The Deviant Dynamics of Death in Heterogeneous Populations

The members of most populations gradually die off or drop out: people die, machines wear out, residents move out, etc. In many such "aging" populations, some members are more likely to "die" than others. Standard analytical methods largely ignore this heterogeneity; the methods assume that all members of a population at a given age face the same probability of death. This paper presents some mathematical methods for studying how the behavior over time of a heterogeneous population deviates from the behavior of the individuals that make up the population. The methods yield some startling results: individuals age faster than populations, eliminating a cause of death can decrease life expectancy, a population can suffer a higher death rate than another population even though its members have lower death rates, population death rates can be increasing even though its members' death rates are decreasing.