Genotype by environment interaction for main winter triticale varieties characteristics at two levels of technology using additive main effects and multiplicative interaction model

The aim of this study was to assess genotype by environment interaction for grain yield, plant height and thousand-grain weight in winter triticale cultivars by the additive main effects and multiplicative interaction (AMMI) model. The study comprised of ten winter triticale varieties i.e.: Algoso, Baltiko, Grenado, Magnat, Moderato, Pawo, Todan, Trimester, Trismart and Witon. Field trials were performed at seven locations in three years (21 environments) in a randomized complete block design, with two replicates at two levels of cultivation technology (standard – A1 and intensive – A2). Field experiments were carried out as part of Post Registration Variety Trials in Wielkopolska region. AMMI analyses revealed significant genotype and environmental effects as well as genotype by environmental interaction with respect to all three observed traits in both levels of cultivation intensity. The cultivars Algoso, Baltiko and Trimester are recommended for further inclusion in the breeding programs because of their stability and good average values of observed traits.


Introduction
Every year, several new varieties are entered in the National List of Registered Agricultural Plant Varieties admitted to use in Poland. In many works in the fields of agronomy, agriculture and biology, there is a need to study the impact of variety, agricultural technology, and the locations on the yield of plants. Such studies in Poland allow Post-Registering Variety Trials (PDO) experiments (Weber et al. 2017). Research conducted in the PDO system is focused on the needs of agricultural practice (Bujak et al. 2013). The main goal of PDO research is to help farmers correctly select the most valuable varieties for cultivation, adapted to local conditions (Padarewski and Rodrigues 2014;Derejko et al. 2016).
The area of winter triticale cultivation is about 3.5 million ha in the world, of which in Poland this cereal covers about 1.2 million ha, which is 1/3 of the total area of the world's crops. This makes our country the largest producer of triticale in the world. The share of winter triticale in Poland in the structure of crops of cereals with cereal mixtures was approximately 18%. Winter triticale is primarily a forage grain and its main advantages are high yield potential and very high forage value. An additional advantage is the possibility of sowing on weaker soils. Triticale is one of the tolerant plants the soil abundance in minerals and acidification. The spring thermal requirements of this cereal are greater than that of rye. Winter triticale later start with vegetation and has a slower growth dynamics in early spring than winter wheat. In the critical period (shooting-heading), the optimum temperature is 6-8 8C, and during the formation of grain-16-18 8C. Most important diseases and pest occurred on triticale are Fusarium spp., Blumeria graminis, Pyrenophora tritici-repentis, Puccinia recondita, and Phaeosphaeria nodorum. Most important pests occurred on triticale are Aphidoidea, Oulema spp., Oscinella frit and Agromyzidae.
In field crop trials, the response of quantitative traits to varied environmental conditions is determined by the additive main effects of genotype (G) and environmental conditions (E), as well as by non-additive effects of genotype-by-environment interactions (GEI). These interactions are well described by the additive main effects and multiplicative interaction (AMMI) model (Zobel et al. 1988). The AMMI model combines the analysis of variance (ANOVA) with additive parameters and the principal component analysis (PCA) with multiplicative parameters in a single analysis. AMMI model is most useful when multiplicative GE terms have agricultural interpretability (Ghaed-Rahimi et al. 2015;Shahriari 2018;Bocianowski et al. 2019b;Singh et al. 2019). The AMMI is, therefore, also known as interaction PCA (Gauch and Zobel 1990).
The aim of this paper was to assess genotype by environment interaction for three traits (grain yield, plant height and thousand-grain weight) in winter Fig. 1 Meteorological conditions (mean temperature and precipitation) in Bobrowniki from 2008 to 2010 triticale cultivars at two levels of cultivation intensity grown in 21 environments by the AMMI model.

