Causal inference for the covariance between breeding values under identity disequilibrium

Area of Science:

• Quantitative genetics
• Statistical genetics
• Animal breeding

Background:

• The covariance matrix of breeding values is crucial for prediction methods.
• Markov causal models offer sparse inverse covariance matrices, reducing computational burden.
• Existing methods often assume gametic equilibrium, neglecting identity disequilibrium.

Purpose of the Study:

• To introduce a novel causal Markov model for predicting breeding values.
• To address the computational complexity of existing models like the ancestral regression (AR).
• To incorporate identity disequilibrium into breeding value prediction.

Main Methods:

• Developed the "ancestral regression to parents" (PAR) causal Markov model.
• Utilized the conditional independence property of the PAR model.
• Derived analytical expressions for covariances between relatives and inbreeding coefficients.

Main Results:

• The PAR model captures identity disequilibrium in breeding value covariances.
• It provides a sparse inverse covariance matrix for efficient computation.
• Analytical expressions for covariances between grandparents, offspring, parents, and collateral relatives were derived.

Conclusions:

• The PAR Markov model effectively accounts for identity disequilibrium.
• It offers computational benefits by producing a sparse inverse covariance matrix.
• This facilitates the solution of mixed model equations in animal breeding.