A total of 20 genotypes used as treatments were organised and planted in a randomised complete block design, replicated thrice. The plot consisted of four rows, each measuring five meters in length, with an inter-row spacing of 0.75 m and an in-row spacing of 0.20 m (Chikobvu 2008). Land ploughing was done and later disked before planting to break soil clods ensuring soil seed contact. Compound D (N7:P14:K7) basal fertiliser application was done at planting, using a rate of 200 kg ha⁻¹ (Chikobvu 2008). During planting, seeds were drilled into the soil, and 2 weeks after germination, the plots were thinned to retain one plant per planting station. Six weeks post crop emergence, ammonium nitrate 34.5% N was applied at 100 kg ha⁻¹ as a top-dressing fertiliser (Chikobvu 2008). Top dressing was applied once in sites with heavy clay soils, while split application at 4 and 7 weeks after germination was done at sites with sandy loam soils. Split application for ammonium nitrate 34.5% N was done in sandy loam soils to reduce nutrient leaching and improve nutrient uptake, issues that are less critical in clay soils (Singh et al. 2024). The trials were raised under rainfed conditions across all the sites. Weeds were controlled manually using hoes at all the sites. Fall armyworm (Spodoptera frugiperda) and stalk borers (Busseola fusca) were controlled using Belt® and Thionex® insecticides at the rate of 0.1 and 1 l ha⁻¹, respectively (Chikobvu 2008).

Data were collected from the net plot, consisting of two central rows, while a 0.5 m border at each end of the rows was discarded to eliminate border effects (Xu 2016). Data were collected on days to 50% flowering, which were recorded as number of days from planting to when 50% of the plants in a plot have shade pollen as well as days to 95% physiological maturity, which were recorded as number of days from planting to the date where 95% of the plants matured on which seeds on the lower part of the panicle formed a black layer (IBPGR & ICRISAT 1993). In addition, panicle length, panicle width, plant height, plant count, 100 grain weight per plant and grain yield were also recorded. The presence of northern leaf blight (Exserohilum turcicum) and sorghum sooty stripe (Ramulispora sorghi) damage was also recorded, which were scored during the grain filling stage using a scale 1–5 with a score of 1 representing very healthy (i.e., disease-free) plants and 5 representing severely diseased plants. Using a ruler, panicle length was measured in centimetres from the base of the panicle to the tip of the panicle, and panicle width was measured in centimetres as the diameter of the head at its widest part after the grain filling stage (IBPGR & ICRISAT 1993). Plant height was measured in centimetres from the base of the stalk at the ground level to the tip of the head. Plant count was recorded as the total number of plants per plot at the harvesting stage. Plant height and plant count were recorded when 95% of the plants in a plot had reached physiological maturity (Wang et al. 2020). The harvested panicles were sundried before being tested for moisture content, which was adjusted to 12.5%. Grain weight per plant was recorded as the weight of dried grain harvested per plant. One hundred grain weight was determined by weighing 100 grains for each genotype, and grain yield was recorded as the weight of dried grain harvested per plot converted to tonnes per hectare (IBPGR & ICRISAT 1993).

Best Linear Unbiased Predictors (BLUPs) were calculated for all traits across five sites over two seasons, as well as for each season, using Multi Environment Trial Analysis with R (META-R) software version 6.0 (Alvarado et al. 2020). Pearson’s correlation coefficients were also generated with the same software. In addition, using R software version 4.3.1, phenotypic and genotypic path analysis was performed based on phenotypic correlations to deduce direct and indirect effects of sorghum grain yield related traits on sorghum yield (Dong 2024; R Core Team 2023).

This article followed all ethical standards for research without direct contact with human or animal subjects.

The existence of positive correlation between some of the secondary traits and grain yield reveals their potential for use in sorghum grain yield improvement programmes as such traits guide selection index (Gasura et al. 2015). In this study, sorghum grain yield was a dependant variable while yield related traits were treated as independent variables. Although correlation studies provide the interrelationships of all the traits under study, generally some correlations between independent variables are not important to breeders. Traits that confirmed same pattern of association in first 2021–2022 season (Table 2), second 2022–2023 season (Table 3) and in combined analysis (Table 4) were discussed in detail. This article observed positive and significant (p ≤ 0.01) phenotypic correlation coefficient (rp) between sorghum grain yield and days to 50% flowering (rp = 0.48) and also days to 95% physiological maturity (rp = 0.59) (Table 4). This association explains prolonged days for the plant to accumulate photosynthates for biomass production which triggers many large sinks, which require more time for grain filling resulting in high yield. These findings corroborate with earlier studies by Jimmy et al. (2017), Senbetay and Belete (2020), and Chauhan and Pandey (2021).

