Optimal design of quantitative-trait loci (QTL) mapping studies requires a precise understanding of the power of QTL linkage versus QTL association analysis, under a range of different conditions. In this article, we investigate the power of QTL linkage and association analyses for simple random sibship samples, under the variance-components model proposed by Fulker et al. After a brief description of an extension of this variance-components model, we show that the powers of both linkage and association analyses are crucially dependent on the proportion of phenotypic variance attributable to the QTL. The main difference between the two tests is that, whereas the power of association is directly related to the QTL heritability, the power of linkage is related more closely to the square of the QTL heritability. We also describe both how the power of linkage is attenuated by incomplete linkage and incomplete marker information and how the power of association is attenuated by incomplete linkage disequilibrium.