1 Introduction

The eastern quadrants of Africa, near the borders of Ethiopia and Sudan, were identified as home to the domesticated sorghum crop [6]. Sorghum is the fifth most common major crop after barley, wheat, rice, and maize [7]. The crop has been used as food, feed and fodder in different parts of the world [1,2,3,4]. It is a staple food for more than half a billion poor and food insecure people worldwide [5]. Despite being referred to as the "camel crop" and predominating in lowland areas, sorghum is more geographically adaptable than all other cereal crops in Ethiopia, growing throughout the nation's lowlands and highlands [6]. Ethiopia is the third largest producer of sorghum in Africa, behind Sudan and Nigeria, and the eighth largest producer of sorghum in the world [7]. However, its production is limited to less than 2.1 tons ha−1 due to both biotic and abiotic constraints [5, 8]. According to [9], nitrogen is one of the scarcest nutrients used in modern agricultural production, yet it is also a vital component of plants that increases crop yield. Additionally, according to [10], it is essential for the synthesis of amino acids, proteins, and plant pigments such as chlorophyll.

Like many crops, nitrogen stress poses challenges to the production and improvement of sorghum crops, and nitrogen stress has been identified as the second most common abiotic stress affecting sorghum production after soil‒water deficit in Ethiopia compared to many Eastern and Southern African countries [5]. Therefore, large-scale applications of synthetic nitrogen fertilizer have been applied to improve yield gain by alleviating nitrogen deficiency in soil. However, because crops have low nitrogen use efficiency [11], approximately only 33% of the nitrogen fertilizer that is applied is absorbed by plants; the remaining 50–70% of the fertilizer is lost to the surroundings as a result of leaching, volatilization, groundwater runoff, and emissions of nitrous oxide from N fertilizer residues [12,13,14,15]. To lessen the overuse of commercial nitrogen fertilizers, their related expenses, and the emissions of nitrous oxide [16] into the atmosphere, NUE traits must be incorporated into crop yield improvement programs, and crop varieties that absorb and metabolize nitrogen in the most efficient way need to be selected [17, 18].

The increasing global population is placing a great deal of pressure on agricultural regions to produce more food and energy per unit area. Within this paradigm, increasing nitrogen use efficiency (NUE) is one component that can be used to maximize yield in eco-friendly manner [19]. Farmers can enhance their return on investment without compromising productivity by using genotypes that are adept at using nitrogen efficiently. This would also protect the environment, human, and animal health. In a similar vein, using nitrogen stress tolerant genotypes could also help in producing a good yield on marginal areas with poor soil. To select genotypes that are resistant to nitrogen stress, scientists have discovered a wide range of reliable indices [20]. The indices are mathematical equations that account for a plant's performance in both stressful and non-stressed environments [21,22,23]. Identifying genotypes resistant to nitrogen stress can be performed efficiently and precisely by using multiple selection indices [24].To date, indices have been applied to screen maize for heat and drought tolerance [25, 26], sorghum [27, 28], bread wheat [21, 29,30,31], barley [32, 33], bean bush [34], kidney bean [35], safflower [36], cotton germplasm [37], salt-tolerant sorghum [38], nitrogen stress tolerance in corn [23], and [24, 39, 40]wheat. Nevertheless, research on the identification of reliable indices Sorghum bicolor L. Moench. To select plants that are susceptible to mild nitrogen stress and those that are not has not yet been published.

Consequently, the specific goals of this study were to evaluate the effectiveness of tolerance indices in classifying sorghum genotypes under consideration into groups that are tolerant and sensitive to nitrogen stress and to identify low-level nitrogen-tolerant sorghum landraces.

2 Materials and methods

2.1 Experimental plant materials

The seeds of the sorghum genotypes considered for this study were obtained from the Melkasa Agricultural Research Centre, Ethiopia, and standard controls (Ks78 and BCK60) were obtained from Kansas State University, USA. Details of the experimental materials used for the current study and their background information are presented in Supplementary Table 1.

