Evaluation of resistance and determination of stability of different sugar beet (Beta vulgaris L.) genotypes in rhizomania‐infected conditions

Abstract Plant diseases are considered one of the main factors reducing yield and quality of crops, which are constantly developing and creating more virulent races and cause the resistance of more genes to break. Identifying resistance sources and including them in breeding programs will improve resistant genotypes. Rhizomania is the most common, widespread, and devastating disease of sugar beet in Iran and worldwide. Breeding genotypes with disease resistance genes is one of the most important ways to deal with this destructive disease. Twenty sugar beet genotypes along with five controls were evaluated in a randomized complete block design with four replications in rhizomania‐infected conditions in four regions of Mashhad, Shiraz, Miandoab, and Hamedan for 2 years. The results of genotypic reaction to rhizomania showed that the genotypes with resistance reaction were much more frequent than those with susceptibility reaction. The analysis of multiplicative effects of the AMMI model showed that the first six components were significant and explained 98.80% of the interaction variations. The biplot obtained from the mean white sugar yield and the first interaction principal component confirmed the superiority of the RM5 genotype due to its high white sugar yield and stability in infected conditions. The results obtained from the first three principal components biplot showed that the RM9 genotype with a mean white sugar yield of 11.91 t. ha−1 was a genotype with vast general stability in all disease‐infected environments. Based on the results of the MTSI index, RM3, RM17, RM9, RM13, and RM15 are introduced as stable genotypes under rhizomania‐infected conditions. In conclusion, it seems that the studied genotypes have valuable and useful genes inherited from their parents to deal with rhizomania disease. Applying these genotypes in sugar beet breeding programs can effectively prevent the threat of rhizomania.

that the first six components were significant and explained 98.80% of the interaction variations. The biplot obtained from the mean white sugar yield and the first interaction principal component confirmed the superiority of the RM5 genotype due to its high white sugar yield and stability in infected conditions. The results obtained from the first three principal components biplot showed that the RM9 genotype with a mean white sugar yield of 11.91 t. ha −1 was a genotype with vast general stability in all disease-infected environments. Based on the results of the MTSI index, RM3, RM17, RM9, RM13, and RM15 are introduced as stable genotypes under rhizomaniainfected conditions. In conclusion, it seems that the studied genotypes have valuable and useful genes inherited from their parents to deal with rhizomania disease.
Applying these genotypes in sugar beet breeding programs can effectively prevent the threat of rhizomania.

