MODELING THE DEPLETION OF A RENEWABLE RESOURCE BY POPULATION AND INDUSTRIALIZATION: EFFECT OF TECHNOLOGY ON ITS CONSERVATION
Article first published online: 5 APR 2011
©2011 Wiley Periodicals, Inc.
Natural Resource Modeling
Volume 24, Issue 2, pages 242–267, May 2011
How to Cite
SHUKLA, J.B., LATA, K. and MISRA, A.K. (2011), MODELING THE DEPLETION OF A RENEWABLE RESOURCE BY POPULATION AND INDUSTRIALIZATION: EFFECT OF TECHNOLOGY ON ITS CONSERVATION. Natural Resource Modeling, 24: 242–267. doi: 10.1111/j.1939-7445.2011.00090.x
- Issue published online: 26 APR 2011
- Article first published online: 5 APR 2011
- Received by the editors on 7th July 2010. Accepted 15th February 2011.
- Mathematical model;
- resource biomass;
- technological effort;
Abstract In this paper, a nonlinear mathematical model is proposed and analyzed to study the depletion of a renewable resource by population and industrialization with resource-dependent migration. The effect of technology on resource conservation is also considered. In the modeling process, four variables are considered, namely, density of a renewable resource, population density, density of industrialization, and technological effort. Both the growth rate and carrying capacity of resource biomass, which follows logistic model, are assumed to be simultaneously depleted by densities of population and industrialization but it is conserved by technological effort. It is further assumed that densities of population and industrialization increase due to increase in the density of renewable resource. The growth rate of technological effort is assumed to be proportional to the difference of carrying capacity of resource biomass and its current density. The model is analyzed by using the stability theory of differential equations and computer simulation. The model analysis shows that the biomass density decreases due to increase in densities of population and industrialization. It decreases further as the resource-dependent industrial migration increases. But the resource may never become extinct due to population and industrialization, if technological effort is applied appropriately for its conservation.