2.2 Design of experiments and field management

The experiments were carried out over the course of two consecutive years, in 2020 and 2021, during the main rainy season at the Haramaya University Research Field. For the purpose of growing sorghum plants, a standard distance of 75 cm was maintained between rows, and 20 cm was maintained between plants in the experimental fields. Each genotype was represented by a single row that was 3 m long in both the control and experimental plots. The study employed a split-plot in randomized complete block design (RCBD), with the main plots receiving nitrogen fertilizer and the subplots receiving sorghum genotypes. The experiments were replicated twice each year. The meteorological data for the sorghum-growing areas are shown in Fig. 1. There was relatively better rainfall in the year 1, 2020/21, during the sorghum growing period interval, which was from April/May to December.

Fig.1
figure 1

Monthly rainfall intensity (mm) in sorghum-growing areas in year 1 and year 2 of the study periods

Full size image

2.3 Fertilizer application management

During sowing, 100 kg of DAP was applied to fertilized plots, and 90 kg ha-1 TSP was applied to unfertilized plots (i.e., plots without N fertilizer). At the knee stage of the sorghum crop, N-fertilized plots received a top dressing of an additional 50 kg ha-1 of urea. In the first year of sorghum cultivation, MARSHAL pesticides were applied to protect against stalk borers and other pests. Every field agronomic practice was carried out in compliance with regional guidelines.

2.4 Soil sample analysis

It was decided to use a field that had not been used to grow leguminous crops for at least two years for this experiment. Soil samples were taken from 0 to 30 cm depth in the experimental fields to estimate the amount of nitrogen available in the soil, given that nitrogen applications made in previous years would have an impact on the availability of nitrogen [41]. After being dried, the collected soil samples were crushed using a mortar and pestle and sieved through a 2 mm screen. The soil samples were analyzed for textural class, soil pH, total nitrogen [42], accessible phosphorus, and soil organic matter at Haramaya University's soil laboratory. Using composite soil and the semimicro-Kjeldahl technique [43], the total nitrogen content was determined. The soil type of the experimental field was alluvial, with a pH of 6.20 prior to crop planting, available phosphorous of 4.79 mg/kg, available potassium of 0.48 mg/kg, and N content of 0.13 mg/kg Table 1. The experimental plots were classified as having a low level of accessible nitrogen based on the average nitrogen level of 0.13% that was obtained overall. Thus, it was concluded that the initial nitrogen conditions of the soil were suitable for conducting the tests.

Table 1 Physicochemical properties of the soils collected from the experimental plots
Full size table

2.5 Evaluation of various yield-based selection indices

A wide range of yield-based selection indices have been proposed based on the mathematical relationships between nitrogen stress and typical circumstances to identify the genotypes that perform best under stress [45]. In the present study, fourteen yield-based indices, SSI, YSI, MP, GMP, STI, HM, RDY, SSPI, LNTI, YI, TOL, K1STI, K2STI, and ATI, were computed to identify genotypes that are stress susceptible and tolerant based on the grain yield values of sorghum genotypes obtained under nitrogen stress and optimal conditions.

The indices considered in the present study were computed as follows:

  1. 1.

    The stress susceptibility index is [46]:

                                                                                                      SSI = (\(1-Ys/Yp)/SI\)

$$SI=1-Yms/Ymp$$

where Ys is the yield of the cultivar under nitrogen stress conditions; Yp is the yield of the cultivar under optimal nitrogen conditions; Yms and Ymp are the mean yields of all cultivars under optimal nitrogen stress and optimal nitrogen conditions, respectively; 1-(Ys/Yp) is the stress intensity; and SI is the stress intensity. Genotypes with an SSI < 1 is more resistant to low nitrogen.

  1. 2.

    The yield stability index [47, 48]:

    $$YSI=Ys/Yp$$

Genotypes with high value are more desirable.

  1. 3.

    Mean productivity is [49]:

    $$MP=Yp+Ys/2$$

More desirable genotypes are those with a high index value.

  1. 4.

    Geometric mean productivity is calculated as [50]:

    $$GMP = \left( {Yp*Ys} \right)1/2$$

High GMP genotypes will be more preferred.

  1. 5.

    Stress tolerance index is calculated as [50]:

    $$STI=Yp*Ys/(Ymp)2$$

Tolerant genotypes are those with a high STI index value.

  1. 6.

    The harmonic mean is as follows: [51]:

    $$HM=(2*Yp*Ys)/(Yp+Ys)$$

Highly coveted genotypes are those with a high index value.

