This research aimed to compare single-step random regression models with third-order Legendre polynomials (RRLP) and splines with four (RRSP4) and five (RRSP5) knots for milk yield (MY) and fat percentage (FP) genomic-polygenic evaluations in the Thai multibreed dairy population. Models were compared using estimates of variance components, genetic parameters, goodness of fit, genomic-polygenic EBV (GPEBV) accuracies, and animal rankings. The dataset included pedigree and monthly test-day records (69,029 for MY; 29,878 for FP) of 7,206 first-lactation cows from 761 farms, and genotypic records (74,144 actual and imputed SNP) from 2,661 animals. Variance components and genetic parameters for MY and FP were estimated using REML procedures. Models contained contemporary group (herd-year-season), calving age, heterozygosity, and population lactation curve regression coefficients as fixed effects. Random effects were animal additive genetic, permanent environment random regression coefficients, and residual. The population lactation curve, additive genetic, and permanent environment effects were fitted using regression coefficients of third-order Legendre polynomials for RRLP, splines of four knots for RRSP4, and five knots for RRSP5. The estimates of 305-day additive genetic variances (${\widehat{\sigma }}_a^2$) and heritabilities ($\widehat{h}$²) were higher for RRLP (MY: ${\widehat{\sigma }}_a^2$ = 279,893.2 kg², $\widehat{h}$² = 0.27; FP: ${\widehat{\sigma }}_a^2$ = 0.10%², $\widehat{h}$² = 0.16) than for RRSP4 (MY: ${\widehat{\sigma }}_a^2$ = 260,178.1 kg², $\widehat{h}$² = 0.19; FP: ${\widehat{\sigma }}_a^2$ = 0.08%², $\widehat{h}$² = 0.11), and for RRSP5 (MY: ${\widehat{\sigma }}_a^2$ = 266,198.0 kg², $\widehat{h}$² = 0.20; FP: ${\widehat{\sigma }}_a^2$ = 0.08%², $\widehat{h}$² = 0.12). Similarly, RRLP yielded better goodness of fit and higher GPEBV accuracies than RRSP4 and RRSP5. The goodness of fit values for RRLP were 293,813 for -2 log-likelihood (-2logL), 293,855 for the Akaike's information criterion (AIC), and 293,915 for the Bayesian information criterion (BIC). The corresponding values for RRSP4 were 362,738 for -2logL, 362,888 for AIC, and 363,101 for BIC, and those for RRSP5 were 354,473 for -2logL, 354,699 for AIC, and 355,020 for BIC. Lastly, the GPEBV accuracies for RRLP were 49.3% for MY and 38.6% for FP, those for RRSP4 were 47.2% for MY and 37.8% for FP, and the ones for RRSP5 were 47.4% for MY, 37.5% for FP. Rank correlations between animal GPEBV from these three models were high ranging from 0.91 to 0.98 for MY and 0.88 to 0.98 for FY. Results indicated that GPEBV from RRLP should be preferred to GPEBV from RRSP4 and RRSP5 to increase selection responses for MY and FP in the Thai multibreed dairy population.

本研究旨在比较单步随机回归模型与三阶勒让德多项式 (RRLP) 和具有四节 (RRSP4) 和五节 (RRSP5) 的样条曲线对产奶量 (MY) 和脂肪百分比 (FP) 基因组多基因评估的影响。泰国多品种奶牛种群。使用方差分量、遗传参数、拟合优度、基因组多基因 EBV (GPEBV) 准确性和动物排名的估计值比较模型。该数据集包括来自 761 个农场的 7,206 头第一次泌乳奶牛的系谱和每月测试日记录（MY 为 69,029；FP 为 29,878），以及来自 2,661 头动物的基因型记录（74,144 实际和推算的 SNP）。使用 REML 程序估计 MY 和 FP 的方差分量和遗传参数。模型包含当代组（畜群-年-季）、产犊年龄、杂合性、和人口泌乳曲线回归系数作为固定效应。随机效应是动物加性遗传、永久环境随机回归系数和残差。使用 RRLP 的三阶勒让德多项式、RRSP4 的四节样条和 RRSP5 的五节样条曲线拟合种群泌乳曲线、加性遗传和永久环境影响。305天加性遗传方差的估计（${\widehat{\sigma }}_{\mathrm{一种}}^2$) 和遗传力 ($\widehat{H}$² ) RRLP 更高（我的：${\widehat{\sigma }}_{\mathrm{一种}}^2$ = 279,893.2 公斤² ,$\widehat{H}$²  = 0.27；计划：${\widehat{\sigma }}_{\mathrm{一种}}^2$ = 0.10% ² ,$\widehat{H}$²  = 0.16) 比 RRSP4（我的：${\widehat{\sigma }}_{\mathrm{一种}}^2$ = 260,178.1 公斤² ,$\widehat{H}$²  = 0.19；计划：${\widehat{\sigma }}_{\mathrm{一种}}^2$ = 0.08% ² ,$\widehat{H}$²  = 0.11），对于 RRSP5（我的：${\widehat{\sigma }}_{\mathrm{一种}}^2$ = 266,198.0 公斤² ,$\widehat{H}$²  = 0.20；计划：${\widehat{\sigma }}_{\mathrm{一种}}^2$ = 0.08% ² ,$\widehat{H}$² = 0.12）。类似地，与 RRSP4 和 RRSP5 相比，RRLP 产生了更好的拟合优度和更高的 GPEBV 准确度。RRLP 的拟合优度值为 -2 对数似然 (-2logL) 的 293,813、Akaike 信息准则 (AIC) 的 293,855 和贝叶斯信息准则 (BIC) 的 293,915。RRSP4 的相应值为 -2logL 为 362,738，AIC 为 362,888，BIC 为 363,101，RRSP5 的相应值为 -2logL 为 354,473，AIC 为 354,699，BIC 为 355,020。最后，RRLP 的 GPEBV 准确率分别为 MY 49.3% 和 FP 38.6%，RRSP4 MY 的 GPEBV 准确率为 47.2%，FP 的 GPEBV 准确率为 37.8%，RRSP5 的 MY 为 47.4%，FP 为 37.5%。来自这三个模型的动物 GPEBV 之间的等级相关性很高，MY 为 0.91 至 0.98，FY 为 0.88 至 0.98。