Field experiments
Field experiments were conducted at seven locations (Wielkopolska region, Poland) of different soil and weather conditions. Soil conditions locations were varied, soils were included in the bonitation classes from II to IVa, e.g.: Kościelna Wieś -bonitation class IIIa, Bobrowniki -IVa, Ś rem -IIIb, Nowa Wieś Ujska -IVa, Borowo -II, Choryń -IIIa, Winna Góra -IIIa. The experiments were carried out during three vegetation seasons (2007/08, 2008/09, 2009/2010) using ten winter triticale varieties (Algoso, Baltiko, Grenado, Magnat, Moderato, Pawo, Todan, Trimester, Trismart and Witon) accepted for research as part of PDO trials in a randomized complete block design, with two replicates. Ten winter triticale cultivars analyzed in paper were on official list of Variety Protected By National Plant Breeders Right (PBR) in years of field experiments. Only variety Trimester was not registered at the Polish National List, in PDO trials variety was tested as a variety registered at the Common catalogue of varieties of agricultural plant species (CCA). The research material selected for the experiments is determined at the annual meetings of the PDO team for each voivodeship. The cultivar selection criteria are factors such as the cultivation acreage of a given cultivar, resistance, and yielding. Two levels of technology were used: standard (A1) and intensive (A2). Intensive technology is characterized by increased nitrogen fertilization, foliar multicomponent preparations, protection against lodging and pests. In experiment we observed three quantitative traits: grain yield [in t ha -1 ], plant height [in cm] and thousand-grain weight [in g]. Obtained data were analysed using AMMI model (Gauch and Zobel 1990) for each trait and for two levels of technology, independently. The AMMI model first fits additive effects for the main effects of genotypes (G) and environments (E) followed by multiplicative effects for GEI by PCA. Environments were defined as combinations of locations and years. Results of AMMI analysis were presented by biplot graphs. The AMMI model (Nowosad et al. 2016) is given by: where y ge is the trait mean of genotype g in environment e, l is the grand mean, a g is the genotypic mean deviations, b e is the environmental mean deviations, N is the number of PCA axis retained in the adjusted model, k n is the eigenvalue of the PCA axis n, c gn is the genotype score for PCA axis n, d en is the score eigenvector for PCA axis n, Q ge is the residual, including AMMI noise and pooled experimental error. The AMMI stability value (ASV) was used to compare the stability of genotype as described by Purchase et al. (2000): where SS IPCA1 is the sum of squares for IPCA1, SS IPCA2 -the sum of squares for IPCA2, the IPCA 1 and IPCA 2 scores are the genotypic scores in the AMMI model. Lower ASV score indicate a more stable genotype across environments . Genotype selection index (GSI) was calculated for each cultivar which incorporates both mean of trait and ASV index in single criteria (GSI i ) as (Farshadfar and Sutka 2003) where RM i is rank of trait mean (from maximal to minimal for grain yield and thousand-grain weight, and from minimal to maximal for plant height) for i-th cultivar, RA i is rank of the ASV for the i-th cultivar. Finally, total genotype selection index (TGSI) was calculated for each cultivar as sum of GSIs for all five traits of study, independently for A1 and A2 as well as for both levels of cultivation intensity.
The relationships between the particular traits (grain yield, plant height and thousand-grain weight) observed in different environments independently for two levels of cultivation technology (standard -A1 and intensive -A2) were assessed based on Pearson's correlation coefficients. These relationships were presented in the form of heatmaps. All the analyses were conducted using the GenStat v. 18 statistical software package.

