Dissecting the genetic basis of phenotypic variation in natural populations is a long-standing goal in evolutionary biology. One open question is whether quantitative traits are determined only by large numbers of genes with small effects, or whether variation also exists in large-effect loci. We conducted genomewide association analyses of forehead patch size (a sexually selected trait) on 81 whole-genome-resequenced male collared flycatchers with extreme phenotypes, and on 415 males sampled independent of patch size and genotyped with a 50K SNP chip. No SNPs were genomewide statistically significantly associated with patch size. Simulation-based power analyses suggest that the power to detect large-effect loci responsible for 10% of phenotypic variance was 0.8 for resequencing of extreme phenotypes (N = 243), but power remained 0.8 when analysing 415 randomly sampled phenotypes. However, power of the 50K SNP chip to detect large-effect loci was nearly 0.8 in simulations with a small effective population size of 1500. These results suggest that reliably detecting large-effect trait loci in large natural populations will often require thousands of individuals and near complete sampling of the genome. Encouragingly, far fewer individuals and loci will often be sufficient to reliably detect large-effect loci in small populations with widespread strong linkage disequilibrium.