Adaptation in asexual populations has often been depicted as a series of selective sweeps, each fixing a new adaptive mutation along with the rest of the genome in which it arose and thereby eliminating genetic variation. Yet even in the artificially simple environments of most microbial evolution experiments, the evolution and persistence of diversity in initially homogeneous populations through frequency-dependent selection have been observed repeatedly. A longstanding hypothesis for the advantage of sex, often referred to as the Fisher-Muller hypothesis, is that by combining mutations from separate lineages, sex relieves the clonal interference that otherwise would result from competition between them. This hypothesis, supported by some microbial evolution experiments, also assumes that the speed of adaptation is set by the rate at which new mutations can be fixed. But the recurrent observation of persistent diversity and ecological specialization in microbial experiments suggests that this is not always the case. Where diversification and specialization occur by the assembly of distinct co-adapted gene complexes in different lineages, outcrossing might impede adaptation, by producing recombinants that are well-adapted to the niche of neither lineage. Results from some yeast evolution experiments are not inconsistent with this suggestion.