Yield Stability and Adaptability of Spring Barley (Hordeum vulgare) Varieties in Polish Organic Field Trials

Abstract

In the next few years, the demand for organic crops, including barley, will grow. Barley is one of the world’s most important crops cultivated for food and feed. With the forecasted increase in cropped area, there is a need for stable, well-adapted and high-yielding varieties. The aim of this study was to assess the yield stability of ten varieties tested in the Polish organic post-registration trials in the years 2020–2022. For this purpose, we fitted a linear mixed model on plot data. Additionally, for each variety, we calculated the probability of the yield falling to a certain threshold. It is shown that the Bente variety was the highest-yielding among the tested varieties. The Pilote variety was the most stable in terms of Shukla’s stability variance. Furthermore, for the three highest-yielding varieties, the lowest values of the simultaneous selection index and the probability of falling below a certain threshold were obtained. We can, therefore, conclude that the highest-yielding varieties should be promoted for cultivation. Moreover, new varieties suitable for organic farming can be bred from the highest-yielding and most stable varieties.

1. Introduction

To ensure sustainable development and climate neutrality in Europe by 2050, the European Commission approved a set of policy initiatives. For this reason, it is believed that, in the next few years, the demand for organic crops and vegetables, including barley, will increase. Barley is one of the world’s major crops. It is cultivated mainly for animal feeding and alcohol production (mainly malt and beer production). It is also used for human consumption in the form of groats and flakes. In 2022, in all the EU countries, organic barley (both spring and winter varieties) was cultivated on 324,415.80 ha [1]. The largest organic barley cultivation areas were recorded in Spain (71,175.38 ha), France (55,369.00 ha), Germany (48,000.00 ha) and Italy (36,313.45 ha) [1]. In Poland, the corresponding area was only 3220 ha. With the forecasted increase in organic cultivation area, the need for stable, well-adapted and high-yielding varieties is also growing.

In Poland, the Research Centre for Cultivar Testing (COBORU) assesses the performance of candidate varieties in value-for-cultivation-and-use (VCU) trials. Since 2022, candidate varieties for organic systems can also be registered in Poland. Next, the newly registered varieties are tested in conventional and/or organic post-registration trials. Since 2018, organic post-registration trials on cereals, peas and soybeans have been performed in cooperation with the Institute of Soil Science and Plant Cultivation-State Research Institute (IUNG-PIB), whereas trials on winter barley, maize and potatoes are performed only by COBORU. Finally, based on the results of these trials, COBORU issues a recommendation to farmers. As in the conventional system, only stable and high-yielding varieties are recommended for cultivation.

The stability and adaptability of varieties is assessed in the course of multi-environmental trials. These trials are typically analyzed by applying a two-stage approach with the use of various statistical models. The most popular models are linear mixed models, the Finlay–Wilkinson model [2], the Eberhard and Russell model [3,4,5], or a genotype main effect and genotype-by-environment interaction (GGE) model [6,7]. In the conventional system, stability analyses of agronomic traits are performed routinely. In contrast, such analyses are rarely performed for traits observed in the organic system. Osman et al. [8] described the most important agronomic traits from the organic farming point of view. At the same time, Rakszegi et al. [9] assessed the stability of winter wheat quality traits using the GGE biplot. In a different study, Kucek et al. [10] used the approach proposed by Annicchiarico [11] to assess the stability of spring and winter wheat genotypes. In that study, the analyses were performed for yield, test weight, falling number and protein. Recently, Massman et al. [12] and Kunze et al. [13] used the Finlay–Wilkinson model to assess the stability of spring and winter naked barley genotypes in terms of grain yield, test weight, heading date, plant height and threshability. In turn, Przystalski and Lenartowicz [14] used the harmonic mean of the relative performance of genotype values to assess the stability of seven potato varieties tested simultaneously in the organic and conventional systems. To calculate these values, they used the predicted variety × environment × system interaction means from a Bayesian linear mixed model.

The aim of this study was to assess the yield stability of ten varieties tested in the Polish organic post-registration trials over the years 2020–2022. For this purpose, we fitted a linear mixed model on plot data. As in [14,15,16,17], the mixed model was fitted under the assumption of heterogeneity in error variance. Next, based on the predicted variety × environment means and the predicted environmental means, the adaptability to agro-meteorological conditions of the ten varieties was assessed using the relative performance of genotypic values (see, e.g., [18,19,20] and the references therein). Additionally, as yields in organic agriculture are more variable than in conventional agriculture [21], we calculated for each variety the probability that the yield would fall below a certain threshold [22,23,24]. Finally, the probability functions of the best-performing varieties from each country were compared using the relative risk concept introduced by Piepho [24].