K E Y W O R D S
adaptation, gene, infection, race, susceptibility

| INTRODUC TI ON
According to United Nations (2019) investigations, the world population is expected to increase from 7.7 billion people in 2019 to 8.5 in 2030, 9.7 in 2050, and 10.9 in 2100. Naturally, with the growth of population, the demand for food will increase significantly. Sugar is a common molecule that has been of special nutritional importance in all eras (Eggleston, 2019). This molecule acts as a tonic matter and provides a large part of the energy in the human diet. Sugar beet is an important agricultural product which is exclusively used in the sugar industry (Akyüz & Ersus, 2021) and is considered one of the most important sources of sugar production after sugar cane (Monteiro et al., 2018;Ribeiro et al., 2016) so that currently, it accounts for 20%-30% of the world sugar production (Iqbal & Saleem, 2015;Monteiro et al., 2018;Ribeiro et al., 2016). Sugar is the main product of sugar beet, but, in addition, many other by-products such as molasses, marc, and ethyl alcohol are also extracted from this plant during the sugar production process (Tomaszewska et al., 2018). In addition, the leaf of this plant has protein compounds (Lammens et al., 2012;Tenorio et al., 2017) and balanced amino acids (Akyüz & Ersus, 2021;Kiskini et al., 2016), which reveals the nutritional quality of sugar beet leaves. Therefore, considering the importance of sugar beet in the nutrition of human societies, it is necessary to pay attention to its yield and quality.
Agricultural production is influenced by biotic and abiotic stresses. These factors challenge the plant's quantitative and qualitative production and destroy a considerable part of agricultural products annually. Diseases and pests are among the most important biotic stresses that affect both quantitative and qualitative aspects of plant products (Abdallah et al., 2003;Oerke, 2006). Sugar beet (Beta vulgaris L.) is no exception to this rule and is influenced by pathogens. Rhizomania is one of the most common diseases of sugar beet in the world (Galein et al., 2018), which can cause a sharp decrease in yield and product quality (Rezaei, 2007). The disease is caused by Beet Necrotic Yellowing Vein Virus (BNYVV) and its vector is Polymyxa betae Keskin (Tamada, 1975;Tamada & Baba, 1973), which has potentially been a destructive disease of sugar beet on a global scale (McGrann et al., 2009) in such a way that the amount of damage caused by it may lead to the destruction of sugar beet fields on a large scale. The first report of the disease published in the world was related to northern Italy in 1952 (Pavli et al., 2011).
This disease in Iran was reported for the first time in Fars province by Izadpanah et al. (1996); subsequently, its existence was proved in sugar beet fields of most parts of the country (Arjmand & Ahun Manesh, 1996). Of course, the spread of rhizomania is not unique to Iran, and currently, this disease is known as the most important cause of damage in sugar beet fields in most countries of the world (Galein et al., 2018;Lennefors, 2006;Tamada, 1999). Therefore, if effective methods are not used to control it, it will significantly reduce crop yield and quality (Rezaei, 2007).
Genetic, chemical, agronomical, and biological control methods have been presented against rhizomania disease. Among the mentioned methods, agronomical and biological methods are not very important due to their low ability to control the disease and compared to the genetic and chemical control methods, they are less used. Control of the disease by chemical compounds is not always practical due to the high cost, the risk of the developing of pathogen's resistance to it, and the possibility of environmental pollution; On the other hand, due to the soil-borne nature of rhizomania disease and the ineffectiveness of conventional methods of combating soilborne diseases, the pioneers of breeding disease-resistant varieties consider genetic resistance as the most effective way to reduce the damage caused by such diseases. In this regard, it is most important to investigate the amount of genetic diversity in cultivars and lines and carry out genetic studies to identify and select disease-resistant genotypes; Therefore, the present study was conducted to evaluate sugar beet genotypes in terms of resistance to rhizomania disease and yield stability to use resistant genotypes in breeding programs and also to introduce them for cultivation in infected environments.

| Disease assessment and measurement of quantitative and qualitative root traits
The disease severity was recorded at harvest stage according to the After harvesting and recording of disease severity and root yield, the roots were washed and a pulp sample was randomly prepared from the roots of each plot; the pulp samples were then examined at the quality control laboratory for quality characteristics including sugar content, alpha-amino N, sodium (Na + ), and potassium (K + ) elements (Kunz et al., 2002). Finally, the obtained values were used to estimate other characteristics such as sugar yield, molasses sugar, white sugar content, white sugar yield, and extraction coefficient of sugar, based on Equations 1 to 5, respectively (Cook & Scott, 1993;Reinfeld et al., 1974).

| Statistical analysis
Before any analysis, the homogeneity of the variances of experimental errors was checked with Bartlett's test (Bartlett, 1937). After the homogeneity of error variances was confirmed, a combined variance analysis was performed on each trait's data. Since the white sugar yield includes the values of other studied traits, it is considered a significant and final trait; Therefore, Additive Main Effect and Multiplicative Interactions (AMMI) stability analysis was performed in terms of this trait. Equation 6 was used to perform stability analysis by the AMMI method (Gauch, 1992): Where Y ge is the yield of genotype g in environment e; is the grand mean; g is the genotype deviation from the grand mean; e is the environment deviation; n is the singular value for IPC n and correspondingly 2 n is its eigenvalue; gn is the eigenvector value for genotype g and component n; en is the eigenvector value for environment e and component n, with both eigenvectors scaled as unit vectors; and ge is the residual. By performing AMMI analysis of variance using R software, the eigenvalues were obtained for each genotype and environment, and by drawing their biplots, the general and specific adaptability of the genotypes was determined. During this study, 13 statistics obtained from the AMMI model were used to identify the stable genotype in disease-infected conditions through Equations 7 to 18: (2) MS = 0.0343 K + + Na + + 0.094(alpha amino N) − 0.31

