Plot size and number of replications for ryegrass experiments. Plot size and number of replications for ryegrass experiments

: The objective of this research was to determine the optimal plot size and the number of replications to evaluate the fresh matter of ryegrass sown to haul. Twenty uniformity trials were conducted, each trial with 16 basic experimental units (BEU) of 0.5 m 2 . At 117, 118 and 119 days after sowing, the fresh matter of ryegrass in the BEUs of 5, 10 and 5 uniformity trials, respectively, were determined. The optimal plot size was determined by the maximum curvature method of the variation coefficient model. Next, the replications number was determined in scenarios formed by combinations of i treatments (i = 3, 4, ... 50) and d minimum differences between means of treatments to be detected as significant at 5% of probability by the Tukey test, expressed in experimental mean percentage (d = 10, 11, ... 20%). The optimal plot size to determine the fresh matter of ryegrass seeded at the haul is 2.19 m 2 , with a variation coefficient of 9.79%. To identify as significant at 5% probability, by the Tukey test, differences between treatment means of 20%, are required five, six, seven and eight replications, respectively, in ryegrass experiments with up to 5, 10, 20 and 50 treatments.


InTROduCTIOn
The ryegrass (Lolium multiflorum L.) is the annual winter pasture with the largest cultivated area in the state of Rio Grande do Sul (BISCaíNo et al., 2018). Ryegrass is an important forage used in dairy production, with ease natural reseeding, disease resistance, high seed production potential and versatility in intercropping (CaSSoL et al., 2011). In this sense, dairy cows grazing ryegrass pasture, with a high forage allowance, can eat more than 16.0 kg dry matter/cow.day and produce more than 20 kg milk/ day (RIBEIRo FILHo et al., 2009). The ryegrass can also be used in no-till system for crop rotation, ensuring high yields of the successor crop, such as corn (VIZIoLI et al., 2018).
For research on ryegrass to be scientifically valid, it is essential to define the experimental planning.
In experimental planning, the optimal plot size can be defined by the maximum curvature Toebe et al. method of the variation coefficient model proposed by PaRaNaíBa et al. (2009). The number of replications can be defined by the iterative process until the convergence, in scenarios formed by combinations of i treatments and d minimum differences among means of treatments to be detected as significant by the Tukey test (CaRGNELuTTI FILHo et al., 2014, 2015. using these methods, was recommended: a plot size of 4.14m 2 and four replications to evaluate the fresh matter of black oats (CaRGNELuTTI FILHo et al., 2014); a plot size of 5.03 m 2 and four replications to evaluate the fresh matter of forage pea (CaRGNELuTTI FILHo et al., 2015); a plot size of 4.97m 2 and five replications to evaluate millet shoot fresh matter (BuRIN et al., 2016); a plot size of 1.57m 2 and four replications to evaluate grain yield in four oat cultivars (LaVEZo et al., 2017); a plot size of 4.52 m 2 and four replications to evaluate the fresh matter of vetch (CaRGNELuTTI FILHo et al., 2017); and, a plot size of 6.08 m 2 and seven replications to evaluate grains yield of rye (CHaVES et al., 2018). The objective of this research was to determine the optimal plot size and the number of replications to evaluate the fresh matter of ryegrass sown to haul.

