The composition of the genome after introgression of a marker gene from a donor to a recipient breed was studied using analytical and simulation methods. Theoretical predictions of proportional genomic contributions, including donor linkage drag, from ancestors used at each generation of crossing after an introgression programme agreed closely with simulated results. The obligate drag, the donor genome surrounding the target locus that cannot be removed by subsequent selection, was also studied. It was shown that the number of backcross generations and the length of the chromosome affected proportional genomic contributions to the carrier chromosomes. Population structure had no significant effect on ancestral contributions and linkage drag but it did have an effect on the obligate drag whereby larger offspring groups resulted in smaller obligate drag. The implications for an introgression programme of the number of backcross generations, the population structure and the carrier chromosome length are discussed. The equations derived describing contributions to the genome from individuals from a given generation provide a framework to predict the genomic composition of a population after the introgression of a favourable donor allele. These ancestral contributions can be assigned a value and therefore allow the prediction of genetic lag.