A1
The three sources of variation were highly significant. In the analysis of variance, the sum of squares for environment main effect represented 21.20% of the total grain yield (in A1) variation. Environmental factors like weather, mainly temperature, rainfall influenced the condition of plants, and thus their susceptibility to diseases or pests occurrence. During the years of experiments, there were favorable meteorological conditions for the development of triticale.
The variability of the yield and the weight of a thousand grains was determined by the variety genotype (Figs. 1,2,3,4,5,6,7). The differences between genotypes explained 3.20% of the total grain yield variation, while the effects of GE interaction explained 71.0% (Table 1). Values for the three principal components were also highly significant and accounted jointly for 75.45% of the whole effect it had on the variation of grain yield. The first principal component (IPCA 1) accounted for 47.50% of the variation caused by interaction, while IPCA 2 and IPCA 3 accounted for 18.04 and 9.91%, respectively. Grain yield of the tested genotypes varied from 2.60 (for Grenado in E18) to 15.15 t ha -1 (for Pawo in E17) throughout the 21 environments, with an average of 12.20 t ha -1 ( Table 2). The cultivar Trimester had the highest average grain yield (10.53 t ha -1 ), and the Grenado had the lowest (9.01 t ha -1 ). The average grain yield per environments also varied from 6.65 t ha -1 in E06, to 13.36 t ha -1 E21 (Table 2). Genotype stability is considered as non significant reaction to changing environmental conditions, agronomic factors, weather conditions, biotic and abiotic stresses. In this study, climatic conditions were the source of this variation component. The stability of tested cultivars can be evaluated according to biplot for grain yield (Fig. 8). Winter triticale cultivars interacted differently with climate conditions in the observed environments. The cultivars Magnat, Tristan and Witon interacted positively with the E03 and E06 environ-ments, but negatively with the E09, E14 and E17 (Fig. 8). The cultivars Moderato, Todan and Trimester interacted positively with the E09, E14 and E17 environments, but negatively with the E01, E03 and E09. The analysis showed that some cultivars have high adaptation; however, most of them have specific adaptability. AMMI stability values (ASV) revealed variations in grain yield stability among the ten cultivars (Table 2). According to Purchase et al. (2000), a stable variety is defined as one with ASV value close to zero. Consequently, the cultivars Algoso and Baltiko with ASV of, respectively, 0.419 and 0.451, were the most stable, while the cultivars Grenado (8.224) and Trismart (2.347) were the least stable ( Table 2). The cultivars Algoso and Trimester with high average grain yield (10.41 and 10.53 t ha -1 , respectively) and ASV equal to, respectively, 0.419 and 0.900 are cultivars with the best genotype selection index (4).

A2
The sum of squares for environment main effect represented 83.78% of the grain yield variation. The differences between cultivars explained 1.18% of the grain yield variation, while the effects of GE interaction explained 12.51% (Table 1). Values for the three principal components were also highly significant and accounted jointly for 68.81% of the whole effect it had on the variation of grain yield (in A2). The IPCA 1 accounted for 34.41% of the variation caused by interaction, while IPCA 2 and IPCA 3 accounted for 19.35 and 15.05%, respectively. Grain yield of the tested cultivars varied from 5.60 (for Grenado in E03) to 17.75 t ha -1 (for Witon in E18) throughout the 21 environments, with an average of 12.20 t ha -1 ( Table 3). The Algoso the highest average grain yield (12.75 t ha -1 ), and the cultivar Grenadohad the lowest (11.45 t ha -1 ). The average grain yield per environments also varied from 8.54 t ha -1 in E01, to 16.88 t ha -1 in E18. The cultivars Tristan and Witon interacted positively with the E02, E06 and E12 environments, but negatively with the E16 and E21 (Fig. 9). The cultivars Baltiko, Magnat, Moderato, Todan and Trimester interacted positively with the E07, E09, E14, E16, E18 and E21 environments, but negatively with the E02 and E14. The cultivar Grenado interacted positively with the E08, E19 and E20 environments, but negatively with the E03 and E15. The cultivars Magnat and Trimester with ASV of, respectively, 0.578 and 0.643, were the most stable, while the cultivars Grenado (4.847) and Witon (1.923) were the least stable (Table 3). The cultivars Algoso and Todan with the average grain yield equal to 12.75 and 12.34 t ha -1 , respectively, and ASV equal to 0.832 and 0.710, respectively, are cultivars with the best genotype selection index (6).

A1
The three sources of variation were highly significant. In the analysis of variance, the sum of squares for environment main effect represented 31.66% of the total plant height variation. The differences between genotypes explained 47.43% of the total plant height variation, while the effects of GE interaction explained 12.49% (Table 1). Values for the first two principal components were also highly significant and accounted jointly for 67.44% of the whole effect it had on the variation of plant height. The first principal component (IPCA 1) accounted for 38.87% of the variation caused by interaction, while IPCA 2 accounted for 28.57%. Plant height of the tested cultivars varied from 79 (for Grenado in E15) to 156 cm (for Witon in E11) throughout the 21 environments, with an average of 115.1 cm ( Table 4). The cultivar Moderato had the highest average plant height (126.3 cm), and the cultivar Baltiko had the lowest (97 cm). The average plant height per environments also varied from 101.2 cm in E15, to 130.8 cm in E10. The stability of tested cultivars can be evaluated according to biplot for plant height (Fig. 10). Winter triticale cultivars interacted differently with climate conditions in the observed environments. The cultivars Baltiko, Grenado and Trimester interacted positively with the E02 and E10 environments, but negatively with the E09, E12 and E18 (Fig. 10). The cultivars Moderato, Pawo and Todan interacted positively with the E06, E09, E12 and E18 environments, but negatively with the E02.  The cultivar Witon interacted positively with the E11 environment. AMMI stability values (ASV) revealed variations in plant height stability among the ten cultivars (Table 4). The cultivars Algoso and Trismart with ASV of 0.957 and 1.919, respectively, were the most stable, while the cultivars Witon (7.860) and Moderato (4.283) were the least stable (Table 4). The cultivar Baltiko with the lowest average plant height (97 cm) and ASV equal to 1.928 is genotype with the best genotype selection index (4) ( Table 4).

