Estimation & Prediction

Derivation of the additive covariance between a continuous and a binary trait on the observed scale and the benefits of the correlated continuous trait on the genomic evaluation of the binary trait

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Abstract

The genomic evaluation of binary traits is challenging with complex data structures such as when the trait is sex-limited and/or many young animals lack phenotypes. In such cases, a convenient strategy is a threshold-linear bivariate model to improve convergence by exploiting the stabilizing effect of a correlated continuous trait. An additional strategy to improve the efficiency of the genomic evaluation for binary traits could be a linear-linear bivariate model; however, to harness the benefit of the correlated continuous trait, the covariance between the two traits is needed on the observed scale. Our objectives in this study were 1) to derive the covariance between a binary and a continuous trait in the observed scale, and 2) to test the benefits of the correlated continuous trait in terms of computing time as well as correlation of estimated breeding values (EBV) on the liability and observed scales. We used data from a Holstein population with 8.1M binary records for heifer conception and 9M records for age at first calving. The pedigree consisted of 15M animals, of which 1.8M were genotyped. Estimates of (co)variance components were estimated with a threshold-linear model. We compared threshold, linear, threshold-linear and linear-linear models by computing time at convergence and the correlation of EBV on the liability and observed scales for the binary trait. The covariance between a binary and a continuous trait in the observed scale is derived as the product of the covariance on the liability scale and the height of the standard normal density at the threshold. The incorporation of the continuous correlated trait reduced the computing time by 5.5-fold when comparing the threshold vs. the threshold-linear model; it also increased the correlation between estimated breeding values from 0.91 to 0.99 for all animals in the pedigree, from 0.92 to 0.99 for animals with phenotypes, from 0.94 to 0.99 for animals with genotypes and from 0.95 to 0.99 for animals with phenotypes and genotypes. The linear-linear model reduced computing time by 69% compared to the threshold-linear model (Table1). Harnessing the information of a continuous correlated trait in a linear-linear model in the genomic evaluation of heifer conception and age at first calving is an efficient and accurate approach compared to the benchmark threshold-linear model when the (co)variance components are correctly transformed from the liability to the observed scale.

Keywords: 2026

How to Cite:

Bussiman, F., de Oliveira Padilha, D., Gonzalez-Peà±a, D., Hidalgo, J., Lourenco, D., Misztal, M., Misztal, I., Sánchez-Castro, M. & Vukasinovic, N., (2026) “Derivation of the additive covariance between a continuous and a binary trait on the observed scale and the benefits of the correlated continuous trait on the genomic evaluation of the binary trait”, World Congress on Genetics Applied to Livestock Production Digital Archive 2026(1): 2284754. doi: https://doi.org/10.31274/wcgalp.23612

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