2. Materials and Methods

2.1. Data

The data set consists of organic spring barley trials performed in the years 2020–2022. Each trial was laid out in a randomized complete block design with four replicates. The trials were conducted at experimental stations (sites) belonging to the Research Centre for Cultivar Testing (COBORU) and the Institute of Soil Science and Plant Cultivation State Research Institute (IUNG-PIB). The trials in Węgrzce (We), Grabów (Gra) and Osiny (Os) were performed at certificated organic fields. In Przecław (Prz), Radostowo (Ra), Skołoszów (Sko), Śrem (Sr) and Tarnów (Tar) (in Lower Silesia Voivodeship), the trials were performed at organically managed fields. On these sites, the field certification procedure is ongoing. In Szepietowo (Sze), the field was organically managed but not certified. The locations of the experimental sites are shown in Figure 1. The geographical coordinates of the experimental sites and the years in which they were used are given in [25]. The soil type and soil fertility at each site are reported in Table S1 (Supplement S1). The sowing of spring barley varieties was performed according to the best agricultural practices. For each site, monthly average temperatures and sums of precipitation are reported in Supplement S2. The optimum sowing date was chosen, depending on the meteorological conditions. In accordance with the rules of organic farming, no mineral fertilizers or chemical plant protection products were used at any of the experimental sites. Spring barley was grown mainly after good forecrops. Only in Osiny was spring barley grown after winter wheat three times in a row. Depending on meteorological conditions, harvests took place from mid-July to the first decade of August.

Each year, a total of 11 varieties were tested. During the three years of study, there were ten common varieties. These were cv. Avatar, Bente, Etoile, Farmer, KWS Vermont, Mecenas, MHR Fajter, Pilote, Radek and Rubaszek. The country of origin and year of registration of the above varieties are given in [25].

According to the methodology used in organic post-registration trials [26], yield is one of the analyzed traits that was observed in plots. For each trial, the plot yields were recalculated to contractual conditions, i.e., with a moisture content of 14%. The observed yields were expressed in tonnes per hectare (t/ha).

2.2. Statistical Analysis

In the present study, a linear mixed model was used to assess the yield stability and adaptability of ten varieties in the series of organic field trials. For clarity, throughout the paper, ‘environment’ refers to a combination of year and location.

Let $y_{ijk}$ denote the observed yield of the i-th variety ($i=1,\dots ,I$) at the j-th environment ($j=1,\dots ,J$) and in the k-th replicate ($k=1,\dots ,K$). Then, the mixed model can be written as follows:

$$y_{ijk}=\mu +{\alpha }_i+u_j+w_{ij}+z_{jk}+e_{ijk},$$

(1)

where $\mu$ denotes the general mean, and ${\alpha }_i$ is the fixed effect of the i-th variety. The random effects of environments, of replicates nested within environments and of errors are denoted in (1) as $u_j$, $z_{jk}$ and $e_{ijk}$, respectively. We assumed that $u_j\sim N\left(0,{\sigma }_u^2\right)$, $z_{jk}\sim N\left(0,{\sigma }_z^2\right)$. Further, we assumed the heterogeneity of error variance between trials; i.e., it was assumed that $e_{ijk}\sim N\left(0,{\sigma }_{e\left(j\right)}^2\right)$.

The variety × environment interaction was assumed to be a random effect, and it is denoted in model (1) as $w_{ij}$. We assumed that the random variety × environment interaction effects followed normal distributions with zero means and variances; ${\sigma }_i^2$, i.e., $w_{ij}\sim N\left(0,{\sigma }_i^2\right)$. According to Piepho [27], the estimates of ${\sigma }_i^2$ can be treated as the estimates of Shukla’s stability variances [28]. Varieties with the smallest values of ${\sigma }_i^2$ tend to be more stable.

The variance components were estimated using REML ([29], numerical implementation Genstat 23.1, VSN International, Hemel Hempstead, UK). These variance estimates were used, and the fixed effects were estimated via generalized least squares. The Wald test statistic with approximate F statistics was used to test the hypothesis

$$H_0:{\alpha }_1={\alpha }_2=\dots ={\alpha }_I.$$

(2)

The test statistic has an approximate F distribution with numerator degrees of freedom (n.d.f.) equal to $I-1$ and denominator degrees of freedom (d.d.f.) calculated using the Kenward–Roger approximation [30]. To obtain all possible variety comparisons at significance level $\alpha$ [31], the vmcomparison function from Genstat was used. For this purpose, we set the options method = fpsd and probability = 0.05 in the vmcomparison function.

