Short communication: Recursive model approach to traits defined as ratios: Genetic parameters and breeding values.

Area of Science:

• Quantitative Genetics
• Animal Breeding
• Statistical Modeling

Background:

• Ratio traits (Y2/Y1) are common in biological and agricultural sciences.
• Traditional methods for analyzing ratio traits can be complex and may not fully capture underlying genetic relationships.
• Accurate analysis of ratio traits is crucial for genetic parameter estimation and evaluation.

Purpose of the Study:

• To propose a novel recursive modeling method for analyzing ratio traits (Y2/Y1).
• To develop a proxy for ratio traits as Y2 adjusted for the effect of Y1 (Y2 - λ × Y1).
• To demonstrate the method's application in estimating genetic parameters and performing genetic evaluations for production traits.

Main Methods:

• Utilized a recursive modeling approach to define a proxy for ratio traits.
• Derived parameter estimates for the recursive model (Y1 → Y2) from an equivalent 2-trait mixed effects model.
• Employed linear (location) and quadratic (dispersion) transformations for parameter derivation.
• Applied the method to milk fat and protein content data using the Canadian test-day model.

Main Results:

• The proposed method provides a viable proxy (Y2 - λ × Y1) for analyzing ratio traits.
• Parameter estimates for the recursive model can be successfully derived from standard multiple-trait models.
• The application to milk production traits demonstrated the method's practical utility.

Conclusions:

• The novel recursive modeling approach offers an effective way to analyze ratio traits.
• This method facilitates the use of standard multiple-trait modeling techniques for ratio trait analysis.
• The approach is potentially useful for genetic parameter estimation and genetic evaluation of various Y2/Y1 traits.