Does runaway sexual selection work in finite populations?

Fisher's runaway process is an explanation for the origin of conspicuous features which make one sex more attractive to the other. It has been suggested that it could lead to the evolution of sexual characters that significantly impair viability. Runaway selection requires a genetic correlation between alleles affecting the sexual character and alleles affecting the preference. Correlations may be expected because of assortative mating when there is variation in both the sexual character and sexual preferences. We contend that such genetic correlations are unlikely to persist in finite populations. We present simulations which confirm our expectations. They suggest that assortative mating is inefficient at generating correlations, especially if sexual selection maintains characters away from their viability optimum. In finite populations, such weak correlations will be overwhelmed by drift.