The thesis focuses on methods to improve GWAS and genomic prediction using combined Holstein populations and investigations G by E interaction. The conclusions are: 1) Prediction reliabilities for Brazilian Holsteins can be increased by adding Nordic and Frensh genotyped bulls and a large G by E interaction exists between populations. 2) Combining data from Chinese and Danish Holstein populations increases the power of GWAS and detects new QTL regions for milk fatty acid traits. 3) The novel multi-trait Bayesian model efficiently estimates region-specific genomic variances, covariances and correlations between Chinese and Nordic Holsteins