Next, all varieties were ranked based on the estimated mean yields and values of Shukla’s stability variances. To combine the rankings, the simultaneous selection index (SSI) was calculated using the equation

$${\mathrm{SSI}}_i=r{m}_i+r{s}_i,$$

(3)

where $r{m}_i$ denotes the rank of the mean yield, and $r{s}_i$ is the rank of Shukla’s stability variance for the i-th variety. The varieties with the lowest rank sum are the most desirable.

Furthermore, predicted environmental means ($M_j$) and variety × environment interaction means ($M_{ij}$) were extracted while the vpredict Genstat function was applied. Next, using the extracted means, respective adaptability indices were calculated. As a measure of a given adaptability of a variety to environments, the relative performance of the genotypic values (RPGV) index was used (see, e.g., [18,19,20]):

$${\mathrm{RPVG}}_i={\displaystyle \frac{1}{J}}\sum _{j=1}^J{\displaystyle \frac{M_{ij}}{M_j}}.$$

(4)

Varieties with higher values of the RPGV index tend to exhibit greater adaptability to their environments.

Furthermore, based on the predicted means $M_{ij}$, mega-environments were created by grouping environments based on their best-performing variety. Environments that shared the same best variety belonged to the same mega-environment.

Next, based on the estimated variety means and variance components, the probabilities of yields of varieties falling below a certain critical level in the environments were calculated. This indicator combines the mean and variance in a meaningful way and can be treated as a different stability measure [22,23]. To calculate the probability that the yield of the i-th variety would fall below a certain critical level in a randomly chosen environment, we assumed that yield follows a normal distribution, and the following formula was applied [22]:

$$p\left(i\right)=P\left(y_{ij}<\delta \right)=\mathrm{\Phi }\left({\displaystyle \frac{\delta -{\widehat{\mu }}_i}{\sqrt{{\widehat{V}}_i}}}\right),i=1,\dots ,I;$$

(5)

where ${\widehat{\mu }}_i$ and ${\widehat{V}}_i$ are the estimates of the mean of the i-th variety, is the variance of the i-th variety across environments (${\widehat{V}}_i={\widehat{\sigma }}_u^2+{\widehat{\sigma }}_i^2$; $i=1,2,\dots ,I$), respectively, and $\mathrm{\Phi }\left(·\right)$ is the standard normal cumulative distribution function (c.d.f.). In the present study, the probabilities of the yields of varieties falling below the general mean were calculated; i.e., with (5) $\delta =\mu$.

Finally, the probability functions of the best-performing varieties from each country were compared using the relative risk concept [24]. For this purpose, we expressed $p\left(i_2\right)$ as a function of $p\left(i_1\right)$

$$p\left(i_2\right)=\mathrm{\Phi }\left({\displaystyle \frac{{\mathrm{\Phi }}^{-1}\left(p\left(i_1\right)\right)\sqrt{{\widehat{V}}_{i_1}}+{\widehat{\mu }}_{i_1}-{\widehat{\mu }}_{i_2}}{\sqrt{{\widehat{V}}_{i_2}}}}\right)$$

(6)

where ${\mathrm{\Phi }}^{-1}\left(·\right)$ is the inverse of the standard normal c.d.f. Next, the relative risks for the best varieties from each country were plotted.

3. Results

Means, standard deviations (SDs), and the minimum (min), median (med) and maximum (max) values of the grain yield in the Polish organic trials are given in

Table 1. Means, standard deviations (SDs), minimums (min), medians (med) and maximums (max) of observations for grain yield in the Polish organic trials.

Year	Mean [t/ha]	SD	Min	Med	Max
2020	4.804	1.426	2.333	4.394	7.914
2021	4.596	1.481	2.282	4.589	7.464
2022	4.777	1.737	1.626	4.659	8.687

. A graphical summary of the data set is shown in Figure 2. Barley yields in Polish organic trials ranged from 1.63 t/ha to 8.69 t/ha. The lowest and the highest mean yields were both observed in 2022.

The analysis of the model provided several estimated parameters and statistics (

Table 2. Variety means, Shukla’s stability variances, values of the simultaneous selection index, the relative performance genotypic performance values adaptability index (RPGV) and the probabilities that the yields of varieties would fall below the general mean.