  1. 7.

    The low Nitrogen Tolerance Index [22]:

    $$LNTI=(Yp-Ys)/Yp$$

More desirable genotypes are those with a low LNTI index value.

  1. 8.

    Tolerance index [49]:

    $$TOL=(Yp-Ys)$$
  2. 9.

    Relative decrease in yield [52]:

    $$RDY = 100 - \left( {\frac{{Ys}}{{Yp}}*100} \right)$$
  3. 10.

    Yield Index [9, 53]:

    $$YI = \left( {\frac{Ys}{{Yms}}} \right)$$
  4. 11.

    Modifies stress tolerance index [54]:

    $$K1STI = \left( {Yp} \right)2/\left( {Ymp} \right)2$$
  5. 12.

    Modifies stress tolerance index [54]:

    $$K2STI = \left( {Ys} \right)2/\left( {Yms} \right)2$$
  6. 13.

    Abiotic tolerance Index [30]:

    $$ATI\, = \,\left( {{{{{\left( {YP - YS} \right)} \mathord{\left/ {\vphantom {{\left( {YP - YS} \right)} {\left( {\frac{Yms}{{Tmp}}} \right)}}} \right. \kern-0pt} {\left( {\frac{Yms}{{Tmp}}} \right)}}} \mathord{\left/ {\vphantom {{{{\left( {YP - YS} \right)} \mathord{\left/ {\vphantom {{\left( {YP - YS} \right)} {\left( {\frac{Yms}{{Tmp}}} \right)}}} \right. \kern-0pt} {\left( {\frac{Yms}{{Tmp}}} \right)}}} {\left( {{\text{Sqrt of}}\,Yp*\,Ts} \right)}}} \right. \kern-0pt} {\left( {{\text{Sqrt of}}\,Yp*\,Ts} \right)}}} \right)$$
  7. 14.

    Stress susceptibility percentage index [30]:

    $$SSPI = \left[ {Yp - \frac{Ys}{{2ymp}}} \right]*100$$

where:

Yp = Yield under optimal nitrogen.

Ys = Yield under nitrogen stress.

Ymp = mean yield over all genotypes evaluated under optimal nitrogen conditions.

Yms = mean yield over all genotypes evaluated under nitrogen stress conditions.

2.6 Statistical analysis

The mean values for the grain yield of sorghum genotypes under optimal nitrogen fertilizer and nitrogen stress conditions were used to compute fourteen stress tolerance indices across the cultivars via Excel 2019 [55]. A Pearson correlation analysis between the 14 indices and grain yield under various fertilizer conditions was conducted with the corrplot R package using R Studio Version 4.3. 2 [56].

In this study, multivariate analysis was also used to distinguish nitrogen stress-tolerant genotypes. Principal component analysis (PCA), biplot diagrams and cluster analysis were used to identify tolerant and susceptible genotypes via the prcomp R package. The PCA biplot was analyzed using the ggplot2 R package [57]. 3D diagram analysis of sorghum genotypes was performed by using the STI, and yield under stress and yield under optimal conditions were used to classify the genotypes into groups using iPASTIC online software [58].

3 Results

3.1 Mean values for grain yields (Kgh−1) of Sorghum genotypes and stress indices

The mean values for the grain yield of sorghum genotypes under optimal nitrogen fertilizer and nitrogen stress conditions and fourteen stress tolerance indices across the cultivars were computed using Excel 2019, and the results are shown in Supplementary Table 2. There is general agreement among many authors on the criteria for the determination of tolerant and stable cultivars, which are high values for the MP, STI, GMP, HM, YSI, modified STI and YI, as well as low values for the RDY, TOL, LNTI, SSPI, ATI and SSI [34, 59,60,61]. Based on this principle, among the 300 sorghum genotypes considered in this study, including two standard controls (KS78 and Bck60), the sorghum genotypes (G250) ETSL101673, (G258) ETSL 100752, (G97) ETSL100568, (G251) ETSL100079, and (G201) ETSL101313 had the highest grain yields (4603, 4566, 4378, 4228, and 4209 kg ha−1, respectively) under optimal nitrogen conditions. These cultivars also had higher values of MP, GMP, HM, YI, YSI, STI, K1ST, and K2STI and lower values of TOL, RDY, LNTI, SSPI, SSI, SSPI, and ATI (Supplementary Table 2).

