Abstract There is considerable interest in assessing genetic gain from breeding efforts, as well as trends from non-genetic sources such as climate change. Long-term data from official variety trials provide an ideal opportunity to do so. Whereas past work on the subject was mainly focussed on trends in mean performance, little attention has been paid to yield stability. The purpose of the present paper therefore is to provide a framework for assessing trends in stability and to exemplify this using long-term data from German variety trials. Specifically, trends in the mean and variance of winter wheat and winter rye yields associated with genotypic, spatial, and climatic covariates were investigated based on a long-term series of multi-environment trials from 1983/1985 to 2016. Yield stability is assessed based on the variance of yield. For climatic covariates, trends were investigated using growth stage-specific covariates which were obtained by dividing the total growth period into five or ten growth stages within which covariates were aggregated. The analysis was done by linear mixed models and forward selection served to identify trends in mean and variance. Specifically, trends in the mean were selected based on a coefficient of determination, R 2 , while variance trends associated with a covariate were selected based on the change in variance attributable to the covariate. For spatial covariates, mean yield increased with the field capacity in up to one meter soil depth in case of rye. For both crops, mean yield was negatively affected by a deficit in available water during the development of vegetative parts while water deficit towards the end of the growth period was positively associated with mean yield. Trends were also selected accounting for interactions of climatic covariates and genotypic groups (wheat: quality type; rye: breeding type), revealing that R 2 generally increased when interactions were taken into account. The responses to covariates were similar for the different groups, meaning the increase in R 2 is mainly attributable to the main effects of the genotypic groups. Variance trends associated with the calendar year were identified for both crops, revealing yield variance slightly increased with time. Based on the selected model, a coefficient of variation was obtained for each year to assess relative yield stability, showing a decrease for wheat and an increase for rye.

中文翻译：

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一系列长期品种试验中冬小麦和黑麦产量的平均表现和稳定性趋势

摘要 人们对评估育种工作的遗传收益以及非遗传来源（如气候变化）的趋势非常感兴趣。来自官方品种试验的长期数据提供了一个理想的机会。过去关于该主题的工作主要集中在平均性能的趋势上，而很少关注产量稳定性。因此，本文的目的是提供一个评估稳定性趋势的框架，并使用德国品种试验的长期数据来举例说明这一点。具体而言，基于 1983/1985 至 2016 年的多环境长期系列试验，研究了与基因型、空间和气候协变量相关的冬小麦和冬黑麦产量的均值和方差趋势。产量稳定性评估基于关于产量的差异。对于气候协变量，使用特定生长阶段的协变量来研究趋势，这些协变量是通过将总生长期分为五个或十个生长阶段而获得的，在这些阶段中聚合了协变量。分析是通过线性混合模型完成的，前向选择用于识别均值和方差的趋势。具体而言，均值的趋势是基于决定系数 R 2 选择的，而与协变量相关的方差趋势是基于可归因于协变量的方差变化来选择的。对于空间协变量，在黑麦的情况下，平均产量随着田间容量的增加而增加，土壤深度可达一米。对于这两种作物，平均产量受到营养部分发育过程中可用水不足的负面影响，而生长期末的水分不足与平均产量呈正相关。还选择了考虑气候协变量和基因型组（小麦：质量类型；黑麦：育种类型）的相互作用的趋势，表明考虑到相互作用时 R 2 通常增加。不同组对协变量的反应相似，这意味着 R 2 的增加主要归因于基因型组的主要影响。两种作物都确定了与日历年相关的差异趋势，表明产量差异随时间略有增加。根据选定的模型，获得每年的变异系数以评估相对产量稳定性，