Natural environments are never truly constant, but the evolutionary implications of temporally varying selection pressures remain poorly understood. Here we investigate how the fate of a new mutation in a fluctuating environment depends on the dynamics of environmental variation and on the selective pressures in each condition. We find that even when a mutation experiences many environmental epochs before fixing or going extinct, its fate is not necessarily determined by its time-averaged selective effect. Instead, environmental variability reduces the efficiency of selection across a broad parameter regime, rendering selection unable to distinguish between mutations that are substantially beneficial and substantially deleterious on average. Temporal fluctuations can also dramatically increase fixation probabilities, often making the details of these fluctuations more important than the average selection pressures acting on each new mutation. For example, mutations that result in a trade-off between conditions but are strongly deleterious on average can nevertheless be more likely to fix than mutations that are always neutral or beneficial. These effects can have important implications for patterns of molecular evolution in variable environments, and they suggest that it may often be difficult for populations to maintain specialist traits, even when their loss leads to a decline in time-averaged fitness.population genetics | fixation probability | fluctuating environment | effective diffusion E volutionary trade-offs are widespread: Adaptation to one environment often leads to costs in other conditions. For example, drug resistance mutations often carry a cost when the dosage of the drug decays (1), and seasonal variations in climate can differentially select for certain alleles in the summer or winter (2). Similarly, laboratory adaptation to specific temperatures (3, 4) or particular nutrient sources (5, 6) often leads to declines in fitness in other conditions. Related trade-offs apply to any specialist phenotype or regulatory system that incurs a general cost to confer benefits in specific environmental conditions (7). Despite the ubiquity of these trade-offs, it is not always easy to predict when a specialist phenotype can evolve and persist. How useful must a trait be on average to be maintained? How regularly does it need to be useful? How much easier is it to maintain in a larger population compared with a smaller one?The answers to these questions depend on two major factors. First, how often do new mutations create or destroy a specialist phenotype, and what are their typical costs and benefits across environmental conditions? This is fundamentally an empirical question, which depends on the costs and benefits of the trait in question, as well as its genetic architecture (e.g., the target size for loss-of-function mutations that disable a regulatory system). In this paper, we focus instead on the second major factor: given that a particular mutation occurs, how does its long-term fate depend on its fitn...