A2
The three sources of variation for the plant height were highly significant. In the ANOVA, the sum of squares for environment main effect represented 41.17% of the total plant height variation. The differences between genotypes explained 40.85% of the total plant height variation, while the effects of GE interaction explained 12.39% (Table 1). Values for the three principal components were also highly significant and accounted jointly for 72.59% of the whole effect it had on the variation of plant height.  (Fig. 11). The cultivars Moderato and Todan interacted positively with the E03, E12 and E21 environments, but negatively with the E02, and E08 (Fig. 11). The cultivars Baltiko and Magnat interacted positively with the E01 and E08 environments, whereas Trimester and Witon with the E11 and E14. The cultivar Algoso with ASV of 1.039, was the most stable, while the cultivars 11.238 (11.238) and Todan (9.048) were the least stable (Table 5). The cultivar Witon with low average plant height (108.7 cm) and ASV equal to 2.276 is cultivar with the best genotype selection index (7).  Thousand-grain weight

A1
In the ANOVA, the sum of squares for cultivars main effect represented 17.21% of the total, and this factor had the highest effect on the thousand-grain weight.
The differences between environments explained 64.75% of the thousand-grain weight variation, while the effects of GE interaction explained 15.36% (Table 1). Values for the three principal components were also highly significant. The three principal components of GE interaction accounted jointly for 73.77% of the whole effect it had on the variation of thousand-grain weight. The first principal component (IPCA 1) accounted for 44.94% of the variation caused by interaction, IPCA 2 accounted for 16.66% while IPCA 3 accounted for 12.17% (Fig. 12). Thousandgrain weight of the tested cultivars varied from 19.45 (for Grenado in E03) to 60.07 g (for Todan in E14) throughout the 21 environments, with an average of 39.21 g ( Table 6). The Todan had the highest average thousand-grain weight (43.87 g), and the Grenado had the lowest (32.49 g). The average thousand-grain weight per environments also varied from 22.20 g in E01 to 49.27 g in E08. The stability of tested lines can be evaluated according to biplot for thousand-grain weight (Fig. 12). The cultivar Trimester interacted positively with the E06 (Fig. 12). The cultivars Baltiko and Magnat interacted positively with the   E03, E13 and E21, but negatively with the E14, E17 and E18. The cultivars Algoso, Grenado and Moderato interacted positively with the E001, E02 and E10, but negatively with the E109, E12 and E18. The cultivar Witon with ASV of 2.014 was were the most stable, while the cultivars such as Todan (9.223) and Grenado (8.928) were the smallest stable (Table 6). A cultivar Algoso with averages of thousand-grain weight equal to 41.74 g and and good ASV (2.231) had the best genotype selection index (6). However, the Grenado has the worst genotype selection index (19).