Variety	Mean a,b [t/ha]	Shukla’s Stability Variance c	SSI	RPVG	Prob
Avatar	4.863 ab [4]	0.149 (0.058) [10]	14	1.029	0.466
Bente	4.931 a [1]	0.061 (0.028) [3]	4	1.045	0.448
Etoile	4.497 c [10]	0.145 (0.059) [9]	19	0.943	0.560
Farmer	4.577c [8]	0.083 (0.037) [4]	12	0.965	0.540
KWS Vermont	4.812 ab [5]	0.125 (0.051) [7]	12	1.017	0.479
Mecenas	4.878 ab [3]	0.040 (0.021) [2]	5	1.034	0.461
MHR Fajter	4.526 c [9]	0.123 (0.049) [6]	15	0.955	0.552
Pilote	4.619 c [7]	0.010 (0.013) [1]	8	0.976	0.529
Radek	4.920 a [2]	0.099 (0.042) [5]	7	1.046	0.451
Rubaszek	4.682 bc [6]	0.133 (0.053) [8]	14	0.991	0.512

^a Standard errors of differences: average = 0.005003, maximum = 0.006975 and minimum = 0.003941. ^b Means not sharing any letter are significantly different at the 5% level of significance. ^c The number in brackets denotes the standard error of an estimate.

). The variance component for environments was equal to 2.27 (s.e. = 0.75), whereas the variance for replicates nested within the environments was equal to 0.60 (s.e. = 0.01). The mean error variance from the series of field trials was 0.10. Furthermore, the inspection of the residual variances showed that the highest values were recorded in the year 2022 and at the Osiny and Tarnów sites (environments 22 Os and 22 Tar). Both variance components were approximately equal to 0.4. Furthermore, based on standardized residuals, the normality of the error assumption was verified (Figure 3). It can be seen that the points on the Q–Q plot were located along the $y=x$ line. Thus, the assumption of the normality of the errors was relatively well satisfied.

The Wald test statistic for testing variety effects amounted to 52.76. The approximate F statistic was 5.32 (n.d.f. = 13; d.d.f. = 53.4), and it was highly significant ($p<0.001$).

In column two of Table 2, the variety means are given. It can be seen that the Bente variety had the highest mean yield among the tested varieties. This variety was also the best of the German varieties. Among the Polish varieties, the Radek variety was the best. This variety was also ranked second overall. The Swiss variety Pilote ranked seventh. Furthermore, based on variety means, all pairwise comparisons with a letter display were performed. As a result, three groups of varieties can be distinguished: high-yielding varieties, poor-yielding varieties and moderate-yielding varieties. The poor-yielding group included the following varieties: Etoile, Farmer, MHR Fajter and Pilote.

Shukla’s stability variances are given in the third column of Table 2. It can be seen that the Pilote variety had the smallest value for Shukla’s stability variance. This means that this variety was the most stable among the tested varieties. The third best-yielding variety (Mecenas) was the second best in terms of Shukla’s stability variance and the most stable among the Polish varieties. The highest-yielding variety ranked third and was the best among the German varieties. On the other hand, the highest values of Shukla’s stability variance were recorded for the Avatar and Etoile varieties, which means these two varieties were the most unstable.

Values of the simultaneous selection index are given in the fourth column of Table 2. The lowest value of the SSI index was obtained for the highest-yielding variety, while the Mecenas variety was second best. The values of the SSI index for these two varieties were equal to four and five, respectively. This means that these two varieties were the most desirable for organic farming. The second highest-yielding variety (Radek) ranked third.

Based on the predicted environmental and variety × environment interaction means (Supplement S3), RPGV values were calculated. The values are given in the fifth column of Table 2. It can be seen that the highest values for RPGV were obtained for the Radek and Bente varieties. This means that these two varieties exhibited high adaptability to the agro-meteorological conditions of the environments. The third highest-yielding variety was also the third best in terms of RPGV. To illustrate these patterns (Figure 4), we plotted the variety × environment interaction means against environments, which were ordered longitudinally.

Furthermore, based on variety × environment interaction means (see also Figure 4), six mega-environments can be distinguished. The largest mega-environment was mega-environment M1 (21Tar, 21We, 22Ra, 22Sr, 22Sze and 22We), in which Bente was the best-performing variety. In the second largest mega-environment (M2), Avatar was the highest-yielding variety. This mega-environment included 20Gra, 20Sze, 21Sko and 22Gra. In the third mega-environment, M3 (20Os, 20We, 21Os and 21Sze), the Radek variety was the highest yielding. The smallest mega-environments, M4 (20Sko and 22Tar), M5 (20Os and 22Prz) and M6 (20Tar and 21Gra), were composed of the KWS Vermont, Mecenas and Rubaszek varieties, respectively.

