Population dynamics are affected by changes in both the mean and standard deviation of climate, e.g., changes in average temperature are likely to affect populations, but so are changes in the strength of year-to-year temperature variability. The impacts of increases in average temperature are extensively researched, while the impacts of changes in climate variability are less studied. Is the greater attention given to changes in mean environment justified? To help answer this question we developed a simple population model, explicitly linked to an environmental process. We used the model to compare the sensitivities of a population's long-term stochastic growth rate, a measure of fitness, to changes in the mean and standard deviation of the environment. Results are interpreted in light of a comparative analysis of the relative magnitudes of change in means and standard deviations of biologically relevant climate variables in the United States. Results show that changes in the variability of the environment can be more important for many populations. Changes in mean conditions are likely to have a greater impact than changes in variability on populations far from their ideal environment, for example, populations near species range boundaries and potentially of conservation concern. Populations near range centres and close to their ideal environment are more likely to be affected by changes in variability. Among pest and insect disease vectors, as well as species of commercial value, populations likely to be of greatest economic and public health significance are those near species range centers, living in a near-ideal environment for the species. Observed changes in the variability of climate variables may benefit these populations.