Sparse testing in genome-enabled prediction in plant breeding can be emulated throughout different line allocations where some lines are observed in all environments (overlap) and others are observed in only one environment (nonoverlap). We studied three general cases of the composition of the sparse testing allocation design for genome-enabled prediction of wheat (Triticum aestivum L.) breeding: (a) completely nonoverlapping wheat lines in environments, (b) completely overlapping wheat lines in all environments, and (c) a proportion of nonoverlapping/overlapping wheat lines allocated in the environments. We also studied several cases in which the size of the testing population was systematically decreased. The study used three extensive wheat data sets (W1, W2, and W3). Three different genome-enabled prediction models (M1–M3) were used to study the effect of the sparse testing in terms of the genomic prediction accuracy. Model M1 included only main effects of environments and lines; M2 included main effects of environments, lines, and genomic effects; whereas the remaining model (M3) also incorporated the genomic × environment interaction (GE). The results show that the GE component of the genome-based model M3 captures a larger genetic variability than the main genomic effects term from models M1 and M2. In addition, model M3 provides higher prediction accuracy than models M1 and M2 for the same allocation designs (different combinations of nonoverlapping/overlapping lines in environments and training set sizes). Overlapped sets of 30–50 lines in all the environments provided stable genomic-enabled prediction accuracy. Reducing the size of the testing populations under all allocation designs decreases the prediction accuracy, which recovers when more lines are tested in all environments. Model M3 offers the possibility of maintaining the prediction accuracy throughout both extreme situations of all nonoverlapping lines and all overlapping lines.

中文翻译：

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多环境小麦试验中稀疏测试的基因组预测

植物育种中基于基因组的预测中的稀疏测试可以在不同的品系分配中进行模拟，其中一些品系在所有环境中都观察到（重叠），而其他品系仅在一种环境中观察到（非重叠）。我们研究了小麦基因组预测的稀疏测试分配设计组成的三个一般案例 ( Triticum aestivumL.) 育种：(a) 环境中完全不重叠的小麦品系，(b) 所有环境中完全重叠的小麦品系，和 (c) 分配在环境中的非重叠/重叠小麦品系的比例。我们还研究了几个案例，其中测试人群的规模系统地减少了。该研究使用了三个广泛的小麦数据集（W1、W2 和 W3）。三种不同的基因组预测模型（M1-M3）用于研究稀疏测试在基因组预测准确性方面的影响。模型 M1 仅包括环境和线路的主要影响；M2包括环境主效应、谱系效应和基因组效应；而剩下的模型（M3）也结合了基因组×环境相互作用（GE）。结果表明，基于基因组的模型 M3 的 GE 组件比模型 M1 和 M2 的主要基因组效应项捕获了更大的遗传变异性。此外，对于相同的分配设计（环境中非重叠/重叠线和训练集大小的不同组合），模型 M3 比模型 M1 和 M2 提供更高的预测精度。在所有环境中重叠的 30-50 行提供了稳定的基因组预测准确性。在所有分配设计下减少测试群体的大小会降低预测准确性，当在所有环境中测试更多线路时，预测准确性会恢复。模型 M3 提供了在所有非重叠线和所有重叠线的极端情况下保持预测准确性的可能性。