Ecologically driven sympatric speciation has received much attention recently. We investigate a multilocus model of a quantitative trait that is under frequency-dependent selection caused by intraspecific competition and acts as mating character for assortment. We identify the conditions that lead to the establishment of reproductively isolated clusters. This may be interpreted as evolutionary splitting or sympatric speciation. In our model, there are parameters that independently determine the strength of assortment, the costs for being choosy, and the strength of frequency-dependent natural selection. Sufficiently strong frequency dependence leads to disruptive selection on the phenotypes. The population consists of (sexual) haploid individuals. If frequency dependence is strong enough to induce disruptive selection and costs are absent or low, the result of evolution depends in a distinctive nonlinear way on the strength of assortment: under moderately strong assortment, less genetic variation is maintained than under weak or strong assortment, and sometimes there is none at all. Evolutionary splitting occurs only if frequency dependence and assortment are both strong enough and costs are low. Even then, the evolutionary outcome depends on the genetics and the initial conditions. The roles of the number of loci, of linkage, and of asymmetric selection are also explored.