Sex and recombination are widespread, but explaining these phenomena has been 
one of the most difficult problems in evolutionary biology. Recombination is 
advantageous when different individuals in a population carry different 
advantageous alleles. By bringing together advantageous alleles onto the same 
chromosome, recombination speeds up the process of adaptation and opposes the 
fixation of harmful mutations by means of Muller's ratchet. Nevertheless, 
adaptive substitutions favour sex and recombination only if the rate of adaptive 
mutation is high, and Muller's ratchet operates only in small or asexual 
populations. Here, by tracking the fate of modifier alleles that alter the 
frequency of sex and recombination, we show that background selection against 
deleterious mutant alleles provides a stochastic advantage to sex and 
recombination that increases with population size. The advantage arises because, 
with low levels of recombination, selection at other loci severely reduces the 
effective population size and genetic variance in fitness at a focal locus (the 
Hill-Robertson effect), making a population less able to respond to selection 
and to rid itself of deleterious mutations. Sex and recombination reveal the 
hidden genetic variance in fitness by combining chromosomes of intermediate 
fitness to create chromosomes that are relatively free of (or are loaded with) 
deleterious mutations. This increase in genetic variance within finite 
populations improves the response to selection and generates a substantial 
advantage to sex and recombination that is fairly insensitive to the form of 
epistatic interactions between deleterious alleles. The mechanism supported by 
our results offers a robust and broadly applicable explanation for the 
evolutionary advantage of recombination and can explain the spread of costly 
sex.