The Study of Increasing Environmental Temperature on the Dynamical Behaviour of a Prey-Predator System: A Model
It is well recognized that the green house gases such
as Chlorofluoro Carbon (CFC), CH4, CO2 etc. are responsible
directly or indirectly for the increase in the average global temperature
of the Earth. The presence of CFC is responsible for
the depletion of ozone concentration in the atmosphere due to
which the heat accompanied with the sun rays are less absorbed
causing increase in the atmospheric temperature of the Earth. The
gases like CH4 and CO2 are also responsible for the increase in
the atmospheric temperature. The increase in the temperature level
directly or indirectly affects the dynamics of interacting species
systems. Therefore, in this paper a mathematical model is proposed
and analysed using stability theory to asses the effects of increasing
temperature due to greenhouse gases on the survival or extinction of
populations in a prey-predator system. A threshold value in terms
of a stress parameter is obtained which determines the extinction or
existence of populations in the underlying system.
[1] H. Kopka and P. W. Daly, A Guide to LATEX, 3rd ed. Harlow, England:
Addison-Wesley, 1999.
[2] F. Stordal, Isaken ISA, USEPA and UNEP. Washington, DC,1, 1986.
[3] S. F. Singer, Stratospheric Ozone: Science, Policy, Global Climate
Change. Paragon House, New York, 1989.
[4] O. L. Petchey, U. Brose, B. C. Rall, Predicting the Effects of Temperature
on Food Web Connectance. Phil. Trans. R. Soc., B 365(2010) 2081-
2091.
[5] G. Yvon-Durocher, J. I. Jones, M. Trimmer, G. Woodward, J. M.
Montoya, Warming Alters the Metabolic Balance of Ecosystems. Phil.
Trans. R. Soc., 365(2010) 2117-2126.
[6] H. Sarmento, J. M. Montoya, E. Vazquez-Dominguez, D. Vaque, J. M.
Gasol, , Warming Effect on Marine Food Web Processes: How Far can We
Go When It Comes to Predictions? Phil. Trans. R. Soc., B 365(2010)
2137-2149.
[7] J. H. Brown, J. F. Gillooly, A. P. Allen, V. M. Sanage, G. B. West, Toward
a Metabolic Theory of Ecology Ecology, 85(2004) 1771-1789.
[8] G. B. West, J. H. Brown, B. J. Enquist, A General Model for the Origin
of Allometric Scaling Laws in Biology. Science, 276(1997) 122-126.
[9] W. Voigt, et al., Trophic Level are Differentially Sensitive to Climate.
Ecology, 84(2003) 2444-2453.
[10] O. J. Schmitz, E. Post, C. E. Burns, K. M. Johanston, Ecosystem
Response to Global Climate Change: Moving Beyond Color Mapping.
BioScience, 53(2003) 1199-1205.
[11] D. J . Wollkind, J. A. Logan, Temperature-Dependent Predator-Prey Mite
Ecosystem on Apple Tree Foliage. J. Math. Biol., 6(1978) 265-283.
[12] D. J. Wollkind, J. B. Collings, J. A. Logan, Metastability in a
Temperature-Dependent Model System for Predator-Prey Mite Outbreak
Interactions on Fruit Trees. Bull. Math. Biol., 50(1988) 379-409.
[13] D. J. Wollkind, J. B. Collings, M. C. B. Barba, Diffusive Instabilities
in One-Dimensinonal Temperature-Dependent Model System for a Mite
Predator-Prey Interaction on Fruit Trees: Dispersal Motility and Aggregative
Preytaxis Effects. J. Math. Biol., 29(1991) 339-362.
[14] J. B. Collings, D. J. Wollkind, M. E. Moody, Outbreaks and Oscillations
in a Temperature-Dependent Model for a Mite Predator-Prey Interaction.
Theoret. Popul. Biol., 38(1990) 159-191.
[15] J. B. Collings, Nonlinear Behavior of Parametrically Forced
Temperature-Dependent Model for a Mite Predator-Prey Interaction.
Chaos, Solitons and Fractals, 2(1992) 105-137.
[16] J. B. Collings, Bifurcation and Stability Analysis of a Temperature
Dependent Mite Predator-Prey Interaction Model Incorporating a Prey
Refuge. Bull. Math. Biol., 57(1995) 63-76.
[17] J. D. Logan, W. Wolesensky, A. Jpren, Tempeature Dependent Phenology
and Predation in Arthropod System. Ecological Modelling,
196(2006) 471-482.
[18] J. D. Logan, W. Wolesensky, An Index to Measure the effects of
Temperature Change on Trophic Interaction. J. Theroet Biol., 246(2007)
366-376.
[19] J. Norberg, D. Deangelts, Temperature Effects on Stocks and Stability
of a Phytoplankton Zooplankton Model and the Dependence on Light and
Nutrients. Ecological Modelling, 95(1997) 75-86.
[20] X. Zhang, J. R. G. Kreis, Importance of Temperature in Modeling Food
Web-Bioaccmulation in large Aquatic Systems. Ecological Modelling,
218(2008) 315-322.
[1] H. Kopka and P. W. Daly, A Guide to LATEX, 3rd ed. Harlow, England:
Addison-Wesley, 1999.