The last column of Table 2 gives the probabilities that the yields of the varieties would fall below the general mean (Prob). A graphical presentation of the results is shown in Figure 5a. The vertical dashed red line indicates the general mean (Figure 5a). For a given variety, the value of Prob is the intersection of the risk function for that variety with the vertical dashed red line.

The lowest value of probability was recorded for the Bente variety, and it amounted to 0.448. For the Radek variety, the probability that the yield could fall below the general mean was equal to 0.451. Furthermore, for the Avatar, Bente, KWS Vermont, Mecenas and Radek varieties, the values of Prob were less than 0.5. For the other varieties, the values of Prob exceeded 0.5. This means that, for farmers, it would be risky to choose these varieties for organic cultivation. Moreover, it can be observed that the group of high-risk varieties overlaps with the group of poor-yielding varieties.

Finally, the relative risks for the Bente, Pilote and Radek varieties are plotted in Figure 5b–d. When the Bente and Radek varieties are compared (Figure 5b), it can be noted that these two varieties presented an equal risk. In a comparison of Pilote with Bente and Radek, it is evident that Pilote was more risky than the Bente and Radek varieties (Figure 5c,d).

4. Discussion

In the present study, we assessed the yield stability and adaptability of spring barley varieties in an organic system. In the literature on the subject of the stability of agronomic traits in organic and conventional systems, multi-environmental trials were assessed. These trials were further analyzed using either a two-stage or a one-stage approach (see, e.g., [6,10,13,14,17,32,33,34] and the references therein). In the former approach, each trial was analyzed separately, and afterwards, the means from all trials were analyzed using linear mixed models or the regression of the environmental mean approach. In the latter approach, the plot data were analyzed in a single stage.

In the present study, the plot data were analyzed using linear mixed models. This approach was preferred for several reasons. First of all, by using this approach, we fitted a linear mixed model with heterogeneous error variances across environments. The main advantage of modelling the heterogeneity of error variances is that a greater weight is ascribed to environments with higher-quality data, as defined according to a lower error variance [16]. Moreover, from the practical point of view, this assumption reflects reality more reliably than the homogeneity-of-error assumption used in the literature (see, e.g., [33,35]). Hu et al. [36,37] studied the impact of the homogeneity-of-error assumption on variety comparisons and stability analysis. They found that the residual homogeneity assumption may limit variety evaluations. Moreover, they showed that the homogeneity assumption also influences the reliability of variety recommendations. The heterogeneity of error variances was also assumed in [17]. In that study, the authors assessed the stability of eight potato varieties. Dias et al. [15] used the same assumption in their study on the application of probability concepts to variety recommendations. Next, using the described approach, it was possible to model the heterogeneity of the genotype × environment interaction. We thus accounted for the uncertainty regarding variety performances in different environments. According to Piepho [27], estimates of variances can be treated as estimates of Shukla’s stability variances. In the same study, he also showed that the most popular stability measures can be obtained by considering different covariance matrices for the vector genotype × environment interaction effects and/or by modifying the list of random effects in a linear mixed model. However, with an increasing number of trials and/or varieties, computational problems may occur. To solve these problems one can model only the heterogeneity of the genotype × environment interaction or fit a linear mixed model with heterogeneous error variances across environments and assess the stability of a given genotype across J environments based on the variance of genotype × environment interaction effects [15]. Another approach to addressing this issue is to fit a simple model with a single variance component for each random effect and use the harmonic mean of the relative performance of genotypic values as a stability measure [14,33]. Finally, using the described approach, we were able to calculate the probability that the mean of a given variety would exceed the general mean. Przystalski and Lenartowicz [14] used a similar approach and calculated the probability that the mean of a given variety for a given system would exceed the mean of control varieties in that system. In a different study, Dias et al. [15] introduced Eskridge’s Bayesian risk index and calculated the pair-wise probabilities of superior performance for 36 maize hybrids. According to Baker et al. [38], yield is the most important trait for US organic growers, whereas Knapp and van der Heijden [21] showed that yields in organic agriculture are more variable than in conventional agriculture. Thus, using risk analysis, plant breeders, crop experts and farmers can express their willingness to accept low yields in terms of probability. For this reason, we recommend supplementing stability analysis with risk analysis. For the most popular stability measures, the safety-first-selection index can also be used. The formulas are given in [22,23].

