Assessing the efficiency of variance balance design and row column design in comparison to randomized complete block design

Introduction

Plant breeding programmes rely on effective mating and environmental designs to achieve successful outcomes. Among environmental designs, Randomized Complete Block Design (RCBD) is widely used but assumes one-way soil fertility heterogeneity in experimental units. In diallel experiments with an increasing number of parents, two-way heterogeneity in soil fertility becomes a challenge, necessitating alternative approaches. In this context, Incomplete Block Designs offer potential solutions. Row Column Design, proposed by Gupta and Choi (1998) [4] and Varghese et al. (2015) [10] , arranges crosses in a manner where each row and column contain the crosses at most once, enabling estimation of general combining ability (GCA) and specific combining ability (SCA) effects. However, this design requires a greater number of replications. On the other hand, Sharma and Fanta (2010) [9] proposed Variance Balanced Design, which requires less experimental area while also providing estimation for gca and sca effects. This study compares three environmental designs: Randomized Complete Block Design, Row Column Design, and Variance Balanced Design, in evaluating the performance of the segregating generation (F2) generated using diallel method-IV. Through this comparative analysis, we aim to provide insights into the most suitable environmental design for diallel method-IV experiments, considering factors such as estimation accuracy, required replication levels, and experimental area requirements. The findings of this research contribute to improving the design and execution of plant breeding programmes, ultimately enhancing the quality and efficiency of breeding outcomes.

Materials and Methods

The study was conducted at the Agronomy Farm, Anand Agricultural University, Anand during the Late Kharif season of 2021.

The F 1 crosses were generated at Main Vegetable Research Station (MVRS), AAU, Anand and subsequent selfing was performed to obtain F 2 populations at the Agronomy Farm, AAU, Anand, in the Late Kharif season of 2020. The generated material was then evaluated during the Late Kharif season of 2021 at the same location. Fifteen diallel crosses were produced using the six brinjal genotypes, namely GOB1, JBGR1, KS331, AB 15-06, AB 17-17, and AB 17-28. The F 2 populations derived from these crosses were evaluated using three environmental designs, viz., Randomized Complete Block Design (RCBD), Row Column Design (RCD), and Variance Balanced Design (VBD). Each plot consisted of three rows, with eight plants in each row, spaced at 90 cm × 60 cm (inter-row × intrarow). The observations were recorded for yield per plant (YPP), number of fruits per plant (NFP), average fruit weight (AFW), fruit length (FL), and fruit girth (FG) from eight randomly selected F 2 plants in each plot. The data obtained from the field study were analyzed to assess the performance and variability of the F 2 populations derived from the diallel crosses.

Statistical Analysis

Statistical analysis was performed on the data obtained from all three environmental designs using appropriate methods given below:

Griffing (1956) [13] RCD y kl(m) = μ + τ ij(m) + α k + β l +ε kl(m) Varghese et al. (2015) [10] VBD y = μ1 + Xτ + Dβ + ε Sharma and Fanta (2010) [9] Relative efficiency (RE) of Experimental Designs using Error mean Square (EMS) was calculated using formula Ghosh and Ahuja (2017) given below:

Error mean square of RCBD, RCD and VBD, respectively

Relative Efficiency using SEm and CV was calculated by taking ratio of SEm and CV of reference design (RCBD) to test design (VBD and RCD). The gain in efficiency was computed using formula mentioned here:

Gain in efficiency = RE -100

The Chi square (χ 2 ) test is used to test dependency of sign and significance of gca and sca effects of traits studied on environmental designs viz., RCBD, RCD and VBD (Gupta and Kapoor, 2020).

Results and Discussions

The results (Table 1) indicated significant or highly significant differences among the F 2 progeny for all studied traits across the three environmental designs. Furthermore, the analysis revealed substantial genotypic variation in the traits among the crosses. Notably, the gca effects exhibited high significance across all three experimental designs for YPP, NFP, AWF and FL. Fruit girth yielded highly significant variation in RCD, significant variation in VBD and non-significant in RCBD. The sca effects demonstrated highly significant or significant differences among crosses for YPP, AFW, FL, and FG across all experimental designs.

