# Computational and modeling approaches for US threshold genetic evaluations of calving ease

## TL;DR

This paper compares different models and solvers for evaluating calving ease genetics in US dairy cattle, finding that they produce consistent results with varying computational efficiency.

## Contribution

The study introduces and evaluates two genetic evaluation models for calving ease using different computational solvers in US dairy cattle.

## Key findings

- The SMGS and SMAT models produced highly correlated genomic estimated breeding values.
- Newton-Raphson was faster and more computationally efficient than expectation maximization.
- Both models are suitable for routine genetic evaluation of calving ease in US dairy cattle.

## Abstract

Summary: We proposed 2 models for the US calving ease genetic evaluation, each tested with 2 different threshold model solvers. Both models produced consistent correlations, and the solvers yielded comparable results, with the Newton-Raphson-based solver demonstrating faster computational performance. MGS = maternal grandsire.

Summary: We proposed 2 models for the US calving ease genetic evaluation, each tested with 2 different threshold model solvers. Both models produced consistent correlations, and the solvers yielded comparable results, with the Newton-Raphson-based solver demonstrating faster computational performance. MGS = maternal grandsire.

•The US calving ease genetic evaluation is a sire-maternal grandsire threshold evaluation.•Sire-maternal grandsire and sire-maternal models produce highly correlated genomic estimated breeding values.•Newton-Raphson and expectation-maximization give similar predictions within the same model.

The US calving ease genetic evaluation is a sire-maternal grandsire threshold evaluation.

Sire-maternal grandsire and sire-maternal models produce highly correlated genomic estimated breeding values.

Newton-Raphson and expectation-maximization give similar predictions within the same model.

The US dairy calving ease (CE) genetic evaluation is based on a threshold sire-maternal grandsire (SMGS) model and includes 2 genetic components: one reflecting the sire's direct genetic effect on calving, and the other capturing the maternal influence, modeled through either the dam or the maternal grandsire. This study compared 2 CE evaluation models—SMGS and sire-maternal (SMAT)—using different solving algorithms: Newton-Raphson (NR) and expectation maximization (EM). The analysis used over 24 million CE records provided by the Council on Dairy Cattle Breeding. Correlations of GEBV for phenotyped sires and maternal grandsires were highly consistent across algorithms, exceeding 0.99 within models. The NR algorithm was the most computationally efficient solver, requiring fewer iterations and less computing time than EM. Both SMGS and SMAT models are suitable for routine genetic evaluation of CE in US dairy cattle, with NR and EM offering reliable and efficient solutions for single-trait analysis.