We conclude that Bente, Mecenas and Radek were the highest-yielding varieties among the tested varieties. On the other hand, the lowest yield was recorded for the Etoile variety. In turn, Pilote was the most stable variety among the tested varieties. The highest-yielding varieties were ranked third, second and fifth, respectively. Moreover, the lowest value of Prob was recorded for the Bente variety even though it was susceptible to leaf rust and net blotch [25]. For the other high-yielding varieties, the probabilities were below 0.47. We, therefore, conclude that the Bente, Mecenas and Radek varieties should be recommended for cultivation in organic systems.

In the current study, the mean grain yield was 4.730 t/ha. In a Latvian study, Legzdiņa et al. [39] reported that the mean yield in the years 2019–2021 was 2.02 t/ha. In a US survey study, Baker et al. [38] showed that the barley yield in the organic system in 2019 was 3.32 t/ha. On the other hand, in the Polish conventional post-registration field trials performed through the years 2020–2022, the mean grain yields ranged from 6.31 t/ha to 6.82 t/ha. Thus, the grain yield in the organic system was approx. 30% lower than that in conventional trials. This is in agreement with the results obtained by de Ponti et al. [40], Ponisio et al. [41] and Lesur-Dumulin [42]. However, for the 20Tar, 21Tar, 22Tar and 22Sr environments, the mean grain yields were close to 6.82 t/ha. On the other hand, for the 20Os, 20Sko, 21Gra 21Os, 22Os, 22Sze and 22We environments, the average yields were below 4 t/ha. The low yields in the 20Sko and 22We environments were mainly caused by weather conditions. The former environment experienced heavy rainfall from May to July, and temperatures in June and July exceeded 30 °C (Supplement S2). Moreover, in July, there were storms that caused lodging. In the latter environment, it was hot with little rainfall during the growing season. In the environments 21Gra and 22Sze, low yields can be partially explained by a high weed infestation intensity. The low yields in Osiny can be partially explained by the high net blotch pressure [25] and the fact that the experiment was carried out on podsolic or pseudopodzolic soils. However, the yields in the low-yielding environments can be improved through the use of manure and/or cover crops. Olesen et al. [43] showed that the application of 50 kg of NH₄–Nha⁻¹ in manure (slurry) increased the average barley grain DM yield by 1.0–1.3 MgDMha⁻¹. In the same study, they also showed that the use of catch crops (primarily perennial ryegrass) increased grain DM yield by 0.2–0.4 MgDMha⁻¹ with the smallest effect on loamy sand and sandy loam soils and the greatest effect on coarse sandy soil. Another method of yield improvement is to cultivate barley varieties suitable for organic agriculture. However, to date, no modern variety developed specifically for organic farming has been registered in Poland. Osman et al. [8] characterized varieties suitable for organic farming. From this perspective, the highest-yielding and most stable varieties can be used to breed new varieties. For this purpose, one of the breeding schemes described in [44], or the concepts and strategies of organic plant breeding described in [45], can be used.

Finally, two varieties from our list (Bente and Pilote) were registered in the Czech Republic in 2018. Thus, it would be insightful to compare the performance of these two varieties and other common varieties of the organic systems in Poland and neighboring countries, e.g., the Czech Republic, Germany and Slovakia. For this purpose, the approach proposed by Malik et al. [46] can be modified to analyze results from such a ring test. On the other hand, it would be prudent to determine which agro-meteorological factors influence spring barley grain yields in an organic system. To answer this question, the mixed-model factorial regression introduced by van Eeuwijk et al. [47] may be applied (see also [48]). We plan to explore these topics in future research.

5. Conclusions

The mean yields of ten barley varieties differed significantly. The Bente variety was the highest-yielding among the tested varieties. The lowest-yielding variety was Etoile. Based on all the pairwise comparisons, we distinguished between three groups of varieties: high-, moderate- and poor-yielding varieties. The group of high-yielding varieties included Bente, Mecenas and Radek. On the other hand, the Pilote variety was the most stable among the tested varieties, whereas the highest-yielding variety, Bente, ranked third. According to the RPVG index, the Radek and Bente varieties showed high adaptability to the agro-meteorological conditions in the environments. Finally, the lowest value for the probability that the yield of a given variety would fall below the general mean was recorded for Bente, and it amounted to 0.448. However, for the new highest-yielding varieties, the risk of falling below the overall mean should be reduced.