Introduction

Calculation of the area under the disease-progress curve (AUDPC) as a measure of quantitative disease resistance entails repeated disease assessments (Jeger and Viljanen-Rollinson 2001). Trails related to diseases assessment require work and time to a large extent. There are some limitations (weather, space) how frequently assessments can be made. The use of the calculated AUDPC has increased in recent years and can certainly be recommended when, because of either host phenology or growth, monotonically increasing disease progress is unlikely (Jeger and Viljanen-Rollinson 2001).

Spring barley takes about 10% of the total grain area annually, and the spring form usually occupies four times more area than the winter form. The advantages for spring barley are the lack of wintering problems and less expenditure on cultivation. The spring barley is characterized by high reliability of yield, which results from less sensitivity to rainfall shortage. The cultivation of spring barley takes place mainly for fodder and brewing purposes. Spring barley is also the basic ingredient of cereal mixes used for fodder purposes.

One of the most important diseases occurring od spring barley in Poland is powdery mildew caused by Blumeria graminis f. sp. hordei. Usually winter barley is more seriously affected than spring barley. B. graminis is a genetically diverse pathogen with different special forms and races.

Environmental conditions strongly influence agricultural production, leading to considerable variations in values of quantitative trait. Such influence is discriminated when experiments are performed in various locations and in different years. Such influence is termed genotype-by-environment (GE) interaction. The presence of GE interaction influences production making the selection of genotypes in a complex process (Becker and Leon 1988; Cooper and DeLacy 1994; Heslot et al. 2014; Hassani et al. 2018). Among various statistical techniques used for evaluating GE interaction, the most frequently used is te Additive Main-effects and Multiplicative Interaction (AMMI) model (Gauch 1988; Zobel et al. 1988). The AMMI model uses analysis of variance (ANOVA) and principal component analysis (PCA) to achieve a better understanding of GE interaction, its causes and consequences. A PCs model is fitted to the residuals from the ANOVA and the resulting scores, called the I (for interaction) PCA (IPCA) are calculated for both the genotypes and the trials or environments.

The objective of this paper was to assess GE interaction for area under the disease-progress curve (AUDPC) in spring barley by the AMMI model.

Material and methods

Field experiments with spring barley were carried out at two locations: Bąków (50°42’ N, 18°28′ E) and Kościelna Wieś (51°47’ N, 18°00′ E) in 4 years: 2010–2013. The two sites differed in terms of soil and weather conditions. Cultivars of spring barley (Basza, Blask, Antek, Skarb and Rubinek) as well as all possible two-way mixtures and three-way mixtures combinations were cultivated on plots of 10 m2 (Bąków) and 16.5 m2 (Kościelna Wieś) in the randomized complete block designs with four replicates. The ratio of cultivar components in mixtures was 1:1 or 1:1:1. Rows spacing in plots – 12.5 cm, seed drill type – Oyord (Bąków), SPZ 1.5/2 (Kościelna Wieś). Fertilization – N: 60–60 kg/ha, P: 30–40 kg/ha, K: 50–60 kg/ha. Soil types: podsolic soil and leached brown soil (Bąków); leached brown soil and acid brown soil (Kościelna Wieś). No fungicide treatments were applied in the experiments.

Natural powdery mildew infections on spring barley plants were assessed every 7–10 days during the growing season. The intensity of the disease infection was assessed using following, 9-grade scale: where” 9″ full resistance (no symptoms of the disease, while)” 1″ indicated full susceptibility Tratwal and Bocianowski (2018). The obtained results were expressed as a percentage value of damage caused by the disease to particular plants of pure cultivars and mixtures. Analyses were carried out on individualy-converteed percentage value.

The area under the disease-progress curve (AUDPC) value was calculated according to formula (Jeger and Viljanen-Rollinson 2001; Tratwal and Bocianowski 2014):

$$ AUDPC=\sum \limits_{i=1}^n\left\{\left(\frac{y_i+{y}_{i-1}}{2}\right)\left({x}_i-{x}_{i-1}\right)\right\}, $$

where AUDPC is the area under disease progress curve, yi is the percentage of visible infected area (yi/100) at the i-th observation, xi - day of the i-th observation, and n - the total number of observations (modified from Shaner and Finney 1977).

