 2002. Chaos in three species ratio-dependent food chain. Chaos, Solitons and Fractals 14: 771-778
8 Zlatinka, I.D. and K.V. Nikolay. 2000. Influence of adaptation on the nonlinear dynamics of a system of competing populations. Physics Letters A 272: 368-380
9 Gonzalez-Gascon, F. and D. Peralta Salas. 2000. On the first integrals of lotka?volterra systems, Physics Letters A 266: 336-340
10 Arditi, R., J.M. Abillon and J.V. DaSilva. 1978. A predator- prey model with satiation and intraspecific competition. Ecol. Model. 5: 173-191
11 Klebabnoff, A. and A. Hastings. 1993. Chaos in three species food chains. J. Math. Biol. 32: 427-451
12 Bazykin, A.D. 1998. Nonlinear dynamics of interacting populations. WorldScientific, Singapore. Berryman, A.A. 1991. The biological control paradox. Trends Ecol. Evol. 6: 32