A robust method for quantifying the contribution of transient dynamics to variation in population growth rate

Understanding why population growth rates vary through time is central to ecology, evolution, and conservation. In structured populations, such variation arises from both environmentally-driven fluctuations in vital rates and intrinsic transient dynamics generated by changes in population structure. Despite long-standing recognition of these processes, existing approaches do not provide an exact and general partitioning of their relative contributions. Here, we develop a mathematically rigorous framework that decomposes variation in realized population growth rate into contributions from fluctuations in vital rates and from transient deviations in population structure. Building on stochastic population theory, we derive a first-order decomposition under stationary environmental variation, yielding analytical expressions for the variance components associated with each source. This framework clarifies how damping rate, life-history speed, and covariance among vital rates shape temporal variability in growth. We complement the analytical results with a simulation-based procedure that allows the decomposition to be estimated from time series of population projection matrices without requiring observations of past population structure. Applying the method to empirical case studies spanning plants and animals with contrasting generation times, we show that short-lived species exhibit variability dominated by vital-rate fluctuations, whereas long-lived species can exhibit substantial contributions from transient population structure when vital-rate variation is sufficiently large. Our approach provides a unifying and exact link between stochastic demography and transient dynamics, offering a powerful tool for comparing life histories, testing ecological hypotheses, and evaluating how environmental variability propagates through population structure to influence population growth.