A2
The three sources of variation for the thousand-grain weight were highly significant. In the ANOVA, the sum of squares for environment main effect represented 67.81% of the total thousand-grain weight variation. The differences between genotypes   explained 15.45% of the total thousand-grain weight variation, while the effects of GE interaction explained 14.29% (Table 1). Values for the three principal components were also highly significant and accounted jointly for 76.64% of the whole effect it had on the variation of thousand-grain weight. The first principal component (IPCA 1) accounted for 36.99% of the variation caused by interaction, while IPCA 2 and IPCA 3 accounted for 20.61 and 19.04%, respectively. Thousand-grain weight of the tested cultivars varied from 15.95 (for Grenado in E03) to 64.79 g (for Trismart in E18) throughout the 21 environments, with an average of 40.92 g ( Table 7). The Trismart had the highest average thousand-grain weight (47.72 g), and the Grenado had the lowest (34.01 g). The average thousand-grain weight per environments also varied from 21.72 g in E01, to 52.63 g in E17. The stability of tested cultivars can be evaluated according to biplot for thousand-grain weight (Fig. 13). The cultivars Todan and Trimester interacted positively with the E12 and E21 environments, but negatively with the E03 and E06 (Fig. 13). The cultivar Trismart interacted positively with the E09 and E18, but negatively with the E14 and E17. The cultivar Magnat interacted positively with the E03 and E06. The cultivar Pawo with ASV of 0.568 was the most stable, while the Algoso (5.288) and Trismart (5.020) were the least stable (Table 7). The cultivar Pawo with medium average thousand-grain weight (40.22 g) and the best ASV (0.568) is cultivar with the best genotype selection index (7). The Grenado has the worst genotype selection index (15).   Total genotype selection index The best total genotype selection index we observed for cultivar Algoso (TGSI = 46), while the worst -Grenado (TGSI = 96). For A1 level of cultivation intensity cultivar Algoso was the best TGSI (18), however for A2 -Magnat (TGSI = 25). Cultivar Grenado was the worst in both level of cultivation intensity (49 for A1 nad 47 for A2). The cultivars Algoso, Baltiko and Trimester are recommended for further inclusion in the breeding programs because of their stability and good average values of observed traits.
For thousand-grain weight we observed 101 from 210 significant correlation coefficient at standard level of technology (Fig. 18) and 102 from 201 at intensive level of technology (Fig. 19).

