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Quantitative or complex traitsare controlled by many genes and environmental factors. Most traits inlivestock breeding are quantitative traits. Mapping genes and causativemutations generating the genetic variance of these traits is still a veryactive area of research in livestock genetics. Since genome-wide and denseSNP panels are available for most livestock species, genome-wide associationstudies (GWASs) have become the method of choice in mapping experiments.Different statistical models are used for GWASs. We will review thefrequently used single-marker models and additionally describe Bayesianmulti-marker models. The importance of nonadditive genetic andgenotype-by-environment effects along with GWAS methods to detect them willbe briefly discussed. Different mapping populations are used and will also bereviewed. Whenever possible, our own real-data examples are included toillustrate the reviewed methods and designs. Future research directionsincluding post-GWAS strategies are outlined

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Invited review: Genome-wide association analysis for quantitative traits in livestock – a selective review of statistical models and experimental designs