In the case of AMMI analysis, PCA is applied to the GE interaction effects only after some preliminary verifications are made based on ANOVA analysis. Two-way ANOVA was carried out to determine the effects of genotypes (G), environments (E) and GE interaction on the variability of AUDPC. Least-squares means were simultaneously produced for the AMMI model. The model first fits additive effects for the main effects of G and E followed by multiplicative effects for GE interaction by PCA. The AMMI model (Gauch and Zobel 1990; Nowosad et al. 2017) is given by:

$$ {y}_{ge}=\mu +{\alpha}_g+{\beta}_e+\sum \limits_{n=1}^N{\lambda}_n{\gamma}_{gn}{\delta}_{en}+{Q}_{ge}, $$

where yge is the AUDPC value mean of genotype g in environment e, μ - the grand mean, αg - the genotypic mean effects, βe - the environmental mean effects, N - the number of PCA axis retained in the adjusted model, λn - the square root of the eigenvalue of the PCA axis n, γgn - the genotype score for PCA axis n, δen - the environment score eigenvector for PCA axis n, Qge - the residual. The AMMI stability value (ASV) was used to compare the stability of genotypes as described by Purchase et al. (2000):

$$ ASV=\sqrt{{\left[\frac{SS_{IPCA1}}{SS_{IPCA2}}\left({IPCA}_1\right)\right]}^2+{\left({IPCA}_2\right)}^2}, $$

where SS is the sum of squares, IPCA1 and IPCA2 are the first and the second interaction PC axes, respectively; and the IPCA1 and IPCA2 scores were the genotypic scores in the AMMI model. The higher the IPCA score, either negative or positive, the more specifically adopted a genotype is to certain environments. Lower ASV score indicate a more stable genotype across environments. For the AMMI analysis, statistical package GenStat v. 18.2 was used.

Results

Obtained result indicated that the main effects of genotype and environment as well as GE interaction were highly significant (P < 0.001). The genotypes main effect explained 37.85% of the AUDPC value variation, environment main effect – 13.43%, while the effects of GE interaction – 18.20% (Table 1). The IPCA1 accounted for 76.03% of the variation caused by interaction, while IPCA2 accounted for – 13.18% on the variation of AUDPC value. The average AUDPC values of the tested genotypes varied from 75.3 (for Basza/Rubinek) to 614.3 (for Antek) throughout the eight environments, with an average of 175.3. The average AUDPC value per location also varied from 52.1 in Kościelna Wieś 2012, to 290.4 in Kościelna Wieś 2013.

Table 1 Analysis of variance of main effects and interactions for spring barley AUDPC value
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The AMMI1 biplot (Fig. 1) shows the stability of genotypes and environments, as well as specific GE interactions. Among the tested genotypes, IPCA 1 values ranged from −22.069 (Antek) to 7.137 (Basza/Blask/Skarb), while among tested environments ranged from −22.697 (Kościelna Wieś 2013) to 13.023 (Kościelna Wieś 2012) (Fig. 1). Stability of genotype is considered as consistent reaction to changing environmental conditions, biotic and abiotic stresses, agronomic factors as well as weather conditions. Figure 2 presents the biplot for AUDPC values. The cultivar Antek and mixture Antek/Skarb interacted positively with the KW13 and B13 locations, but negatively with the KW11, KW12 and B11 (Figs. 1 and 2). Mixtures A/Bl/R and A/Ba/R interacted positively with the KW10 location, but negatively with the B10 and B11 locations. Some genotypes have high adaptation; however, most of them have specific adaptability. AMMI stability values (ASV) revealed variations in AUDPC values stability among the 25 genotypes (Table 2). According to Purchase et al. (2000), a stable variety is defined as one with ASV value close to zero. Consequently, the cultivars Skarb (with ASV of 0.37) and Blask (1.45) as well as mixtures Blask/Rubinek (2.83), Antek/Basza/Skarb (3.69) and Antek/Rubinek (4.22) were the most stable, while the cultivar Antek (127.45) and mixtures Antek/Skarb (63.38) and Basza/Blask/Skarb (41.32) were the least stable (Table 2). The mixture Basza/Skarb, with low average AUDPC values (98.8) and good stability (ASV = 6.65) is recommended for further inclusion in the breeding program (Tab. 2, Fig. 2).

