Population Dynamics: Mathematic Models of Population, Development, and Natural Resources

Abstract

Whereas interactions of population and natural resource growth have generally been modeled using large-scale numerical simulation studies, we review small-scale models that permit partially analytical results and can capture some of the salient features observed in history. This article refers only to models that concentrate on renewable resources since these are the most interesting and least understood as regards changes in population structures and dynamics. It starts by reviewing models of population and resource dynamics that refer to subsistence economies. Within this class of models it is possible to investigate how the equilibrium between the resource and population stock changes, dependent on the functional relations that govern the dynamics of population and resources. But as societies become less bound to the land, more urbanized, and more technological, resources might still be at risk, albeit no longer from positive population growth but rather from the environmental costs of consumption and production. To capture the impact of population growth on the environment, demographic impact models have been developed aimed at decomposing the effect on the environment from population on the one hand and that from consumption and technology on the other. The article concludes our review with a look at models of environmental influences on population dynamics.