On the other hand, sorghum genotypes (G221) ETSL101707, (G302) Bck60, (G282) ETSL101860, (G248) ETAL100874, (G144) ETSL100657, (G96) ETSL100642, (G174) ETSL100349, (G157) ETSL100916, (G93) ETSL101845, (G157) ETSL100916, and (1G87) ETSL101848 had the lowest grain yields (poor yields) (1472, 1538, 1556, 1631, 1631, 1659, 1678, 1688, 1688, and 1697 kg h−1, respectively) in the nitrogen stress experimental plots.

Among the top twenty-five genotypes under contrasting nitrogen levels, genotypes (G80) ETSL101255, (G216) ETSL101006, (G35) ETSL101258, (G146) ETSL100813, and (G130) ETSL101671 had the highest grain yield values (4200, 4172, 4050, 4003 and 3966 kgha−1, respectively) under an optimal nitrogen environment and a grain yield of 3281, 3244, 3206, 3234, and 3253 kgha−1, respectively) under nitrogen stress conditions. These genotypes were among the five most stable (nitrogen stress tolerant) and productive genotypes under nitrogen stress- and nitrogen-optimal environmental conditions. The sorghum genotypes (G302) Bck60, (G221) ETSL101707, (G282) ETSL101860, (G265) ETSL100427, and (G4) ETSL101464 had the lowest grain yields (1631, 2391, 2269, 2110 and 2091 kgha−1, respectively) in nitrogen-optimal fields and (1538, 1472, 1556, 1706, and 1706 kgha−1, respectively) in nitrogen-stressed fields. They were also identified as the lowest poor-yielder variety under both nitrogen levels. The genotypes also had low values of MP, GMP, YI, HM, STI, K1STI and K2STI and high values of TOL, SSI, SSPI, LNTI, and ATI. (Supplementary Table 2).

3.2 Correlation analysis results of grain yield and indices

To determine the most effective indices to be used as selection criteria for identifying desirable sorghum landrace genotypes under nitrogen stress, correlations among the yields of sorghum genotypes under nitrogen stress and the optimal environment with all the calculated stress selection indices were determined. The results of the correlation analysis for the grain yield and different stress tolerance indices revealed differences in the strengths and directions of the relationships (Fig. 2).

Fig. 2
figure 2

Pearson correlation coefficients of combined grain yield under stress and normal (Yp)c and fourteen stress indices evaluated across 300 sorghum varieties and two standard check sorghum genotypes. *p < 0.05, **p < 0.01, and ***p < 0.001

Full size image

To determine the indicators to be used in the selection of genotypes under stress [31], recommended conducting a correlation study between stress indices and grain production as a good criterion. In this respect, an appropriate index should have a positive correlation with grain yield [62].

In the present study, grain yield under optimal conditions (Yp) was significantly positively correlated with MP (r = 0.93), GMP (r = 0.90), K1STI (r = 0.99), STI (r = 0.89), HM (r = 0.65), YI (r = 0.65), and K2STI (r = 0.63). Similarly, there were strong positive correlations between grain yield under nitrogen stress and HM (r = 1.0), YI (r = 1.0), K2STI (r = 1.0), GMP (r = 0.92), and the STI (r = 0. 92), MP (r = 0.89), and K1STI (r = 0.64).

3.3 PCA for screening indices and grain yields

PCA was conducted using the tolerance indices, and the genotypes were then subjected to biplot analysis to determine the relationships among the indices. The PCA results for the grain yield and different stress tolerance indices are shown in Table 2.

Table 2 Results of principal component analysis for grain yield under contrasting nitrogen regimes and fourteen screening indices for sorghum landraces and two standard check genotypes
Full size table

The results of the PCA revealed that the total contribution to the first two components of variation was 99.4% (Table 2 and Fig. 3). The first principal component (PC1) contributed 55.1% of the variation and exhibited a positive correlation with Ys, HM, YI, GMP, STI, K2STI, Yp, and K1STI. The second principal component (PC2) contributed 44.3% to the total yield variation, and it had greater positive correlations with RDY and YSI and negative correlations with TOL, LNTI, SSPI, and SSI.

