Invited review: Recursive models in animal breeding: Interpretation, limitations, and extensions

Area of Science:

• Quantitative Genetics
• Animal Breeding
• Statistical Modeling

Background:

• Structural equation models (SEM) enable the analysis of causal relationships between variables, distinguishing between unidirectional (recursive models; RM) and bidirectional (simultaneous models) causality.
• Recursive models (RM) are a type of SEM used in animal breeding to understand causal effects and interpret genetic parameters and estimated breeding values.

Purpose of the Study:

• To evaluate the properties of recursive models (RM) in animal breeding.
• To clarify the interpretation of genetic parameters and estimated breeding values derived from RM.
• To compare RM with mixed multitrait models (MTM) for causal inference in animal genetics.

Main Methods:

• Review and comparison of statistical properties between recursive models (RM) and mixed multitrait models (MTM).
• Analysis of variance-covariance matrices and parameter restrictions for model identification and inference.
• Transformation of estimates between RM and MTM frameworks.

Main Results:

• RM and MTM are statistically equivalent under specific assumptions regarding variance-covariance matrices and model identification.
• Biological interpretations of breeding values differ: MTM breeding values represent the total additive genetic effect, while RM breeding values account for causal traits being held constant.
• Differences in genetic effects between RM and MTM can identify genomic regions influencing trait variation directly or indirectly.

Conclusions:

• RM and MTM provide complementary insights into genetic architecture and causality in animal breeding.
• RM breeding values are useful for identifying causal pathways, while MTM breeding values are recommended for selection purposes.
• Extensions of RM facilitate modeling complex quantitative traits, including sequentially expressed traits and subgroup-specific causality.