Climate changes include concurrent changes in environmental mean, variance and extremes, and it is challenging to understand their respective impact on wild populations, especially when contrasted age-dependent responses to climate occur. We assessed how changes in mean and standard deviation of sea surface temperature (SST), frequency and magnitude of warm SST extreme climatic events (ECE) influenced the stochastic population growth rate log(?s) and age structure of a black-browed albatross population. For changes in SST around historical levels observed since 1982, changes in standard deviation had a larger (threefold) and negative impact on log(?s) compared to changes in mean. By contrast, the mean had a positive impact on log(?s). The historical SST mean was lower than the optimal SST value for which log(?s) was maximized. Thus, a larger environmental mean increased the occurrence of SST close to this optimum that buffered the negative effect of ECE. This 'climate safety margin' (i.e. difference between optimal and historical climatic conditions) and the specific shape of the population growth rate response to climate for a species determine how ECE affect the population. For a wider range in SST, both the mean and standard deviation had negative impact on log(?s), with changes in the mean having a greater effect than the standard deviation. Furthermore, around SST historical levels increases in either mean or standard deviation of the SST distribution led to a younger population, with potentially important conservation implications for black-browed albatrosses.This article is part of the themed issue 'Behavioural, ecological and evolutionary responses to extreme climatic events'.