TA B L E 2 Geographical characteristics of the experimental research stations
where AMGE is the sum across environments of GEI modeled by AMMI (Sneller et al., 1997), ASI is the AMMI stability index (Jambhulkar et al., 2014), ASV is the AMMI stability value (Purchase et al., 2000), ASTAB is AMMI-based stability parameter (Rao & Prabhakaran, 2005), AV AMGE is the sum across environments of the absolute value of GEI modeled by AMMI (Zali et al., 2012), Da is Annicchiarico's D parameter (Annicchiarico, 2002), Dz is Zhang's D parameter (Zhang et al., 1998), EV is the average of the squared eigenvector values (Zobel, 1994), FA is the stability measure based on fitted AMMI model (Raju, 2002), MASI is the modified AMMI stability index (Ajay et al., 2018), MASV is the modified AMMI stability value (Zali et al., 2012), SIPC is the sum of the absolute values of the IPC scores (Sneller et al., 1997), and Za is the absolute value of the relative contribution of IPCAs to the interaction (Zali et al., 2012).
MTSI index was computed to calculate the mean yield and simultaneous stability of root yield, sugar yield, sugar content, white sugar yield, white sugar content, sodium, potassium, alpha-amino nitrogen, extraction coefficient of sugar, and molasses sugar based on Equation 20 (Olivoto et al., 2019): where MTSI i is the multi-trait stability index of the genotype i, ij is the score of the genotype i in the factor j, and j is the score of the ideal genotype in the factor j. Scores were calculated based on factor analysis for genotypes and traits.

| Assessment of genotypic response to disease
The results of examining the reaction of genotypes against rhizomania disease based on the Luterbacher et al. (2005) method are given in Table 3. resistance reaction to the disease during the 2 years of the experiment, and they had a reaction in the semi-resistant to semi-sensitive range. What is certain is that during both years, the infection severity of genotypes in Shiraz was higher than that in Mashhad. Therefore, it can be acknowledged that the environmental conditions in Shiraz for the development and establishment of more virulent isolates of rhizomania were more favorable than the environmental conditions in Mashhad; Therefore, genotypes should be recommended for cultivation in Shiraz that have more effective resistance genes against the disease to prevent its development and causing heavy damages due to the reduction of sugar content and root yield.

| Combined analysis of variance
Bartlett's test (Bartlett, 1937) confirmed the uniformity of error variances in different trials. Therefore, to determine the genotype × environment interaction on the data obtained from the root yield, sugar yield, sugar content, white sugar content, white sugar yield, Na + , K + , alpha-amino N, molasses sugar, and extraction coefficient of sugar, a combined analysis of variance was performed (Table 4). The main effects of year, location, and genotype for all the mentioned traits 0.5 were significant at 1% probability level. Two-way interactions of year × location (except for K + ), year × genotype, and location × genotype were significant for all studied traits at 1% probability level. The three-way interaction of genotype × year × location was significant at 1% and 5% probability levels for all studied traits. The significance of the interactions is due to the large variations in genotypes across the years and locations under investigation, as well as variation in the relative rank of genotypes.  Note: *, **Significant at 5% and 1% probability levels, respectively.

| AMMI analysis
According to the AMMI model results (  (2021) (2018) and Shiraz (2019). RM3 followed by RM15, BTS335, and RM9 had general adaptation due to being close to the origin of coordinates.
To ensure the maximum reliability of the results, the biplot of the first three principal components (Figure 1c) was also used to iden- The results of the average white sugar yield of genotypes and different stability statistics of AMMI analysis can be seen in and Sharifi et al. (2017). They acknowledged that the most accurate model in the AMMI decomposition could be predicted using the first two principal components. Despite the different stability analysis methods, the AMMI model provides useful information to achieve accurate results (Sharifi et al., 2017). Based on the results of the present study, the majority of stable genotypes based on different AMMI stability statistics had an average white sugar yield around the total average. Meanwhile, Ajay et al. (2020) reported that according to these 12 AMMI stability statistics (especially SIPC, MASI, and MASV statistics), high-yielding genotypes can be identified.