Fig. 1
figure 1

Biplot for genotype by environment interaction of AUDPC value in spring barley cultivars and their mixtures in eight environments (two locations in 4 years), showing the effects of primary and secondary components (IPCA 1 and IPCA 2, respectively)

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Fig. 2
figure 2

Biplot for the primary component of interaction (IPCA 1) and average AUDPC value. Vertical line at the centre of biplot is the general grand mean

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Table 2 The AMMI stability value (ASV) of tested spring barley cultivars and their mixtures
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Discussion

Varieties resistant to diseases play a very important role in cultivation and protection of cultivated plants. In modern cereal cultivation, within intensive conventional farming, next to constant modernization of production technology, one may observe a disadvantageous practice of genetic narrowing of cultivated plants and making them more uniform. More and more often one sees large area farms which year after year grow the same species and varieties of cultivated plants in monocultures. From an organizational standpoint it is preferable, but in intensive cereal production one may observe a narrowing of biodiversity, increased sensitivity of the crops to diseases and pests, as well as sensitivity to environment changes. Big areas of single varieties with similar or identical types of resistance to diseases foster fast spread of single physiological strains of pathogens. One of the cheaper and relatively easy ways of diversifying and at the same time increasing the durability of genetic resistance of modern varieties in production conditions is cultivating them in different types of variety mixtures (two or three - ways mixtures). Cultivation of cereal in mixtures restores biodiversity, which thanks to the distinct features of introduced varieties allows for better use of natural diversity of environment and a sustainable agricultural development. Unlike in the case of variety monocultures, in the genetically diversified mixed varieties we may observe different biological (genetic and epidemiological) and ecological mechanisms of disease reduction (Tratwal et al. 2007; Finckh et al. 2000; Tratwal and Walczak 2010). The most important of those mechanisms is resistant plants acting as physical “barriers” for a part of avirulent fomites, induced resistance (biological immunity); the differences in the levels of partial resistance of mixed varieties or interactions between diseases (epidemics) and ecological factors (phenomena of complementation, compensation, competition, aggression and tolerance).

Improved health along with different ecological non-disease related factors limit the need to apply expensive and environment unfriendly fungicide treatments. Thanks to a better use of habitat and agrotechnical conditions mixtures show higher and more stable yielding when compared to that of the varieties of which they are composed. The AMMI stability values for mixtures are better than for cultivars. The ASVs for two-way mixtures ranged from 2.83 (for Blask/Rubinek) to 63.38 (for Antek/Skarb) with an average of 20.20. For three-way mixtures the ASV ranged from 3.69 (for Antek/Basza/Skarb) to 41.32 (for Basza/Blask/Skarb) with an average of 22.06. The ASVs for cultivars ranged from 0.37 (for Skarb) to 127.45 (for Antek) with an average of 37.20 (Table 2).

In our study we observed negative linear correlation between AUDPC values and PC1 values (Fig. 2). This means that the genotypes with higher AUDPC values had the more negative PC1 values, so more variable genotypes across environments are the most susceptible (which makes fully biological sense).

To the best of our knowledge, this is the first research which using additive main effects and multiplicative interaction model to analysis genotype-by-environment interaction for area under the disease-progress curve value in spring barley. AMMI biplot’s graphic analysis provides relatively simple analysis for breeding researchers. Based on the data, it allows conclusions to be drawn concerning phenotypic stability, genotype behavior, genetic divergence between genotypes, and environments with optimal performance (Tolessa 2015; Abakemal et al. 2016; Sa’diyah and Hadi 2016). The AMMI model is one of the most widely used statistical tools in the analysis of genotype-by-environmental interaction. AMMI model permits to determine stability, multi-environments and determining the best adapted genotype to some environment. AMMI analyses revealed significant genotype-by-environment interaction with respect to AUDPC values.