We consider methods for estimating the relative contributions of different demographic components, and their associated vital rates, to population growth. We identify components of the population at time i (including a component for animals not in the population at i). For each such component we ask the following question: 'What is the probability that an individual randomly selected from the population at time i + 1 was a member of this component at i?' The estimation methods for these probabilities ((i) are based on capture-recapture studies of marked animal populations and use reverse-time modeling. We consider several different sampling situations and present example analyses for meadow voles, Microtus pennsylvanicus. The relationship between these (i parameters and elasticities (and other parameters based on projection matrix asymptotics) is noted and discussed. We conclude by suggesting that model-based asymptotics be viewed as demographic theory and that direct estimation approaches be used to test this theory with data from sampled populations with marked animals.