Fig. 3
figure 3

Scree plot of PCA for indices and sorghum yield under nitrogen stress and optimal conditions

Full size image

3.3.1 PCA biplot for indices and yields of Sorghum genotypes

The PCA biplot for stress indices and yield of sorghum genotypes under contrasting nitrogen statuses was generated using R software packages and is presented in Fig. 4. Genotypes with higher PC1 and lower PC2 values yield greater grain yields; genotypes with higher PC2 and lower PC1 values yield lower grain yields. Moreover, it is possible to pinpoint the first axis (PC1) as potentially yielding and stress tolerant, while the second component is identified as susceptible to stress and having a low grain yield in a stressed environment. In general, PC1 and PC2 were designated as having high yield potential and stress susceptibility, respectively. Stable genotypes had higher PC1 but lower PC2 values; in line with the findings of the present study, the same outcome was reported in [40]

The three-dimensional graphs and biplot results also showed that sorghum genotypes (G244) ETSL100292, (G161) ETSL100539, (G240) ETSL100890, (G93) ETSL101845, (G261) ETSL100625, (248) ETSL100874, (G258) ETSL100752, (G142) ETSL100921, and (G135) ETSL100307 exhibited the best performance under nitrogen-optimal and low-performance conditions under stress conditions and were categorized as nitrogen stress-susceptible genotypes. These genotypes had high RDY, ATI, SSI, and LNTI values. Similarly, genotypes (G80) ETSL101255, (G216) ETSL101006, (G35) ETSL101258, and (G281) ETSL101337 had the best performance under both optimal nitrogen and optimal nitrogen stress conditions and were classified as nitrogen stress-tolerant and stable genotypes, and they also showed genotypic plasticity toward nitrogen levels. Unlike the above two conditions, genotypes (G282) ETSL101860, (G144) ETSL100657, and (G221) ETSL101707 had the lowest grain yield under optimal and nitrogen stress conditions (Fig. 4).

Fig. 4
figure 4

Biplot principal component analysis (PCA) of nitrogen stress tolerance indices

Full size image

3.4 Dimensional plots for the STI indices and grain yields

An earlier researcher proposed the idea of classifying genotypes into four groups according to how well they yield under stressful conditions [50]. A 3D diagram based on the STI was drawn using iPASTIC online software [58] to discriminate the sorghum genotypes according to their yield performance (Fig. 5). Based on the 3D biplot results, the sorghum genotypes were classified into quadrants A, B, C, and D and with no genotype in quadrant C. The A quadrant contained genotypes with higher STI values, which indicates a greater yield under optimal and nitrogen stress conditions. The results showed that these genotypes were dominant in both stressed and unstressed environments, were tolerant of nitrogen stress, and were capable of producing more stable and productive hybrids. Genotypes found in quadrant B produced high yields under ideal circumstances and low yields under stressful circumstances. Due to their susceptibility to nitrogen stress, these genotypes require additional nitrogen fertilizer during cultivation. Quadrant D contained genotypes with low STIs, which were low yielders in both environmental scenarios, possibly due to the inherently low yield of the genotypes and/or the ability to adapt/fit to the experimental area.

Fig. 5
figure 5

Three-dimensional biplot for grouping nitrogen stress-tolerant and -susceptible genotypes based on Yp and Ys as well as the STI

Full size image

4 Discussions

4.1 Identifying nitrogen stress-tolerant and susceptible Sorghum landraces

The correlations between grain yield and the MP, GMP, STI, HM, YI, K1STI, and K2STI indices under both production systems were positive, demonstrating that choosing genotypes based on these indices is an appropriate method for identifying stable and productive sorghum genotypes. The results obtained [36]for safflower (Carthamus tinctorius L.) and [50] for mung bean (Viagna Radiata) are consistent with the ability of the MP, GMP, and STI indices obtained in this study to screen genotypes successfully under both nitrogen conditions. In line with this result, the following authors have also observed similar outcomes in maize [23, 26, 63] and rapeseed [64]. ATI, LNTI, RDY, SSI, and SSPI all displayed weak negative correlations with seed yield under nitrogen stress [65], but these indices demonstrated poor positive correlations with seed yield under nitrogen-optimal conditions (Yp) (Fig. 2). As a result, selection based on these indices increased seed production under stress conditions but decreased it under optimal nitrogen conditions. Other studies on safflower [36], wheat [24], and potato [66] have shown that SSI has a limited ability to detect tolerant genotypes.