MATERIALS And METhOdS
Twenty uniformity trials were conducted with ryegrass, BRS Ponteio cultivar, in the experimental area of the Federal university of Pampa, Campus Itaqui, located in the municipality of Itaqui, Rio Grande do Sul State, Brazil, in geographic coordinates latitude 29º 09' 25" S, longitude 56º 33' 16" W and altitude of 74 m. according to Köppen climate classification, the climate of the region is Cfa, subtropical humid without dry season defined (WREGE et al., 2012) and the soil is classified as "Haplic Plinthosol" (SaNToS et al., 2013).
The ryegrass seeds were sown to haul on June 9, 2015, in an area of 720 m 2 , with 25 kg of seeds per hectare. Fertilization was carried out according to the crop recommendation (CqFS, 2004). The cultural practices were performed evenly, as recommended for the uniformity trials (SToRCK et al., 2016). Then, in the experiment central area were delimited 20 uniformity trials, each one of size 8 m 2 (4 m × 2 m), was divided into 16 basic experimental units (BEu) of 0.5 m 2 (1.0 m × 0.5 m), forming a matrix with four rows and four columns. In five trials, at 117 days after sowing (DaS), in ten trials at 118 DaS and in five trials at 119 DAS, in each BEU, the plants were cut near the soil surface and the fresh matter weight determined in grams per 0.5 m.
For each uniformity trial, the following statistics were determined based on the fresh matter weight: first-order spatial autocorrelation coefficient (ρ), variance (s 2 ), mean (m, g), variation coefficient of the trial (CV trial , %), optimal plot size (Xo, in BEu and m 2 ) and the variation coefficient in the optimal plot size (CV Xo , %). The estimate of ρ was obtained in the direction of the rows, according to the equation described by PaRaNaíBa et al. (2009).
Based on the maximum curvature method of the variation coefficient model, proposed by PaRaNaíBa et al. (2009), the optimal plot size and the variation coefficient in the optimal plot size were determined. The means comparisons of the statistics ρ, s 2 , m, CV, Xo, and CV Xo were performed at 5% probability as follows: the three evaluation periods were compared by the Tukey test via bootstrap with 10,000 resampling's, preceded by the variance analysis (a factor, that is, evaluation time with three levels) via bootstrap with 10,000 resampling's. In these variance analyses, the trials were considered replications (independent samples). The variance analysis and the Tukey test via bootstrap were performed in the SISVaR application. These statistical procedures are adequate to circumvent possible impacts of failure to meet the errors normality assumptions and the residual variances homogeneity (FERREIRa, 2014).
For the replications number calculation, it was started from the least significant difference (d) of the Tukey test, expressed in percentage of the experiment general mean, estimated by the equation, where q α(i; DFE) is the critical value of the Tukey test at level α of error probability (α = 0.05, in this study), i is the number of treatments, DFE is the number of freedom degrees of the error, i.e., [i(r-1)] for the completely randomized design and [(i-1) (r-1)] for the randomized block design, MSE is the error mean square, r is the replicates number and m is the experiment mean. Thus, replacing the expression of the experimental variation coefficient , in percentage, in the expression for the calculation of d and isolating r, we have . In the study, the CV is expressed as a percentage and corresponds to the CV Xo , since this is the CV expected for the experiment with the optimal plot size (Xo) determined.
From the mean of CV Xo , between the evaluation times, the number of replications (r), by the iterative process until convergence, was determined for experiments in completely randomized design and randomized block design, in scenarios formed by combinations of i treatments (i = 3, 4, ... 50) and d minimum differences among treatments means to be detected as significant at 5% probability by the Tukey test, expressed as a percentage of the experiment mean (d = 10%, 11%, ... 20%). Statistical analyses were performed with the aid of the Microsoft Office Excel ® application and the software SISVaR (FERREIRa, 2014)

RESuLTS And dISCuSSIOn
There were no differences between the three evaluation times for estimates of the first-order spatial autocorrelation coefficient (ρ), variance (s 2 ), mean (m), variation coefficient of the trial (CV trial ), optimal plot size (Xo) and the variation coefficient in the optimal plot size (CV Xo ) of the fresh matter weight for ryegrass seeded on the haul (Table 1). This is expected given the proximity between the evaluation dates. Thus, the mean values of the statistics were used based on the 20 uniformity trials.
The fresh matter weight of ryegrass ranged between 1166 and 1705 g per BEu of 0.5 m 2 , with an overall mean of 1397 g per BEu or 27940 kg ha -1 ( Table 1). The overall mean of the first-order spatial autocorrelation coefficient was close to zero, Table 1 -First-order spatial autocorrelation coefficient (ρ), variance (s 2 ), mean (m), variation coefficient of the trial (CV), optimal plot size (Xo, in BEu of 0.5m 2 and in m 2 ) and the variation coefficient in the optimal plot size (CVXo) for the fresh matter of ryegrass (Lolium multiflorum L.) -BRS Ponteio cultivar seeded to haul -evaluated in uniformity trials at 117, 118 and 119 days after sowing.
Days after sowing (1) Each uniformity trial of size 8 m 2 (4 m × 2m) was divided into 16 basic experimental units of 0.5m 2 (1.0m × 0.5m), forming a matrix with four rows and four columns.
(2) For each statistic (ρ, s 2 , m, CV, Xo, and CVXo), the means not followed by the same letter in the column (comparison of means between the evaluation times) differ, at 5% probability, by the Tukey test via bootstrap with 10,000 resampling's.

