Plot size and replications number for triticale experiments

ABSTRACT: The hybridization between wheat and rye crops resulted in the triticale crop, which presents rusticity, versatility in animal and human food and possibility of use as a cover plant. The objective of this research was to determine the optimal plot size and the replications number to evaluate the fresh weight of triticale in two evaluation moments. An experiment was carried out with the triticale cultivar IPR111. The experimental area was divided into 48 uniformity trials, each containing 36 basic experimental units of 0.51 m2. The fresh weight was evaluated in 24 uniformity trials at 99 days after sowing (DAS) and in 24 uniformity trials at 127 DAS. The optimal plot size was determined by the method of the maximum curvature of the coefficient of variation and the replications number was determined in scenarios of treatments number and differences between means to be detected as significant by Tukey test. To determine the fresh weight of triticale, the optimal plot size is 3.12 m2, with coefficient of variation of 13.69%. Six replications are sufficient to identify as significant, differences between treatment means of 25% for experiments with up to seven treatments and of 30% for experiments with up to 28 treatments, regardless of the experimental design.

Toebe et al. number were used, for example, plots of 6 m 2 to 16.8 m 2 , evaluation areas in plots from 0.25 m 2 to 1.2 m 2 and three to four repetitions (SuCu & ÇIfCI, 2016;ALBREChT et al., 2018). The lack of experimental protocols indicating the optimal plot size and number of replications, may result in experiments with low reliability or requiring excessive use of human, financial and time resources. Therefore, the objective of this research was to determine the optimal plot size and the replications number to evaluate the fresh weight of triticale in two evaluation moments.
An experiment was carried out with triticale cultivar IPR111 in the experimental area situated in latitude 29º 09' 25" S, longitude 56º 33' 16" W and altitude of 74 m, with Cfa climate and soil classified as "Haplic Plinthosol" (SANToS et al., 2013). The seeding procedure was performed on June 3, 2016, with spacing of 0.17 m between rows and final plant population in the harvest of 1294117 plants ha -1 . Basic fertilization was carried out with 20 kg ha -1 of N, 80 kg ha -1 of P 2 o 5 and 80 kg ha -1 of K 2 o and two topdressing fertilizations were performed with 40 kg ha -1 of N in each one.
The useful area of the experiment was divided into 48 uniformity trials. Each uniformity trial of size 6 m × 3.06 m (18.36 m 2 ), was divided into 36 basic experimental units (BEu) of 1.0 m × 0.51 m (0.51 m 2 -one meter × three rows), forming a matrix of six rows and six columns. The fresh weight was evaluated in each BEu of 24 uniformity trials at 99 days after sowing (DAS) and in each BEu of 24 uniformity trials at 127 DAS, respectively, in anthesis completed and soft dough stages, as described by ZADoKS et al. (1974). Plants were cut near the soil surface and the fresh weight determined in grams per 0.51 m 2 .
for each uniformity trial with fresh weight of 36 BEU, were determined the first-order spatial autocorrelation coefficient (obtained in the rows direction), variance, mean, variation coefficient of the trial, optimal plot size and the variation coefficient in the optimal plot size, using the equations described by PARANAíBA et al. (2009) and applied by CARgNELuTTI fILho et al. (2014). Next, the number of replications was determined in scenarios formed by combinations of i treatments (i = 3, 4, ..., 100) and d minimum differences among means of treatments to be detected as significant at 5% probability by Tukey test, expressed as a percentage of experiment mean (d = 10%, 15%, ..., 40%), by iterative process until convergence, as detailed and applied by CARgNELuTTI fILho et al. (2014). Statistical analyzes were performed with Microsoft Office Excel ® and software R (R DEvELoPMENT CoRE TEAM, 2020).
There were no significant differences between the two evaluation moments (99 and 127 DAS) for the variables first-order spatial autocorrelation coefficient and mean (Table 1). For the variation coefficient of the trial, the optimal plot size and the variation coefficient in the optimal plot size, higher values were observed in the first evaluation moments, indicating greater variability between BEu in anthesis completed stage in relation to the soft dough stage. Among the 48 uniformity trials, the fresh weight ranged from 684.73 g to 1178.21 g per BEu (13426 kg ha -1 to 23102 kg ha -1 ), with a overall mean of 904.93 g per BEu (17744 kg ha -1 ). In the evaluation of forage yields at the dough stage in triticale lines, SuCu & ÇIfCI (2016) obtained forage production of up to 44.28 t ha -1 of fresh weight. Several genetic and management factors may explain the lower values of fresh weight in the present study, but the main one is related to the condition of lowland soils (haplic Plinthosol), susceptible to waterlogging in which the experiment was conducted. Conversely, using the same cultivar as the present study, ALBREChT et al. (2018) obtained lower fresh weight values in two-years experiments (5655 kg ha -1 and 7145 kg ha -1 ), perhaps by the use of larger spacing.
The variation coefficient of the trial ranged from 13.56% to 34.21% (Table 1), with a mean value of 21.30% and the optimal plot size ranged from 1.61 m 2 to 3.12 m 2 , with a mean value of 2.15 m 2 ( Table  1). The variation coefficient in the optimal plot size ranged from 7.04% to 13.69% among the 48 uniformity trials, with a mean value of 9.44%, considered low by PIMENTEL-goMES (2009). In order to ensure greater reliability in the experimental design, the highest optimal plot size among the 48 uniformity trials (3.12 m 2 ) was recommended for use in the evaluation of the fresh weight of triticale in anthesis completed and soft dough stages. The correspondent variation coefficient in the optimal plot size (13.69%), was used to calculate the number of replications for experiments in the completely randomized design and in the complete randomized block design.
The replications number varied between 2.7 and 69.5 (figures 1A, B), with similar behavior for completely randomized and complete randomized block designs. The replications number increases with increasing number of treatments and of desired precision, i.e., with the lowest level of d (d = 10%), as expected and described in the literature (CARgNELuTTI fILho et al., 2014). The number Table 1 -first order spatial autocorrelation coefficient (ρ), variance (s 2 ), mean (m, in grams per basic experimental unit of 0.51 m 2 ), trial coefficient of variation (CV, in %), optimal plot size (Xo, in BEU of 0.51 m 2 and in m 2 ) and the coefficient of variation in the optimal plot size (CvXo, in %) for the fresh weight of triticale cultivar IPR111 in two evaluation moments (99 and 127 days after sowing).