Considering the highest MP, GMP, and STI values, sorghum genotypes (G80) ETSL101255, (G216) ETSL101006, (G35) ETSL101258, and (G146) ETSL100813 had the highest grain yield values (4200, 4172, 4050, and 4003 kgha−1, respectively) under an optimal nitrogen environment and grain yields (3281, 3244, 3206, and 3234 kgha−1, respectively) under nitrogen stress conditions. These genotypes were among the four most stable (nitrogen stress tolerant) and productive genotypes under both nitrogen stress- and nitrogen-optimal environmental conditions. The results revealed that the above indices could be used for primary screening of nitrogen stress-tolerant sorghum genotypes, which should be further supported by other morphological, physiological, and molecular results. The efficiency of the above indices for selecting nitrogen stress-tolerant genotypes has also been reported by other authors [34, 60, 61]. Similarly, the unique advantage of the STI for screening stress-tolerant genotypes that are stable under stress and optimal conditions has also been reported [50].

The same indices listed above were also identified for the (G244) ETSL100292, (G161) ETSL100539, (G240) ETSL100890, (G93) ETSL101845, and (G261) ETSL100625 and (G248) ETSL100874 sorghum genotypes, which exhibit high performance under optimal nitrogen conditions and low grain yield under nitrogen stress conditions. The genotypes had low MP, GMP, STI, HM, YSI, and YI but high SSI, LNTI, SSPI, ATI and RDY. The abovementioned sorghum genotypes are nitrogen stress-susceptible varieties, and they perform very well only under optimal nitrogen conditions; hence, their cultivation should be supplemented with an adequate amount of nitrogen fertilizer.

Unlike the above two groups of sorghum genotypes, (G302) Bck60, (G282) ETSL101860, (G144) ETSL100657, and (G221) ETSL101707 resulted in low yields under both nitrogen treatments. Most of the low-yield plants in this group were low-yield plants. The reason for their low yield might be their inability to adapt to the cold temperature in the experimental area, which is a highland area where the lowland genotypes had never been exposed before now. Similarly, the inherent low-yield genetic nature of the sorghum genotypes could also be another reason for the low yields of the above and akin genotypes obtained under both nitrogen regimes.

From the above results, we verified that the GMP, MP, STI, YI, K1STI, K2STI, and HM indices collectively represent the characteristics of stable and high yield for sorghum plants by considering the strong positive correlation between grain yield under both optimal and nitrogen stress conditions. This result is in line with those of other researchers who reported the application of GMP, MP, STI, and HM for the identification of stable and tolerant genotypes in other crops [9, 26, 63]. In general, the application of selection indices, PCA biplots, and a3D biplots were able to identify desirable sorghum genotypes with high yield performance under optimal nitrogen and nitrogen stress conditions.

5 Conclusions

According to the study's findings, choosing genotypes for nitrogen stress breeding purposes requires careful consideration of the screening indices MP, GMP, and STI in combination. The results of the PCA, biplot and 3D plot analyses indicated that the sorghum genotypes were grouped into three clusters: genotypes that are stable and productive under nitrogen stress and ideal circumstances (i.e., stable and nitrogen stress tolerant), high performance under optimal conditions and low yields under nitrogen stress (i.e., nitrogen stress susceptible), and poor performance under both conditions, which could be due to the low-yield genetic nature of the sorghum genotypes as well as the difficulty of adapting to the experimental area. Finally, we concluded that the indices could be used to screen sorghum genotypes for tolerant, susceptible and poor yielders under contrasting nitrogen regimes. The genotypes identified by the above indices should be further evaluated according to other supportive morphological, physiological and molecular results. The combined results could support the identification of genotypes that could be used as basic germplasms for future nitrogen stress-tolerant sorghum crop breeding to improve the nitrogen use efficiency of sorghum, which in turn could help to minimize agricultural inputs, decrease food prices, especially in developing countries, and alleviate the issue of environmental pollution resulting from excessive fertilizer application.