In the case of NFP, significant differences were observed among sca effects in the RCBD. However, the sca effect did not exert significant differences in NFP in the RCBD and RCD designs.

The results indicate a consistent trend of error variance, σ ̂eRCBD

for all studied traits. This trend indicated that the incomplete block designs RCD and VBD were helpful in lowering variation caused by uncontrolled sources like soil fertility, entering in the data (results), as compared to RCBD. In this respect VBD was better than RCD. Replication effect in RCBD and row and column effect in RCD were found non-significant while in case of VBD block effects were found highly significant for all the character studied. The resultant information (Table 1) revealed that the area used to accommodate RCBD and RCD (in general) was uniform in fertility variation. On other side blocking within replication (VBD) had helped in lowering experimental error. The results obtained from Bartlett's test showed heterogeneity in error variances for YPP, NFP and AFW. Lower error mean square provides higher precision for estimates. It could be generalized that error estimates calculated through ANOVA can be used to judge the precision (efficiency) of the field experimental designs. Considering error mean square (EMS), the average relative efficiency (Table 2) of Variance Balanced Design (VBD) in comparison to RCBD and RCD was 152.70, 147.83 percent whereas the relative efficiency of RCD over RCBD was 220.80 percent. Relative efficiency of VBD was 142.80 and 214.00 percent over RCBD and 102.99 and 186.11 percent over RCD considering SEm and CV percent, respectively. Considering SEm and CV (%), relative efficiency of RCD over RCBD was 139.73 and 115.18 percent, respectively. Overall, the gain in efficiency was 92.53 and 45.71 percent for VBD over RCBD and RCD, whereas it was 35.87 for RCD over RCBD. Results revealed that Incomplete Block Designs viz., RCD and VBD were efficient as compared to RCBD. VBD was the best from gain in efficiency view point followed by RCD in comparison to RCBD for field experiments on F 2 s of brinjal crops. Present findings are in line to those reported by Yates (1936) [11] who used pseudo factorial arrangement; Goulden (1937) [2] who used uniformity trials data; Yau (1997) [12] who used lattice design; Masood et al. (2008) [7] ; Khan et al.

(2015) [5] ; Kumar et al. (2020) [6] who used alpha lattice design and Popat (2021) [8] who used Variance Balanced Design (VBD). All these researchers had worked out efficiency in relation to RCBD. They found IBD as efficient design. The 𝜒 2 test for the frequency distributions (Table 3) for sign and significance of gca/sca estimates showed that the sign (positive/negative) of gca/sca estimates were independent of experimental designs used in the comparisons, whereas significance of the estimates were not independent of experimental designs.

Results revealed a significant 𝜒 2 estimate while comparing gca estimates between RCBD and VBD, indicating statistical significance. Furthermore, the 𝜒 2 test also found significant while comparing the sca effect of RCBD with RCD and VBD. The number of significant gca and sca estimates (Table 3) were high in both the incomplete block designs compared to RCBD. Here also VBD proved better than RCD. The number of non-significant gca and sca estimates were high in RCBD. Results indicated that the inbuilt parameters of the field experimental designs influence(s) the precision of the estimate(s). This holds true for VBD and RCD which proved better than RCBD.

Conclusion

Findings revealed that VBD outperformed both RCBD and RCD, with an average relative efficiency of 192.53% over RCBD and 145.71% over RCD. This indicates that VBD provides improved estimation accuracy and efficiency in terms of resource utilization. Furthermore, the significance of general combining ability (gca) and specific combining ability (sca) estimates varied among the designs, emphasizing the influence of experimental design on the precision of these estimates. It suggests that VBD is the most suitable environmental design for diallel method-IV experiments in brinjal crops. This design offers improved estimation accuracy, requires less experimental area and effectively handles the challenges of soil fertility heterogeneity. The outcomes of this research contribute valuable insights to the field of plant breeding, providing guidance for researchers and breeders in selecting appropriate environmental designs for diallel method-IV experiments. Implementing VBD in plant breeding programs can enhance the design and execution of experiments, leading to improved breeding outcomes.

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