Plot size and number of replicates for ryegrass experiments sowed in rows

− The objective of this work was to determine the optimal plot size and the number of replicates for the evaluation of the fresh weight of ryegrass sowed in rows. Seventy uniformity trials were performed with 'Barjumbo' ryegrass, in 16 basic experimental units (BEUs) of 0.51 m 2 each. The fresh weight of ryegrass in the BEUs of 18, 18, 6, 6, and 22 uniformity trials was determined, respectively, at 130, 131, 133, 134, and 137 days after sowing. The optimal plot size was determined through the method of the maximum curvature of the coefficient of variation. The number of replicates was determined in scenarios formed by combinations of treatments and differences between means to be detected as significant by Tukey’s test, at 5% probability. The optimal plot size ranged from 1.73 to 3.18 m 2 , and the variation coefficient in the optimal plot size from 7.58 to 13.96%. The number of replicates varied from 3.95 (~4) to 32.27 (~33), depending on the experimental design, the number of treatments, and the adopted minimum difference. The optimal plot size is 2.29 m 2 , and, in experiments with up to 50 treatments, eight replicates are required to identify as significant the differences between treatment means of 20.24%.


Introduction
Ryegrass (Lolium multiflorum L.) is one of the most cultivated forage species, and it can be used either alone or in mixtures to eliminate the lack of forage in southern Brazil, during the winter (Flores et al., 2008). The expansion of research on ryegrass is significant because of the importance of this crop to phytotechnology, soil conservation, phytosanitary defense, and animal nutrition (Flores et al., 2008;Agostinetto et al., 2017;Vizioli et al., 2018;Salazar et al., 2019;Toebe et al., 2020a). In this sense, it is important to define experimental protocols, to optimize the quality and reliability of research, as well as to minimize expenditures with financial, human, and time resources. Therefore, knowing the plot size and number of replicates for combinations of the number of treatments, experimental designs, and precision levels, is essential to consolidate the scientific development in agricultural crops.
Several studies have used the method of the maximum curvature of the coefficient of variation, proposed by Paranaiba et al. (2009), to scale plot size. The number of replicates has been defined in scenarios formed by combinations of differences among means to be detected as significant by Tukey's test and the number of treatments, in an iterative process until convergence, according to the method described by Cargnelutti Filho et al. (2014a). These two methods have been applied in experimental planning to determine the fresh weight of forage crops (Cargnelutti Filho et al., 2014a, 2020Burin et al., 2015;Chaves et al., 2018;Lavezo et al., 2018;Toebe et al., 2020b). These methods have been also applied for the determination of plot size and the number of replicates, to evaluate the fresh weight of broadcastseeded ryegrass (Toebe et al., 2020a).
The sowing systems and the spatial arrangement of plants interfere with the growth, development, and productivity of crops, and they are able to alter the recommendations of the number of replicates and plot size. In this sense , Cargnelutti Filho et al. (2014b) identified differences in the experimental design of turnip sowed both in rows and broadcasted. Thus, although the number of replicates and the plot size for ryegrass sowing by broadcast have already been carried out by Toebe et al. (2020a), this information for ryegrass experiments sowed in rows has not been reported in the literature yet.
The objective of this work was to determine the optimal plot size and the number of replicates for the evaluation of the fresh weight of ryegrass sowed in rows.

