Environmental stochasticity impacts population dynamics and their viability. As such, understanding how organisms cope with this variability is crucial. Here, we investigate demographic buffering, the ability of populations to maintain stable growth despite environmental fluctuations. We integrate well-established stochastic and deterministic approaches to investigate characteristics of demographic buffering, analysing stochastic elasticities and self-second derivatives of deterministic population growth rate. We test the hypothesis that buffered species exhibit low stochastic elasticity to temporal variability and signs of concave selection (i.e. negative second derivatives of population growth rate with respect to demographic processes), reducing variance in key demographic processes. Analysing 43 natural populations of 37 mammal species, we find limited support for this hypothesis. Indeed, while primates often show low stochastic elasticity, concave selection is less prevalent than expected. Our findings highlight the complex and dynamic relationship between demographic processes, environmental variability, and selection pressures in determining population persistence.