[2] F. Stordal, Isaken ISA, USEPA and UNEP. Washington, DC,1, 1986.
[3] S. F. Singer, Stratospheric Ozone: Science, Policy, Global Climate
Change. Paragon House, New York, 1989.
[4] O. L. Petchey, U. Brose, B. C. Rall, Predicting the Effects of Temperature
on Food Web Connectance. Phil. Trans. R. Soc., B 365(2010) 2081-
2091.
[5] G. Yvon-Durocher, J. I. Jones, M. Trimmer, G. Woodward, J. M.
Montoya, Warming Alters the Metabolic Balance of Ecosystems. Phil.
Trans. R. Soc., 365(2010) 2117-2126.
[6] H. Sarmento, J. M. Montoya, E. Vazquez-Dominguez, D. Vaque, J. M.
Gasol, , Warming Effect on Marine Food Web Processes: How Far can We
Go When It Comes to Predictions? Phil. Trans. R. Soc., B 365(2010)
2137-2149.
[7] J. H. Brown, J. F. Gillooly, A. P. Allen, V. M. Sanage, G. B. West, Toward
a Metabolic Theory of Ecology Ecology, 85(2004) 1771-1789.
[8] G. B. West, J. H. Brown, B. J. Enquist, A General Model for the Origin
of Allometric Scaling Laws in Biology. Science, 276(1997) 122-126.
[9] W. Voigt, et al., Trophic Level are Differentially Sensitive to Climate.
Ecology, 84(2003) 2444-2453.
[10] O. J. Schmitz, E. Post, C. E. Burns, K. M. Johanston, Ecosystem
Response to Global Climate Change: Moving Beyond Color Mapping.
BioScience, 53(2003) 1199-1205.
[11] D. J . Wollkind, J. A. Logan, Temperature-Dependent Predator-Prey Mite
Ecosystem on Apple Tree Foliage. J. Math. Biol., 6(1978) 265-283.
[12] D. J. Wollkind, J. B. Collings, J. A. Logan, Metastability in a
Temperature-Dependent Model System for Predator-Prey Mite Outbreak
Interactions on Fruit Trees. Bull. Math. Biol., 50(1988) 379-409.
[13] D. J. Wollkind, J. B. Collings, M. C. B. Barba, Diffusive Instabilities
in One-Dimensinonal Temperature-Dependent Model System for a Mite
Predator-Prey Interaction on Fruit Trees: Dispersal Motility and Aggregative
Preytaxis Effects. J. Math. Biol., 29(1991) 339-362.
[14] J. B. Collings, D. J. Wollkind, M. E. Moody, Outbreaks and Oscillations
in a Temperature-Dependent Model for a Mite Predator-Prey Interaction.
Theoret. Popul. Biol., 38(1990) 159-191.
[15] J. B. Collings, Nonlinear Behavior of Parametrically Forced
Temperature-Dependent Model for a Mite Predator-Prey Interaction.
Chaos, Solitons and Fractals, 2(1992) 105-137.
[16] J. B. Collings, Bifurcation and Stability Analysis of a Temperature
Dependent Mite Predator-Prey Interaction Model Incorporating a Prey
Refuge. Bull. Math. Biol., 57(1995) 63-76.
[17] J. D. Logan, W. Wolesensky, A. Jpren, Tempeature Dependent Phenology
and Predation in Arthropod System. Ecological Modelling,
196(2006) 471-482.
[18] J. D. Logan, W. Wolesensky, An Index to Measure the effects of
Temperature Change on Trophic Interaction. J. Theroet Biol., 246(2007)
366-376.
[19] J. Norberg, D. Deangelts, Temperature Effects on Stocks and Stability
of a Phytoplankton Zooplankton Model and the Dependence on Light and
Nutrients. Ecological Modelling, 95(1997) 75-86.
[20] X. Zhang, J. R. G. Kreis, Importance of Temperature in Modeling Food
Web-Bioaccmulation in large Aquatic Systems. Ecological Modelling,
218(2008) 315-322.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:52535", author = "O. P. Misra and Preety Kalra", title = "The Study of Increasing Environmental Temperature on the Dynamical Behaviour of a Prey-Predator System: A Model", abstract = "It is well recognized that the green house gases such
as Chlorofluoro Carbon (CFC), CH4, CO2 etc. are responsible
directly or indirectly for the increase in the average global temperature
of the Earth. The presence of CFC is responsible for
the depletion of ozone concentration in the atmosphere due to
which the heat accompanied with the sun rays are less absorbed
causing increase in the atmospheric temperature of the Earth. The
gases like CH4 and CO2 are also responsible for the increase in
the atmospheric temperature. The increase in the temperature level
directly or indirectly affects the dynamics of interacting species
systems. Therefore, in this paper a mathematical model is proposed
and analysed using stability theory to asses the effects of increasing
temperature due to greenhouse gases on the survival or extinction of
populations in a prey-predator system. A threshold value in terms
of a stress parameter is obtained which determines the extinction or
existence of populations in the underlying system.", keywords = "Equilibria, Green house gases, Model, Populations,Stability.", volume = "5", number = "8", pages = "1187-7", }