Grain yield was positively and highly significantly (p ≤ 0.05) correlated with panicle length (rp = 0.61) and panicle width (rp = 0.47) (Table 4). This means that as panicle length increases, grain yield tends to increase as well and as panicle width increases, grain yield increases. This suggests that both panicle length and panicle width are important traits influencing grain yield as they enhance the number of grains per panicle (Zhang, Li & Tong 2018). Plant breeders should offer due consideration to these traits when selecting for sorghum grain yield. El-Raheem and Tag (2020) and Chauhan and Pandey (2021) supported these findings. Moreover, Khandelwal et al. (2015) and Shivaprasad et al. (2019) reported a positive and significant correlation between sorghum grain yield and panicle length while Jimmy et al. (2017) observed a significant association of grain yield and panicle width.

A significant (p ≤ 0.01) and positive association was found between sorghum grain yield and plant height (rp = 0.31). This result aligns with earlier studies of Amare et al. (2015), Shivaprasad et al. (2019), El-Raheem and Tag (2020), Enyew et al. (2021) and Chauhan and Pandey (2021). The positive and significant relationship for grain yield and plant height, which was observed, is true because plant height affects the number of nodes and leaves that a plant can produce (Zhang et al. 2017). Taller plants tend to yield more nodes and leaves which are responsible for the increases in photosynthetic factories and subsequent numerous bigger flowers and sink sizes (Faralli & Lawson 2020; Wu et al. 2019).

Sorghum grain yield had a positive and significant (p ≤ 0.05) association with 100 grain weight (rp = 0.36) (Table 4). Previous sorghum studies have reported positive and significant correlations between grain yield and 100 grain weight (Chauhan & Pandey 2021; El-Raheem & Tag 2020; Jimmy et al. 2017; Khandelwal et al. 2015;). A high 100 grain weight translates to superior seed size which promotes germination, plant stand and final yield.

Strong and highly significant (p ≤ 0.001) correlation between grain yield and grain weight per plant (rp = 0.85) was observed in this present study, further emphasising its importance as a yield component. Earlier findings by Amare et al. (2015) and Senbetay and Belete (2020) supported the present results as the authors reported a positive and significant phenotypic correlation between grain yield and grain weight per plant. Non- significant correlation was noted between grain yield and sorghum sooty stripe in both seasons (Table 2 and Table 3). It indicates that the disease showed non-significant variations in different genotypes for grain yield. The genotypes under study were tolerant to sorghum sooty stripe. Conversely, positive correlations were exhibited between grain yield and northern leaf blight (rp = 0.4). This kind of relationship explains the disease tolerance of the genotypes used in this study. Most fungal diseases thrive in the presence of prolonged high humidity and hot temperatures. The prevailing effects of global warming not limited to random long dry spells are not warranting conducive environment for disease development; hence, sorghum sooty stripe revealed a non-significant correlation with grain yield per season and in combined analysis.

Positive and significant correlations between grain yield and yield components; days to 50% flowering, days to 95% physiological maturity, panicle length panicle width, plant height, 100 grain weight and grain weight per plant over the two seasons across sites paves the way for simultaneous trait improvement (Table 2, Table 3 and Table 4). It also facilitates effective indirect selection saving resources in sorghum grain yield improvement programmes (Gasura et al. 2013).

It is of paramount importance for sorghum breeders to consider genotypic correlations, which are more important than phenotypic correlations. The reliability of genotypic correlations is on the exclusion of environmental and/or genotype by environment interaction effects when being computed (Azimi, Marker & Bhattacharjee 2017). The environmental effects reduce the precision of correlation among traits.

It is crucial for sorghum breeders to consider genotypic associations, which are more important than phenotypic correlations. The reliability of genotypic correlations is on the exclusion of environmental and/or genotype by environment interaction effects, which reduce precision of correlation among traits. In this study, sorghum grain yield had significant (p ≤ 0.05) and positive genotypic correlation coefficient (rg) with days to 50% flowering (rg = 0.53), days to 95% physiological maturity (rg = 0.31), panicle length (rg = 0.57) and 100-grain weight per plant (rg = 0.45) (Table 2, Table 3 and Table 4). The significant and positive association suggests that simultaneously selecting these traits enhances the efficiency of sorghum yield improvement. An earlier study by Thant et al. (2021) reported a significant and positive genotypic correlation coefficient of days to 50% flowering, days to 95% physiological maturity, panicle length and grain weight per plant which was in agreement with our findings.

