Relative efficiency of Variance Balanced Design (VBD) and Alpha Lattice Design (ALD) in diallel crosses of brinjal

Introduction

Field experiments play a crucial role in agricultural research, allowing scientists to study the effects of various treatments or measures under actual growing situations. While designing field experiments, researchers often encounter the need to allocate treatments efficiently to minimize bias and maximize the precision of the estimates (Johnston & Poulton, 2018) [6] . Agricultural field experimenters are experiencing the problem of soil heterogeneity which is one of the major causes of variability in experimental data/results. A survey carried out under the "Statistical evaluation of experimental variability for improving the efficiency of field experimentation" project on the use of experimental designs by Research Scientists in Gujarat state revealed that more than 95% of the field experiments are being conducted in the RCBD (Anon., 2016) [1] . The accuracy of this design depends on the control of heterogeneity within blocks (replications). But the use of RCBD is inefficient and unsuitable when the number of genotypes (treatments) is as large as sixteen in a single block (Yang et al., 2004) [13] because of failure to adequately minimize the effect of soil heterogeneity (Lentner and Bishop, 1993) [7] . There are certain trade-offs between the two designs, though. CBD requires a greater number of blocks than IBD since each treatment must be present in every block. When the experimental area is small or achieving block homogeneity is difficult, this requirement can be a restriction. In such circumstances, IBD is a more appealing option making it more viable and cost-effective (Dean et al., 1981) [3] . The practical utility of comparing complete block design vs incomplete block design is that it allows researchers to make conclusion regarding which design is best suited for their investigations. Good field designs help to ensure efficient/precise estimates of treatment effects.

For effective control of experimental error due to soil heterogeneity relatively small blocks are a must. Incomplete Block Designs (IBD) and Balanced Incomplete Block Designs (BIBD) help in achieving this goal through the concept of local control (one of the basic requirements of field experimentation). The treatments/entries/genotypes are grouped theoretically and allotted into small blocks within replication. Consequently, there is a gain in precision in the experimental results. The gain in efficiency / precision of one design over another design is measured by Relative Efficiency (RE). The advantage of alpha lattice design is that it is easy to construct and can be constructed in cases where balanced incomplete block designs and lattice designs don't exist. In the early phase/stage of introduction of alpha lattice design the aim was to control variation down the columns of plots in the field. This is often adequate when plots are long and narrow. Patterson and Hunter (1983) [8] have demonstrated the value of alpha designs in terms of gain in efficiency. Yau (1997) [14] reported the use of alpha lattice design in 714 international yield trials of barley, durum wheat and bread wheat from 1990-91 to 1992-93 and found average efficiency 18% higher than the RCBD. Though IBD and its forms are relatively more efficient (resource-saving) than RCBD, these designs are not in use on all Crop Research Stations/Centres functioning in the Gujarat state. Scientists accept theory and results on the basis of the "seeing is believing" concept. Many researchers observed that alpha lattice design is more efficient than RCBD and has the potential to replace RCBD (Patterson and Silvey, 1980; Patterson et al., 1978; Patterson and Hunter, 1983; Pilarczyk, 1991; Yau, 1997; Campbell and Bauer, 2007) [9,10,8,11,14,2] .

Materials and Methods

Experimental Site

Crossing of genotypes was carried out to generate F 1 populations in Late Kharif, 2021 at the Main Vegetable Research Station, AAU, Anand. Further the generated material was evaluated in Late Kharif, 2022 at the Agronomy Farm, AAU, Anand. Anand is located in Agro Climatic Zone-III (Middle Gujarat) of Gujarat State. Geographically, Anand is situated at 22º 58' N latitude and 72º 92' E longitude with an elevation of 45.1 meters above the mean sea level. The soil of the experimental site is sandy loam, the typical "Goradu" soil of the "Charotar" tract, which has less organic matter content with 8.1 to 8.3 soil pH and 0.20 to 0.25 EC. It is very deep, well-drained and fairly moisture retentive. The climatic condition of the area represents the tropical condition with a semi-arid climate. Anand is the head quarter of the Anand Agricultural University.

Experimental Material

Ten brinjal genotypes (Table 1) were used as parents to make diallel crosses. The seeds of parents were sown in nursery and transplanted into field after 30 days to form crossing block in Late Kharif, 2022. Crossing was carried out in all possible combinations excluding reciprocal crosses in crossing block for making 45 hybrids (Table 2) among all the parents. The diallel crosses were made as per Griffing's Method IV (Griffing, 1956) [5] . The relative efficiency of the VBD compared to the RCBD based on the EMS was 133.88% for fruit yield and 81.11% for the number of fruits in brinjal (Table 4). VBD showed a gain of 63.22% in fruit yield and 19.18% in the number of fruits over the ALD, while ALD exhibited a gain of 43.29% and 51.98% over RCBD, respectively. Based on the S.Em, VBD's relative efficiency compared to RCBD was 60.73% for fruit yield and 41.16% for the number of fruits (Table 4). The efficiency gain of VBD over ALD was 34.14% for fruit yield and 14.51% for the number of fruits, whereas ALD's efficiency gain over RCBD was 19.82% and 23.27%, respectively. In terms of the CV%, VBD's relative efficiency compared to RCBD was 65.54% for fruit yield and 44.56% for the number of fruits ( Overall, the results emphasize the significance of VBD and ALD, both being incomplete block designs, over RCBD. VBD emerged as the preferred choice from an efficiency viewpoint for evaluating F 1 populations of crosses in the brinjal crop. Similar results were reported by Popat (2021) [12] . Experiment conducted in VBD on the F 1 generation of brinjal produced through a diallel mating design, yielded more precised results compared to ALD and RCBD. Blocking within replication (VBD) played a significant role in reducing experimental error. Thus, it can be inferred that VBD was more effective and the estimates obtained from VBD were more precise compared to ALD and RCBD. When compared the estimates of RCBD with ALD (Table 3), ALD was better choice than RCBD for field experiments on brinjal crosses.

Conclusion

From the present investigation it can be concluded that the incomplete block designs viz., Variance Balanced Design (VBD) and Alpha Lattice Design (RCD) are efficient in differentiating performances of crosses than Randomized Complete Block Design (RCBD). The trend of error variance proved effectiveness of VBD and ALD. The present study encompasses experiments with larger sets of crosses, providing valuable insights into the efficacy of experimental designs. In general, IBD (ALD & VBD) provided smaller EMS, SEm, CV% and larger F values compared to RCBD increasing efficiency in comparing crosses. Therefore, plant breeders are advocated to use VBD and ALD in place of RCBD for evaluating breeding materials.

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