DAS
Trial (  .., 100) and d least differences between treatment means to be detected as significant at 5% probability by Tukey test, expressed in percentage of the overall experimental mean (d = 10, 15, ..., 40%), to evaluate the fresh weight of triticale from optimal plot size (Xo = 3.12 m 2 ) and coefficient of variation in optimal plot size (CV Xo = 13.69%).
up to 28 treatments and of 35% for experiments with up to 100 treatments, regardless of the experimental design used. In black oats, CARgNELuTTI fILho et al. (2014) recommended plots of 4.14 m 2 and four replications to identify as significant differences between treatment means of 26.7%.
In an experiment of triticale conducted by SuCu & ÇIfCI (2016) in Bursa, Turkey, plots of 6 m 2 and three replications were used in a complete randomized block design. however, for the evaluation of forage yields at the dough stage, forage samples were harvested in an area of 1.2 m 2 . for experiments with triticale and six other species of cover crops, ALBREChT et al. (2018) used a complete randomized block design with four replications and plot of 16.8 m 2 . however, for the evaluation of fresh and dry matter, they used a sample are of 0.25 m 2 . In conclusion, to determine the fresh weight of triticale, the optimal plot size is 3.12 m 2 , with coefficient of variation of 13.69%. Six replications are sufficient to identify as significant, differences between treatment means of 25% for experiments with up to seven treatments and of 30% for experiments with up to 28 treatments, regardless of the experimental design used.