Department of Animal and Dairy Science, University of Georgia, Athens, GA 30602, USA.
Angus Genetics Inc., American Angus Association, St. Joseph, MO 64506, USA.
J Anim Sci. 2024 Jan 3;102. doi: 10.1093/jas/skae307.
Threshold models are often used in genetic analysis of categorical data, such as calving ease. Solutions in the liability scale are easily transformed into probabilities; therefore, estimated breeding values are published as the probability of expressing the category of main interest and are the industry's gold standard because they are easy to interpret and use for selection. However, because threshold models involve nonlinear equations and probability functions, implementing such a method is complex. Challenges include long computing time and convergence issues, intensified by including genomic data. Linear models are an alternative to overcome those challenges. Estimated breeding values computed using linear models are highly correlated (≥0.96) with those from threshold models; however, the lack of a transformation from the observed to the probability scale limits the use of linear models. The objective of this study was to propose transformations from observed to probability scale analogous to the transformation from liability to probability scale. We assessed computing time, peak memory use, correlations between estimated breeding values, and estimated genetic trends from linear and threshold models. With 11M animals in the pedigree and almost 965k genotyped animals, linear models were 5× faster to converge than threshold models (32 vs. 145 h), and peak memory use was the same (189 GB). The transformations proposed provided highly correlated probabilities from linear and threshold models. Correlations between direct (maternal) estimated breeding values from linear and threshold models and transformed to probabilities were ≥0.99 (0.97) for all animals in the pedigree, sires with/without progeny records, or animals with phenotypic records; therefore, estimated genetic trends were analogous, suggesting no loss of genetic progress in breeding programs that would adopt linear instead of threshold models. Furthermore, linear models reduced computing time by 5-fold compared to the threshold models; this enables weekly genetic evaluations and opens the possibility of using multi-trait models for categorical traits to improve selection effectiveness.
阈模型常用于分类数据的遗传分析，如产犊容易度。在隶属度尺度上的解很容易转换为概率；因此，估计的育种值被公布为表达主要感兴趣类别的概率，是行业的黄金标准，因为它们易于解释和用于选择。然而，由于阈模型涉及非线性方程和概率函数，因此实现这种方法很复杂。挑战包括长计算时间和收敛问题，包括基因组数据会加剧这些问题。线性模型是克服这些挑战的一种替代方法。使用线性模型计算的估计育种值与阈模型的高度相关（≥0.96）；然而，缺乏从观察值到概率尺度的转换限制了线性模型的使用。本研究的目的是提出从观察值到概率尺度的转换，类似于从隶属度到概率尺度的转换。我们评估了线性和阈模型的计算时间、峰值内存使用、估计育种值之间的相关性以及估计的遗传趋势。在系谱中有 1100 万头动物，近 96.5 万头动物被基因分型，线性模型的收敛速度比阈模型快 5 倍（32 小时对 145 小时），峰值内存使用量相同（189GB）。提出的转换提供了来自线性和阈模型的高度相关的概率。对于系谱中的所有动物、有/无后代记录的父本或有表型记录的动物，线性和阈模型的直接（母系）估计育种值的转换为概率的相关性≥0.99（0.97）；因此，估计的遗传趋势是类似的，这表明采用线性模型而不是阈模型的育种计划不会损失遗传进展。此外，线性模型的计算时间比阈模型减少了 5 倍；这使得每周进行遗传评估成为可能，并为提高选择效率的分类性状的多性状模型的使用开辟了可能性。
