The equation for response to selection and its use for prediction

Area of Science:

• Evolutionary Computation
• Quantitative Genetics
• Bioinformatics

Background:

• The Breeder Genetic Algorithm (BGA) is inspired by livestock breeding principles.
• Predicting breeding experiment outcomes relies on the response to selection (RS) equation.
• The RS equation links fitness changes to selection intensity and realized heritability.

Purpose of the Study:

• To derive an exact RS equation for proportionate selection under linkage equilibrium.
• To compare Mendelian two-parent recombination with gene-pool recombination (UMD algorithms).
• To compute an exact RS equation for binary tournament selection and assess heritability estimation.

Main Methods:

• Derivation of the exact RS equation for proportionate selection in infinite populations at linkage equilibrium.
• Comparison of Mendelian recombination with univariate marginal distribution (UMD) algorithms.
• Computation of an exact RS equation for binary tournament selection.

Main Results:

• The derived RS equation is an exact form, containing Fisher's fundamental theorem as an approximation.
• UMD algorithms maintain linkage equilibrium, allowing for exact long-term RS prediction.
• Mendelian recombination primarily utilizes additive genetic variance; binary tournament selection yields different realized heritability estimates compared to proportionate selection.

Conclusions:

• The study provides an exact RS equation applicable to UMD algorithms for precise long-term predictions.
• Mendelian recombination's effectiveness is linked to additive genetic variance.
• Classical heritability estimation methods may be inaccurate for binary tournament selection.