Discussion
Field experiments carried out under PDO system are a valuable source of information for farmers in terms of selection of varieties for cultivation. Every year, several new varieties entered into the National Register of Varieties of Agricultural Plants are admitted for using in Poland. In addition, after Poland's accession to the structures of the European Union, legal regulations at the EU level, allow the placing on the market of plant varieties registered in any Community country. The result is that the farmer has the option of choosing up to several dozen varieties of crops, e.g. triticale 1000. This can cause serious difficulties in choosing the right variety even for the best growers in its specific soil and climate conditions. PDO system on the base of an extensive system of post-registration Fig. 12 Biplot for genotype by environment interaction of thousand-grain weight in winter triticale cultivars at standard level of technology (A1) in 21 environments, showing the effects of primary and secondary components (IPCA 1 and IPCA 2, respectively) Table 7 Average thousand-grain weight (g), for genotypes and environments, principal component analysis values, AMMI stability value (ASV), rank of the AMMI stability value (RA), rank of trait mean (RM, from maximal to minimal), and genotype selection index (GSI) of tested winter triticale cultivars at intensive level of technology (A2) Env  experiments and recommendation of varieties for particular species of arable crops significantly facilitates the selection of the right variety for specific farming conditions, which is one of the requirements of integrated protection. Poland in the EU ranks third in terms of cereal sown area, and the world's first in triticale production. The growing interest in triticale and the ever-increasing selection of new, improved varieties, often focused on specific use in the food or feed industry, requires research to confirm their usefulness. The most important and the most valuable effect of research conducted in the PDO system for farmers is an annual ''List of cultivars recommended for cultivation in the area of the province''. Research carried out in the system of PDO are directed directly at the needs of agricultural practice. Growers thanks to this type of research have continuous information about the value of varieties, including selection of the right varieties cultivated crop species. The grain yield, plant height and thousand-grain weight in winter triticale are traits determined by multiple genes that cause change in the performance of genotypes depending on the cultivation environment. That is why the importance of GEIs in plant breeding programs have been a focus of attention for triticale breeders (Miedaner et al. 2001;Motzo et al. 2001;Fig. 13 Biplot for genotype by environment interaction of thousand-grain weight in winter triticale cultivars at intensive level of technology (A2) in 21environments, showing the effects of primary and secondary components (IPCA 1 and IPCA 2, respectively) Santiveri et al. 2004;Oettler and Wahle 2008). GEI is an important and challenging issue for plant breeders especially in developing new improved varieties. Multi-environment trials are used to determine sites representing the target environment and can identify superior cultivars for recommendation to breeders (Goyal et al. 2011). Goyal et al. (2011) characterized of triticale genotypes for stability of yield and other quality traits, as well as GEI and adaptability, constitute a starting point towards the development of new breeding populations for the improvement of yield, and quality traits in triticale for southern and central Alberta, Canada. These results provide impetus for using triticale feedstock in the biorefinery industry, and show that germplasm is available to enhance cultivar development. Data collected from such trials are needed for precise estimation of genotype value and yield stability (Yan and Hunt Fig. 14 Heatmap for linear Pearson's correlation coefficients between grain yield observed in different environments (E01 -E21see Table 1) at standard level of technology (A1); r critical = 0.5760 2001). These trials facilitate quantification of the environment and GEIs. Differences in environmental conditions may cause large GEIs, especially under drought-prone environments (Bocianowski et al. 2019a).
The AMMI model was often used in study of many species (Branković-Radojčić et al. 2018;Fotso et al. 2018;Hassani et al. 2018;Bocianowski et al. 2019c). The AMMI model provides a useful tool in diagnosing GEI patterns and improving the accuracy of response estimates. It enables clustering of genotypes based on similarity of response characteristics and identifying potential trends across environments (Bocianowski et al. 2018). The suggested strategy could extract more information from the GEI, thereby aiding researchers in identifying specific cultivars with competitive yields across diverse environments. The genotype and environment main effects as well as GEI had the Fig. 15 Heatmap for linear Pearson's correlation coefficients between grain yield observed in different environments (E01 -E21see Table 1) at intensive level of technology (A2); r critical = 0.5760 strongest effect on all three observed traits (grain yield, plant height and thousand-grain weight), in both levels of cultivation intensity (standard and intensive), expression in Wielkopolska region Poland. AMMI analyses permits estimation of interaction effect of a genotype in each environment and it helps to identify cultivars best suited for specific environmental conditions. AMMI analyses revealed significant GE interaction with respect to all three traits in both levels of cultivation intensity. The AMMI stability value exposed high cultivars stability. Yang et al. (2009) reported that biplot, based on AMMI, is a useful Fig. 16 Heatmap for linear Pearson's correlation coefficients between plant height observed in different environments (E01 -E21 -see Table 1) at standard level of technology (A1); r critical = 0.5760 visualization techniques to find similarity or dissimilarity among genotypes or environments. Yang et al. (2009) also cautions against the use of a biplot beyond a visual descriptive tool as the method utilizes only a sample of the full data set and does not involve any statistical hypothesis testing. The AMMI results displayed on the GE biplot enables determination of the main effect of the genotype, the environment, and the most meaningful GEIs.
In general, environments with scores near zero have little interaction across cultivars and provide low discrimination among cultivars (Anandan et al. 2009). In this study, these patterns were observed in E10, E13 and E20 environments (Figs. 8,9,10,11,12,13). AMMI models are capable of measuring the weight of the environments, the genotypes and their interactions throughout a value that measures how stable a genotype is in all environments in terms of particular Fig. 17 Heatmap for linear Pearson's correlation coefficients between plant height observed in different environments (E01 -E21see Table 1) at intensive level of technology (A2); r critical = 0.5760 observed traits. The cultivars Algoso, Baltiko and Trimester are recommended for further inclusion in the breeding programs because of their stability and good average values of observed traits. For these cultivars we obtained the best total (calculated for all three traits in both levels of cultivation intensity) genotype selection index (TGSI = 46, 52 and 53, respectively).

Conclusions
Obtained results show that genotypes, environments and GEI are highly significant indicating the existence of a wide range of variation between the cultivars, environments and their interactions. The existence of such significant GEI indicated possibility of selection of stable cultivars across the environments. Sources of genetic resistance used in cultivars Algoso, Baltiko and Trimester breeding programs are recommended Fig. 18 Heatmap for linear Pearson's correlation coefficients between thousand-grain weight observed in different environments (E01 -E21see Table 1) at standard level of technology (A1); r critical = 0.5760 for further inclusion in the breeding programs because of their stability and good average values of observed traits. For these cultivars we obtained the best total genotype selection index.

Compliance with ethical standards
Conflict of interest Authors declare that they have no conflict of interest.
Ethical approval This article does not contain any studies with human participants or animals performed by any of the authors.
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