Hill was distinguished for his theoretical contributions to the study of the population and quantitative genetics of finite populations, in particular with respect to multilocus problems. He was the first to present formulae for the expected association of linked genes in finite populations due to random sampling of gametes and for the estimation of these associations from genotype frequencies. He has made major contributions to the analysis of quantitative variation in random breeding populations, both in the design and interpretation of selection experiments and in the analysis of similarity between relatives. He applied these concepts in his own selection experiments in the laboratory and in farm animal improvement programmes.