Abstract
ObjectiveA formula is needed that is practical for current livestock breeding methods and that predicts the approximate rate of inbreeding (ΔF) 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.MethodsThe 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.ResultsWe 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%.ConclusionThe formula we developed here would be highly useful as a practical method for predicting the approximate rate of inbreeding (ΔF) in populations where selection is performed according to four-path programs.
Highlights
Deterministic predictions of response to multi-trait genomic selection in a single generation in a population with four-path programs, was developed [1, 2]
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
Rates of inbreeding can be expressed in terms of the expected contributions of these categories, [6, 9, 10, 11 10]: E (ΔF) =2 1′ NE(u2 ) + 8 1′Nδ, where 1′ = (1 1 1 1), N is a 4×4 diagonal matrix containing the number of selected parents for element (i, i) as Ni,i, N1,1 is the number of sires in SS and is referred to as NSS, N2,2 is the number of sires in SD and is referred to as NSD, N3,3 is the number of dams in DS and is referred to as NDS, and N4,4 is the number of dams in DD and is referred to as NDD
Summary
Deterministic predictions of response to multi-trait genomic selection in a single generation in a population with four-path programs, was developed [1, 2]. When creating formulas for calculating the asymptotic response to index or single-trait selection in four-path selection programs rather than in a single generation, the initial genetic response in generation 0 overestimated the asymptotic response due to the decrease in equilibrium genetic variance from generation 0 onwards [3]. To safeguard the genetic variation of the population over the long term, the rate of inbreeding needs to be restricted to an acceptable level. One needs to know the expected rate of inbreeding as well as the equilibrium genetic response before choosing a breeding scheme. A population with discrete generations under mass selection in a four-path selection program is modeled to predict the rate of inbreeding in the long term. When sires in the SS path are used with constant selection intensity and in equal number throughout the usage period of several years, every SS sire belongs to a single or exclusive category
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