Toebe et al.
ranging from -0.38 to 0.45. The variation coefficient ranged from 12.71 to 31.42% between the 20 trials, being considered from medium to very high by classification of PIMENTEL-GoMES (2009). on a mean, the variation coefficient was high (21.33%).
The optimal plot size in BEus ranged from 3.15 to 5.71 with a mean value of 4.38 BEus (Table 1). In the area unit, the optimal plot size ranged from 1.58 to 2.85 m 2 , with a mean value of 2.19 m 2 . as expected, trials with higher variability showed higher final values of optimal plot size; however, no differences were observed between evaluation times. The variation coefficient in the optimal plot size ranged from 7.05% to 12.76%, with a mean value of 9.79%, considered low by classification of PIMENTEL-GoMES (2009). The optimal plot size to determine fresh matter weight of ryegrass (2.19 m 2 ) is lower than that described in the literature to determine fresh matter weight of other foragers as black oats (4. . However, the variation coefficient in the optimal plot size (CV Xo = 9.79%) was similar to that described for other forages in the abovementioned studies (9.25%≤CV Xo ≤11.24%).
The number of replicates for experiments in completely randomized design, varied between 3.82 replicates (three treatments and d = 20%) and 30.69 replicates (50 treatments and d = 10% - Table 2). For experiments in the randomized complete block design, the number of replications varied between 4.25 (three treatments and d = 20%) and 30.69 (50 treatments and d = 10%) (Table 3). So, it is verified that to obtain a high precision (d = 10%) the number of replications is too high, making experimental conduction unfeasible. For cases of i = 50 treatments and d = 10% in completely randomized design and randomized block design experiments, it was verified the need to use 27.41 to 62.98 replications (CaRGNELuTTI FILHo et al., 2014, 2015BuRIN et al., 2016;LaVEZo et al., 2017;CHaVES et al., 2018), indicating the infeasibility of experimental conduction at this precision level.
The replicates number to determine the ryegrass fresh matter weight in a small number of treatments was lower in the completely randomized design in relation to the randomized block design (Tables 2 and 3). This behavior is expected due to the efficiency of the completely randomized design on homogeneous areas and has been described in other experimental planning studies (CaRGNELuTTI FILHo et al., 2014, 2015BuRIN et al., 2016;LaVEZo et al., 2017;CHaVES et al., 2018). For a high treatments number, the number of replications tends to equalize between the two experimental designs. It has also been reported that the number of replicates increases as the number of treatments increases for fixed d and CV Xo . This pattern has also been reported in the literature (CaRGNELuTTI FILHo et al., 2014, 2015BuRIN et al., 2016;LaVEZo et al., 2017;CHaVES et al., 2018).
For the combination of a higher treatments number and lower precision (50 treatments and d = 20%), the number of replications recommended would be 7.79 replications (Tables 2 and 3). as this replications number cannot be used, we can calculate d as a function of eight replications use in completely randomized design and randomized complete block design. Thus, with 50 treatments, for the completely randomized design and for the randomized complete block design So, in experiments with up to 50 treatments and eight replications, differences between treatment means of 19.73% of the experiment mean are identified as significant at 5% probability, by the Tukey test. Still, for experiments with up to five, ten and 20 treatments, five, six and seven replications, respectively, are required to identify as significant at 5% probability, by the Tukey test, differences between treatment means of 20% of the experiment mean.
In the evaluation of dry matter in seven populations and three ryegrass cultivars evaluated at two sites, it was used a randomized complete block design with four replications and plots of 3 m 2 (1.5 m × 2 m) in one site and of 6 m 2 in another site, with a collection area of 0.25 m 2 per plot (0.5 m × 0.5 m) (FLoRES et al., 2008). In an experiment with three different ryegrass managements (treatments) under a succession of corn, it was used a randomized complete block design with three replicates and plots of 100m 2 (10 m × 10 m) to evaluate soil physical components under no-till (VIZIoLI et al., 2018). In two experiments conducted in a greenhouse, in a completely randomized design, it was used four and eight replications for the first and second experiment, respectively, with 4 to 128 plants per pot (aGoSTINETTo et al., 2017). already to evaluate the yield and structural composition of oat and ryegrass subjected to different periods of cutting and nitrogen fertilization, CaSSoL et al. (2011) used a randomized complete block design with four .  (i = 3, 4, ..., 50) and d least differences between treatment means to be detected as significant at 5% probability by the Tukey test, expressed in percentage of the overall experimental mean (d = 10, 11, ... 20%), to evaluate the fresh matter of ryegrass (Lolium multiflorum L.) -cultivar BRS Ponteio seeded to haul -from optimal plot size (Xo = 2.19m 2 ) and the variation coefficient in optimal plot size (CVXo = 9.79%). Toebe et al. Table 3 -Number of replications for experiments in the randomized complete block design, in scenarios formed by combinations of i treatments (i = 3, 4, ..., 50) and d least differences between treatment means to be detected as significant at 5% probability by the Tukey test, expressed in percentage of the overall experimental mean (d = 10, 11, ... 20%), to evaluate the fresh matter of ryegrass (Lolium multiflorum L.) -cultivar BRS Ponteio seeded to haul -from optimal plot size (Xo = 2.19m 2 ) and the variation coefficient in optimal plot size (CVXo = 9.79%). replications and plots of 108 m 2 (6 m × 18 m) and subplots of 36 m 2 (6 m × 6m).

COnCLuSIOn
The optimal plot size to determine the fresh matter weight of ryegrass seeded at the haul is 2.19m 2 , with a variation coefficient of 9.79%. To identify as significant at 5% probability, by the Tukey test, differences between treatment means of 20%, are required five, six, seven and eight replications, respectively, in ryegrass experiments with up to five, ten, 20 and 50 treatments.