Population inertia and its sensitivity to changes in vital rates or initial conditions

Many studies have examined Keyfitz’s population momentum, a special case of inertia in long-term population size resulting from demographic transition to the stationary population growth rate. Yet, population inertia can be produced by any demographic perturbation (i.e., not just perturbations that produce stationary growth). Insight into applied population dynamics, population ecology, and life history evolution has been gained using perturbation analysis of the population growth rate. However, a similar, generalized framework for perturbation analysis of population inertia has not been developed. We derive general formulas for the sensitivity of population inertia to change in any vital rate or initial population structure. These formulas are readily computable, and we provide examples of their potential use in life history and applied studies of populations.