Individual heterogeneity in vital parameters and demographic stochasticity

Most population models assume that individuals have equal opportunities for survival and reproduction, although many natural populations consist of individuals with different vital parameters that remain different over time. Individual heterogeneity in vital parameters, which may depend on age or stage, can alter many population characteristics compared with a homogeneous population, affecting both deterministic and stochastic properties of the population process. Demographic variance is an important parameter influenced by heterogeneity. However, whether heterogeneity leads to increased or decreased demographic variance has been an unresolved question, except for special cases. Here, we present a general stochastic matrix model for a heterogeneous population that allows us to examine effects of heterogeneity on population dynamics, even when the degree of heterogeneity depends on age. Using this model, we found that the demographic variance may increase, decrease, or remain unaltered compared with a homogeneous comparison model, depending on the vital parameter values and on how these are distributed among individuals at each time step. Furthermore, if the reproductive value is the same for all individuals, heterogeneity has no effect on the demographic variance. Thus, we provide a general theoretical framework for analyzing how individual heterogeneity caused by different biological mechanisms affects fluctuations of especially small populations.