It is already known that competition among individuals within a population leads to frequency dependent changes in the genotypic fitnesses at a single locus. In this study, we show that competition can also lead to frequency dependent changes in the epistatic interactions between loci. In particular, some common forms of competition can result in frequency dependent negative epistasis at the level of the realized fitnesses. This leads in turn to the build-up of significant levels of negative linkage disequilibrium among the alleles that affect fitness. Consequently, intraspecific competition may be an important factor in the maintenance of sexual reproduction.