The paper by W. G. Hill and Alan Robertson explores the impact of linkage on the limits of artificial selection in small populations. They extend Robertson's earlier work on single genes to the case of multiple loci, focusing on two additive loci. The authors use Monte Carlo simulations to investigate the effects of linkage on the rate and extent of selection, particularly in the context of quantitative traits. Key findings include: 1. **Basic Theory**: The authors derive a diffusion equation to describe the change in gene frequency over time, considering both additive and selective advantages. They show that the chance of fixation of a gene is a function of the initial gene frequency, population size, and selection coefficients. 2. **Monte Carlo Simulation**: They simulate the selection process using a high-speed computer, focusing on the effects of linkage, recombination, and initial gene frequencies. The simulations reveal that tight linkage can significantly reduce the rate of selection advance, even when recombination is present. 3. **Results**: - **Influence of the Second Locus**: Segregation at a second locus has minimal impact on the chance of fixation at the first locus unless its effect is significantly greater than that of the first locus. - **Recombination Frequency**: The rate of selection advance is influenced by the recombination frequency, with tight linkage reducing the advance in the early generations. - **Effective Selection Parameter**: The effective selection parameter at the first locus is influenced by the presence of the second locus, with tight linkage reducing the effective selection intensity. - **Population Size**: Larger populations have a more linear relationship between the chance of fixation and the recombination frequency. - **Chance of Fixation of Gametes**: The chance of fixation of different gametes is influenced by both the initial frequencies and the effects of the loci, with tight linkage affecting the balance between favorable and unfavorable gametes. 4. **Discussion**: The authors discuss the implications of their findings for artificial selection programs, suggesting that the intensity of selection should be adjusted to maximize the advance, especially when multiple linked loci are involved. They also address the contradiction between their theoretical predictions and simulation results, attributing it to the effective population size and the development of negative disequilibrium during selection. Overall, the study provides valuable insights into how linkage affects the efficiency of artificial selection in small populations, highlighting the importance of considering linkage in genetic improvement programs.The paper by W. G. Hill and Alan Robertson explores the impact of linkage on the limits of artificial selection in small populations. They extend Robertson's earlier work on single genes to the case of multiple loci, focusing on two additive loci. The authors use Monte Carlo simulations to investigate the effects of linkage on the rate and extent of selection, particularly in the context of quantitative traits. Key findings include: 1. **Basic Theory**: The authors derive a diffusion equation to describe the change in gene frequency over time, considering both additive and selective advantages. They show that the chance of fixation of a gene is a function of the initial gene frequency, population size, and selection coefficients. 2. **Monte Carlo Simulation**: They simulate the selection process using a high-speed computer, focusing on the effects of linkage, recombination, and initial gene frequencies. The simulations reveal that tight linkage can significantly reduce the rate of selection advance, even when recombination is present. 3. **Results**: - **Influence of the Second Locus**: Segregation at a second locus has minimal impact on the chance of fixation at the first locus unless its effect is significantly greater than that of the first locus. - **Recombination Frequency**: The rate of selection advance is influenced by the recombination frequency, with tight linkage reducing the advance in the early generations. - **Effective Selection Parameter**: The effective selection parameter at the first locus is influenced by the presence of the second locus, with tight linkage reducing the effective selection intensity. - **Population Size**: Larger populations have a more linear relationship between the chance of fixation and the recombination frequency. - **Chance of Fixation of Gametes**: The chance of fixation of different gametes is influenced by both the initial frequencies and the effects of the loci, with tight linkage affecting the balance between favorable and unfavorable gametes. 4. **Discussion**: The authors discuss the implications of their findings for artificial selection programs, suggesting that the intensity of selection should be adjusted to maximize the advance, especially when multiple linked loci are involved. They also address the contradiction between their theoretical predictions and simulation results, attributing it to the effective population size and the development of negative disequilibrium during selection. Overall, the study provides valuable insights into how linkage affects the efficiency of artificial selection in small populations, highlighting the importance of considering linkage in genetic improvement programs.