Inequality, heterogeneity, and chance: Multiple factors and their interactions

A heterogeneous population is a mixture of groups differing in vital rates. In such a population, some of the variance in demographic outcomes (e.g., longevity, lifetime reproduction) is due to heterogeneity and some is the result of stochastic demographic processes. Many studies have partitioned variance into its between-group and within-group components, but have focused on single factors. Especially for longevity, variance due to stochasticity is far greater than variance due to heterogeneity. Here we extend such analyses to multiple-factor studies, making it possible to calculate the contributions to variance of each factor and each of the interactions among factors. We treat the population as a mixture and use the marginal mixing distributions to compute variance components. Examples are presented: longevity as a function of sex, race and U.S. state of residence; and lifetime reproduction among a set of developed countries and as a result of resource availability and pesticide exposure.