Information on the correlation between two traits is important for the concurrent selection of traits, which speeds up progress in crop breeding. The only analysis and interpretation of the association magnitude usually results in a poor selection strategy in the presence of pleiotropism. A genetic phenomenon, pleoitrophy is when a single gene influences multiple unrelated traits, which occurs because the gene produces proteins that are involved in multiple biological pathways (Stearns 2010). Therefore, analysing the cause-and-effect relationships through path analysis to differentiate between the direct and indirect effects of independent (secondary traits) variables on the dependent variable (grain yield) is crucial (Dong 2024). Highly significant (p ≤ 0.01) positive direct effect on sorghum grain yield was observed on panicle length (Pp = 0.036), 100 grain weight (Pp = 0.109) and grain weight per plant (Pp = 0.545) in 2021–2022 season (Table 5), and the same pattern was observed in 2022–2023 season on panicle length (Pp = 0.354), 100 grain weight (Pp = 0.268) and grain weight per plant (Pp = 0.361) (Table 6). Grain weight per plant had the highest positive direct effect on sorghum grain yield. Northern leaf blight (Pp = −0.015) exhibited significant (p ≤ 0.05) negative direct effects on grain yield showing that an improvement in any of these traits can directly support sorghum grain yield thereby indicating the efficiency of indirect selection (Table 6).

Lenka and Mishra (1973) classified path coefficients as negligible, low, moderate, high and very high when association effects are 0.00–0.09, 0.10–0.19, 0.20–0.29, 0.30–0.99 and > 1.0, respectively. In order to increase accuracy and precision in sorghum breeding, more emphasis is given to high path coefficients. Accordingly, panicle length had a high positive phenotypic direct effect (Pp = 0.354) on sorghum grain yield (Table 6). Highly positive and direct effects of panicle length on grain yield were also reported by Khandelwal et al. (2015), Shivaprasad et al. (2019) and Senbetay and Belete (2020). Such a relationship indicates that panicle length is one of the most important yield component traits. The phenotypic path analysis showed that grain weight per plant had very high positive direct effect (Pp = 0.361) on sorghum grain yield indicating the importance of grain weight per plant as yield related character that directly increases grain yield potential. This is in agreement with Chauhan and Pandey (2021) who reported a very high positive direct effect on sorghum grain yield by grain weight per plant.

Significant (p ≤ 0.05) positive genotypic direct effects on sorghum grain yield was observed on days to 50% flowering (Pg = 0.280), days to 95% physiological maturity (Pg = 0.201), panicle length (Pg = 0.194) and grain weight per plant (Pg = 0.291) (Table 5, Table 6 and Table 7). These are moderate path coefficients whose traits can be used as selection indices (Lenka & Mishra 1973). Endalamaw, Adugna and Mohammed (2017) reported that days to 50% flowering and panicle length had positive significant (p ≤ 0.05) direct effects on sorghum grain yield and these findings corroborate with results of this study. Khadakabhavi et al. (2017) reported similar findings, particularly regarding panicle length, which exhibited positive and significant (p ≤ 0.05) genotypic direct effects on sorghum grain yield. In contrast, 100-grain weight showed negative direct effects on grain yield, as revealed by a cross-site path coefficient analysis, indicating that it is not suitable for indirect selection for yield improvement. Grain weight per plant had significant p ≤ 0.05) positive genotypic direct effects on sorghum grain yield. However, it cannot be used as a reliable predictor of yield as it is measured only after harvest. In addition, relying on this trait can delay breeding programmes, particularly in seasons with frequent terminal droughts, which hinder grain filling. This challenge is further exacerbated by the ongoing impacts of climate change (Ajeigbe et al. 2018).

Desirable traits that are significantly and positively correlated and exhibit high heritability can be used efficiently as selection indices for grain yield in sorghum breeding (Gasura et al. 2013). Traits with < 30%, 40% – 60% and > 60% heritability are considered to have low, moderate and high heritability, respectively, making their selection easy (Johnson, Robinson & Comstock 1955). Accordingly, days to 50% flowering and panicle length had high heritability of 0.72 and 0.86, respectively (Table 8). Although days to 95% physiological maturity have positive and significant (p ≤ 0.05) genotypic direct effects on sorghum grain yield, indirect selection for yield is not rewarding because it has a low heritability of 0.25 (Table 8). Moreover, days to 50% flowering and panicle length had a significant (p ≤ 0.05) and positive correlation at both phenotypic and genotypic level, and it follows that breeders can successfully use either one of the two for indirect selection of sorghum grain yield. In this case, days to 50% flowering is easier, quicker and cheaper to use than panicle length, which requires more time.