In the face of a changing climate, yield stability is becoming increasingly important for farmers and breeders. Long-term field experiments (LTEs) generate data sets that allow the quantification of stability for different agronomic treatments. However, there are no commonly accepted guidelines for assessing yield stability in LTEs. The large diversity of options impedes comparability of results and reduces confidence in conclusions. Here, we review and provide guidance for the most commonly encountered methodological issues when analysing yield stability in LTEs. The major points we recommend and discuss in individual sections are the following: researchers should (1) make data quality and methodological approaches in the analysis of yield stability from LTEs as transparent as possible; (2) test for and deal with outliers; (3) investigate and include, if present, potentially confounding factors in the statistical model; (4) explore the need for detrending of yield data; (5) account for temporal autocorrelation if necessary; (6) make explicit choice for the stability measures and consider the correlation between some of the measures; (7) consider and account for dependence of stability measures on the mean yield; (8) explore temporal trends of stability; and (9) report standard errors and statistical inference of stability measures where possible. For these issues, we discuss the pros and cons of the various methodological approaches and provide solutions and examples for illustration. We conclude to make ample use of linking up data sets, and to publish data, so that different approaches can be compared by other authors and, finally, consider the impacts of the choice of methods on the results when interpreting results of yield stability analyses. Consistent use of the suggested guidelines and recommendations may provide a basis for robust analyses of yield stability in LTEs and to subsequently design stable cropping systems that are better adapted to a changing climate.

Key message Breeding progress of resistance to fungal wheat diseases and impact of disease severity on yield reduction in long-term variety trials under natural infection were estimated by mixed linear regression models. Abstract This study aimed at quantifying breeding progress achieved in resistance breeding towards varieties with higher yield and lower susceptibility for 6 major diseases, as well as estimating decreasing yields and increasing disease susceptibility of varieties due to ageing effects during the period 1983–2019. A further aim was the prediction of disease-related yield reductions during 2005–2019 by mixed linear regression models using disease severity scores as covariates. For yield and all diseases, overall progress of the fully treated intensity (I2) was considerably higher than for the intensity without fungicides and growth regulators (I1). The disease severity level was considerably reduced during the study period for mildew (MLD), tan spot (DTR) and Septoria nodorum blotch (ear) (SNB) and to a lesser extent for brown (leaf) rust (BNR) and Septoria tritici blotch (STB), however, not for yellow/stripe rust (YLR). Ageing effects increased susceptibility of varieties strongly for BNR and MLD, but were comparatively weak for SNB and DTR. Considerable yield reductions under high disease severity were predicted for STB (−6.6%), BNR (−6.5%) and yellow rust (YLR, −5.8%), but lower reductions for the other diseases. The reduction for resistant vs. highly susceptible varieties under high severity conditions was about halved for BNR and YLR, providing evidence of resistance breeding progress. The empirical evidence on the functional relations between disease severity, variety susceptibility and yield reductions based on a large-scale multiple-disease field trial data set in German winter wheat is an important contribution to the ongoing discussion on fungicide use and its environmental impact.

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Corresponding author (Hans-Peter.Piepho@ uni-hohenheim.de). Assigned to Associate Editor Manjit Kang.Abbreviations: AMMI, additive main effects and multiplicative interaction; CV, cross-validation; EM, expectation maximization; GCV, generalized cross-validation criterion; GEI, genotype ´ environment interaction; GGE, genotype and genotype ´ environment interaction; MET, multi-environment trial; MSED, mean squared error of differences; MSEPD, mean squared error of predicting differences; n, number of multiplicative terms retained in the AMMI or the GGE model; N, true number of multiplicative terms; RCBD, randomized complete block design; rIBD, resolvable incomplete block design; SVD, singular value decomposition; TMORR, true model order recovery rate.

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Breeding for traits with polygenic inheritance is a challenging task that can be done by phenotypic selection, marker-assisted selection (MAS) or genome-wide selection. We comparatively evaluated the predictive abilities of four selection models on a biparental lettuce (Lactuca sativa L.) population genotyped with 95 single nucleotide polymorphisms and 205 amplified fragment length polymorphism markers. These models were based on (i) phenotypic selection, (ii) MAS (with quantitative trait locus (QTL)-linked markers), (iii) genomic prediction using all the available molecular markers, and (iv) genomic prediction using molecular markers plus QTL-linked markers as fixed covariates. Each model's performance was assessed using data on the field resistance to downy mildew (DMR, mean heritability ~0.71) and the quality of shelf life (SL, mean heritability ~0.91) of lettuce in multiple environments. The predictive ability of each selection model was computed under three cross-validation (CV) schemes based on sampling genotypes, environments, or both. For the DMR dataset, the predictive ability of the MAS model was significantly lower than that of the genomic prediction model. For the SL dataset, the predictive ability of the genomic prediction model was significantly lower than that for the model using QTL-linked markers under two of the three CV schemes. Our results show that the predictive ability of the selection models depends strongly on the CV scheme used for prediction and the heritability of the target trait. Our study also shows that molecular markers can be used to predict DMR and SL for individuals from this cross that were genotyped but not phenotyped.