Predicting the rate of inbreeding in populations undergoing four-path selection on genomically enhanced breeding values

Objective: A formula is needed that is practical for current livestock breeding methods and that predicts the approximate rate of inbreeding (???F) in populations where selection is performed according to four-path programs (sires to breed sons, sires to breed daughters, dams to breed sons, and dams to breed daughters). The formula widely used to predict inbreeding neglects selection, we need to develop a new formula that can be applied with or without selection.Methods: The core of the prediction is to incorporate the long-tern genetic influence of the selected parents in four-selection paths executed as sires to breed sons, sires to breed daughters, dams to breed sons, and dams to breed daughters. The rate of inbreeding was computed as the magnitude that is proportional to the sum of squared long-term genetic contributions of the parents of four-selection paths to the selected offspring.Results: We developed a formula to predict the rate of inbreeding in populations undergoing four-path selection on genomically enhanced breeding values and with discrete generations. The new formula can be applied with or without selection. Neglecting the effects of selection led to underestimation of the rate of inbreeding by 40% to 45%. Conclusion: The formula we developed here would be highly useful as a practical method for predicting the approximate rate of inbreeding (Delta F) in populations where selection is performed according to four-path programs.