We examine the behavior of sexual and asexual populations in modular multipeaked fitness landscapes and show that sexuals

can systematically reach different, higher fitness adaptive peaks than asexuals. Whereas asexuals must move against selection

to escape local optima, sexuals reach higher fitness peaks reliably because they create specific genetic variants that “skip over”

fitness valleys, moving from peak to peak in the fitness landscape. This occurs because recombination can supply combinations

of mutations in functional composites or “modules,” that may include individually deleterious mutations. Thus when a beneficial

module is substituted for another less-fit module by sexual recombination it provides a genetic variant that would require either

several specific simultaneous mutations in an asexual population or a sequence of individual mutations some of which would be

selected against. This effect requires modular genomes, such that subsets of strongly epistatic mutations are tightly physically

linked. We argue that such a structure is provided simply by virtue of the fact that genomes contain many genes each containing

many strongly epistatic nucleotides. We briefly discuss the connections with “building blocks” in the evolutionary computation

literature. We conclude that there are conditions in which sexuals can systematically evolve high-fitness genotypes that are

essentially unevolvable for asexuals.