Visualization of changes in relationships among traits over time; example in type traits

Genetic evaluations usually include many correlated traits. Their evaluation and use in the selection index rely on genetic parameters that change over time, with these changes potentially accelerating under genomic selection. However, estimating the changes with current methods and large genomic information is computationally prohibitive, and interpreting changes in relationships among many traits is difficult. The purpose of this study is to present a methodology to visualize changes in complex relationships among traits over time. Data included genetic correlations among 18 linear conformation traits of US Holsteins, computed by GPP (Genetic Parameters via Predictivity), for yearly time slices from 2010 to 2020, using all available pedigree, phenotypic, and genomic information. GPP relies on predictivity of adjusted phenotypes from validation population on EBV from reference population and allows estimation by time slices using complete commercial data. In 2010, the reference population included cows born in 2000-2008, and the validation population included cows born in 2009-2011. In subsequent years, the population advanced by one year. Using genetic correlations for the year 2020, each trait was regressed on 2, 3, and 4 remaining conformation (also known as type) traits chosen by the best fit (R²). Regression coefficients were then recomputed for the years 2010-2019. Graphs of the coefficients over time for each trait and 2-4 traits in the regression indicated changing relationships among the traits over time. For example, with 2 traits in the regression, fore udder attachment was estimated as a function of udder depth and rear udder width (R² = 0.84); the addition of stature increased R² by 0.03 and adding body depth increased R² by an additional 0.04. Biplots of 2 principal components in the 4-trait model indicated that the impact of rear udder width was similar to that of body depth and stature in 2010 but more differentiated in 2020. In general, predictions with 4 traits were less stable. Changes in the dynamics of correlated traits can be visualized by regression coefficients from equations involving 2 to 4 correlated traits and corresponding biplots of the 2 principal components.