ABSTRACT
Demographic population models are derived from descriptions of how individuals move through their life cycles. In this sense all demographic models are based on information about individuals. Individuals are described in terms of their i-states (sensu Metz and Diekmann), which provide the information necessary to specify the response of an individual to its environment. Age, size, and physiological state are typical i-state variables. The state of the population, or p-state, is derived from the i-states. If all individuals experience the same environment (we refer to this condition as mixing), the p-state is a distribution function over the set of i-states. Most demographic models assume this condition; we call these models i-state distribution models. When the mixing assumption fails, for example due to local interactions among individuals, each individual must be followed; we call these models i-state configuration models. We use this framework to examine examples of the relations between the individual and the population in demography, including multi-type branching processes and stable population theory, micro-simulations of reproduction and family structure, epidemic models and percolation theory, and hazard analysis.