| MTSI analysis
Factor analysis was done based on principal component analysis, and interpretation of results was performed after Varimax rotation. The results of factor analysis are presented in Table 7. Factors with eigenvalues greater than 1 were selected, and the variance of each factor was expressed as a percentage, which indicates its importance in interpreting the overall variations in the data. In this analysis, three independent factors explained 90.83% of data variation. The first factor explained 42.79% of data variance and had an eigenvalue of 3.85. This factor had high and negative coefficients for white sugar content, Na + , K + , sugar content, extraction coefficient of sugar, and molasses sugar. The second factor with an eigenvalue of 2.56 and justification of 28.53% of total variance, included high and positive factor coefficients for root yield, white sugar yield, and sugar yield. The third factor explained 12.57% of data variation, and with an eigenvalue of 1.13 displayed a high and negative factor coefficient for alpha-amino N. The MTSI stability index of the studied genotypes was calculated based on factor scores of the three mentioned factors.
According to the MTSI index, if the genotype value is less than this index, it is less distant from the ideal genotype. On the other hand, if the MTSI value is higher for the genotype, it means that it is more distant from the ideal genotype and should not be selected (Olivoto et al., 2019). In Figure 2a, genotypes. This increase in the value of traits was aimed at the intended goals. The goal that is followed in Na + , K + , alpha-amino N, and molasses sugar is to reduce their value, and the selected genotypes showed have a lower value in terms of these traits. In general, the selected genotypes caused a favorable selection differential in all traits except sugar content and white sugar content (  RM3 and RM15, which had the lowest value in the first factor for sugar content, Na + , K + , white sugar content, extraction coefficient of sugar, and molasses sugar, and the highest factor coefficients in this factor, are close to the ideal genotype. The ideal genotype is defined according to the traits contained in each factor and the goals that are intended to improve those traits. RM15, RM17, RM3, and TA B L E 7 Eigenvalues, relative and cumulative variance as well as factor coefficients after varimax rotation in factor analysis based on principal component analysis

| CON CLUS ION
Rhizomania disease is one of the main factors in reducing quantitative and qualitative yield of sugar beet. Breeding genotypes with disease resistance genes is one of the most important solutions to deal with this destructive disease. Identifying sources of resistance and including them in breeding programs will improve resistant genotypes. For this purpose, in the present study, the resistance level of sugar beet genotypes against rhizomania disease was investigated in terms of the infection severity and quantitative and qualitative traits. The analysis of variance for the studied traits in different areas infected with the disease showed significant genetic diversity among the genotypes. The results of the genotypes evaluation in terms of reaction to rhizomania disease showed that the number of genotypes with resistance reaction is much more than the number of genotypes with sensitivity reaction. Examining the genotypes yield stability in disease-infected environments by different statistics introduced somewhat different genotypes as stable ones in terms of white sugar yield, but overall, the majority of stability analysis methods agreed on the stability of RM18, RM3, RM9, and BTS335; However, the MTSI stability statistic considering all the traits presented somewhat different results and introduced RM3, RM17, RM9, RM13, and RM15 as stable genotypes in terms of all the investigated traits under disease-infected conditions.

ACK N OWLED G M ENTS
The authors are thankful to technicians at Sugar Beet Seed Institute (SBSI), Karaj, Iran for their assistance in conducting the experiments.
F I G U R E 2 (a) Ranking of genotypes in ascending order based on MTSI index and (b) Strengths and weaknesses of selected genotypes as the ratio of each factor in the calculated MTSI index. Abbreviations: SD, selection differential; SD perc, selection differential in percentage; SG, selection gain; SG perc, selection gain in percentage; Xo, original value; Xs, selected value.

FU N D I N G I N FO R M ATI O N
This work was supported by the Sugar Beet Seed Institute (SBSI), Karaj, Alborz, Iran. The funding body was involved in the material creation.

CO N FLI C T O F I NTE R E S T
The authors report no conflicts of interest in this work. The authors alone are responsible for the content and writing of this article.

DATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.