The paper discusses the impact of linkage on the limits of artificial selection in small populations. It builds on earlier work by Robertson (1960) and extends it to consider the effects of linkage between two additive loci. The study uses Monte Carlo simulations to analyze how linkage affects the response to artificial selection, particularly in the context of linkage disequilibrium and the chance of fixation of alleles. The paper begins by reviewing the theoretical framework for selection in finite populations, emphasizing the role of gene frequency distribution and the diffusion equation. It then presents the general differential equation describing the selection process for multiple loci, including the effects of gametic frequencies, linkage disequilibrium, and recombination. The study uses Monte Carlo simulations to explore the effects of linkage on the response to artificial selection. It finds that linkage can significantly reduce the response to selection, even when there are no interactions between loci. The results show that the chance of fixation of alleles is influenced by the initial gene frequencies and the effect of the loci on the character under selection. The paper also discusses the relationship between the recombination fraction and the response to selection, showing that higher recombination rates can increase the response. The paper further examines the effects of linkage on the population mean under artificial selection. It finds that the response to selection is reduced when genes are tightly linked, especially when both genes have a low initial frequency and large effect. The study also shows that the response to selection is influenced by the initial frequencies and effects of the loci, and that the chance of fixation of alleles is affected by the tightness of linkage. The paper concludes that the effects of linkage on the limits of artificial selection are complex and depend on various factors, including the initial frequencies and effects of the loci, the recombination fraction, and the population size. The results suggest that tight linkage can significantly reduce the response to selection, even in the absence of interactions between loci. The study also highlights the importance of considering the effects of linkage in the design of artificial selection programs.The paper discusses the impact of linkage on the limits of artificial selection in small populations. It builds on earlier work by Robertson (1960) and extends it to consider the effects of linkage between two additive loci. The study uses Monte Carlo simulations to analyze how linkage affects the response to artificial selection, particularly in the context of linkage disequilibrium and the chance of fixation of alleles. The paper begins by reviewing the theoretical framework for selection in finite populations, emphasizing the role of gene frequency distribution and the diffusion equation. It then presents the general differential equation describing the selection process for multiple loci, including the effects of gametic frequencies, linkage disequilibrium, and recombination. The study uses Monte Carlo simulations to explore the effects of linkage on the response to artificial selection. It finds that linkage can significantly reduce the response to selection, even when there are no interactions between loci. The results show that the chance of fixation of alleles is influenced by the initial gene frequencies and the effect of the loci on the character under selection. The paper also discusses the relationship between the recombination fraction and the response to selection, showing that higher recombination rates can increase the response. The paper further examines the effects of linkage on the population mean under artificial selection. It finds that the response to selection is reduced when genes are tightly linked, especially when both genes have a low initial frequency and large effect. The study also shows that the response to selection is influenced by the initial frequencies and effects of the loci, and that the chance of fixation of alleles is affected by the tightness of linkage. The paper concludes that the effects of linkage on the limits of artificial selection are complex and depend on various factors, including the initial frequencies and effects of the loci, the recombination fraction, and the population size. The results suggest that tight linkage can significantly reduce the response to selection, even in the absence of interactions between loci. The study also highlights the importance of considering the effects of linkage in the design of artificial selection programs.