We present methods for linkage and association mapping of quantitative traits for a founder population with a large, known genealogy. We detect linkage to quantitative-trait loci (QTLs) through a multipoint homozygosity-mapping method. We propose two association methods, one of which is single point and uses a general two-allele model and the other of which is multipoint and uses homozygosity by descent for a particular allele. In all three methods, we make extensive use of the pedigree and genotype information, while keeping the computations simple and efficient. To assess significance, we have developed a permutation-based test that takes into account the covariance structure due to relatedness of individuals and can be used to determine empirical genomewide and locus-specific P values. In the case of multivariate-normally distributed trait data, the permutation-based test is asymptotically exact. The test is broadly applicable to a variety of mapping methods that fall within the class of linear statistical models (e.g., variance-component methods), under the assumption of random ascertainment with respect to the phenotype. For obtaining genomewide P values, our proposed method is appropriate when positions of markers are independent of the observed linkage signal, under the null hypothesis. We apply our methods to a genome screen for fasting insulin level in the Hutterites. We detect significant genomewide linkage on chromosome 19 and suggestive evidence of QTLs on chromosomes 1 and 16.