A major question in ecology is how age-specific variation in demographic parameters influences population dynamics. Based on long-term studies of growing populations of birds and mammals, we analyze population dynamics by using fluctuations in the total reproductive value of the population. This enables us to account for random fluctuations in age distribution. The influence of demographic and environmental stochasticity on the population dynamics of a species decreased with generation time. Variation in age-specific contributions to total reproductive value and to stochastic components of population dynamics was correlated with the position of the species along the slow-fast continuum of life-history variation. Younger age classes relative to the generation time accounted for larger contributions to the total reproductive value and to demographic stochasticity in "slow" than in "fast" species, in which many age classes contributed more equally. In contrast, fluctuations in population growth rate attributable to stochastic environmental variation involved a larger proportion of all age classes independent of life history. Thus, changes in population growth rates can be surprisingly well explained by basic species-specific life-history characteristics.