Baseline models of spatial population dynamics

ABSTRACT

To understand human population dynamics fully, before considering complex human agency it may be useful to construct baseline models to see where such agency may and may not be necessary. In fact, the dynamics of human populations may be amenable to mathematical modeling with relatively parsimonious mechanisms. We review some of the more prominent of such models, namely, the spatial Galton-Watson (GW) model, modifications of the GW model that add migration and immigration, and the Bolker-Pacala model, in which mortality (or birth rate) is affected by competition. We show that change in the distribution of population density over the last century for 12 American rural states may be captured by the simplest of the models, the spatial GW model.

KEYWORDS:

• Galton-Watson process
• Markov models
• mathematical models
• population dynamics