Materials and Methods
Seventy uniformity trials with ryegrass were carried out in the experimental area of Universidade Federal do Pampa, Itaqui Campus, located in the municipality of Itaqui, in the state of Rio Grande do Sul, Brazil (29º09'25"S, 56º33'16"W, at 74 m altitude). The region shows a Cfa climate, according to the Köppen-Geiger's classification. The soil is classified as Plintossolo Háplico according to the Brazilian soil classification system (Santos et al., 2018), which corresponds to the Ultisol classification (Soil Survey Staff, 1999). 'Barjumbo' ryegrass seed were sowed with 25 kg ha -1 , on June 8, 2015, in rows spaced at 0.17 m between rows, in 1,800 m 2 area. The fertilization was carried out following the recommendations for the crop (Tedesco et al., 2004), and the cultural practices were performed evenly within the experimental area.
Seventy uniformity trials were delimited in the central area of the experiment. Each uniformity trial of 4×2.04 m (8.16 m 2 ) was divided into 16 basic experimental units (BEUs) of 1.0×0.51 m (0.51 m 2 , 1.0 m × three rows), forming a matrix of four rows and four columns. The plant collection for determining fresh weight was performed as follows: 18 trials were collected 130 days after sowing (DAS); 18 trials, 131 DAS; 6 trials, 133 DAS; 6 trials, 134 DAS; and 22 trials, 137 DAS, in each BEU. Plants were cut near the soil surface, and the fresh weight was determined (g 0.51 m -2 ).
Based on the fresh weight in the 16 BEUs of each uniform trial, the first-order spatial autocorrelation coefficient (ρ), variance (s 2 ), mean (m, g), coefficient of variation of the trial (CV trial , %), optimal plot size (Xo, in BEU and m 2 ), and the coefficient of variation in the optimal plot size (CV Xo , %) were determined. The estimate of ρ was obtained in the direction of the rows, and the statistics Xo and CV Xo were obtained using the equations described by Paranaiba et al. (2009)  The comparisons of means of the statistics ρ, s 2 , m, CV trial , Xo, and CV Xo among the evaluation days were performed using Tukey's test via bootstrap with 10,000 resamplings, at 5% probability, as detailed and applied by Toebe et al. (2020a).
The number of replicates was defined from the least significant difference (d) of Tukey's test (in percentage of the overall experimental mean), estimated through the following equation: where q α(i;DFE) is the critical value of Tukey's test at level α of probability error (α=0.05, in the present study); i is the number of treatments; DFE is the number of degrees of freedom of error [i(r-1)], for the completely randomized design, and [(i-1) (r-1)] for the randomized block design; EMS is the error mean square; r is the number of replicates; and m is the mean of the experiment. By replacing the expression of the experimental coefficient of variation ( / ), CV EMS m u 100 in percentage, in the expression for the calculation of d, and isolating r, the following expression is obtained: In this study, the CV, expressed as a percentage, corresponds to the CV Xo , since this is the CV expected for an experiment with the optimal plot size (Xo) determined. The number of replicates (r) was determined for experiments with completely randomized design and randomized block design, by an iterative process until convergence, using the mean of CV Xo among the evaluation days. The r was determined in scenarios formed by combinations of i treatments (i = 3, 4, ..., 50) and d minimum differences among means of treatments to be detected as significant by Tukey's test at 5% probability, expressed as a percentage of the experimental mean (d = 10%, 11%, ..., 20%), according to Cargnelutti Filho et al. (2014a) and Toebe et al. (2020a), in ryegrass sown to haul. Statistical analyses were performed with Microsoft Office Excel, R (R Core Team, 2020), and Sisvar softwares (Ferreira, 2014).

Results and Discussion
There were no significant differences among the evaluation time in days for ρ and s 2 (Tables 1 and 2). For the mean of fresh weight per BEU, differences were found among evaluation days, with means ranging between 1281 g and 1534 g per BEU. Among all the 70 uniformity trials, the mean productivity of fresh weight was 1449 g per BEU of 0.51 m 2 (28,412 kg ha -1 ), ranging from 1179 g per BEU (23,118 kg ha -1 in the trial 2, at 134 DAS) to 1751 g per BEU (34,333 kg ha -1 in the trial 1, at 131 DAS). The variation of the fresh weight is important for the experimental design, as it contemplates real situations of variability that occur in experimental areas. The mean productivity of fresh weight was higher than the one obtained by Toebe et al. (2020a) for the broadcast-seeded 'BRS Ponteio' ryegrass, in the same experimental area and year. This difference is possibly due to the cultivar and the type of sowing.
The overall coefficient of variation was 22.96% (Table 2), which is considered high according to Pimentel-Gomes (2009). Among the 70 uniformity trials, the CV trial oscillated between 14.09 and 39.80%, respectively, for trials 11 (at 131 DAS) and 5 (at 130 DAS), that is, the CV fluctuated from medium to very high values, according to the classification by Pimentel-Gomes (2009). However, no significant differences were verified among the evaluation days (18.86% ≤ CV ≤ 25.59%).
The optimal plot size based on the 70 trials was 4.49 BEUs or 2.29 m 2 , and no significant differences occurred among the evaluation days (2.06 m 2 ≤ Xo ≤ 2.41 m 2 -Tables 1 and 2). The optimal plot size calculated for each uniform trial ranged between 1.73 and 3.18 m 2 , respectively for trial 11, at 131 DAS, and trial 5, at 130 DAS. These two trials showed the lowest and highest CV values, respectively, as previously discussed. The coefficient of variation in the optimal plot size ranged between 7.58% and 13.96%, with an overall mean of 10.04%, which is considered to be at the limit between the low and medium percentages according to Pimentel-Gomes (2009). As for the ρ, s 2 , CV trial , and Xo statistics, no significant differences were identified for CV Xo between the evaluation dates (9.03% ≤ CV Xo ≤ 10.57%). Therefore, the means of Xo and CV Xo statistics based on the 70 uniformity trials were used for the calculation of the number of replicates.
Pesq. agropec. bras., Brasília, v.57, e02976, 2022 DOI: 10.1590/S1678-3921.pab2022.v57.02976 The number of replicates varied between 3.95 and 32.27 (Tables 3 and 4), depending on the experimental design, the number of treatments (i), and the minimum differences (d). As already described [Cargnelutti Filho et al. (2014a, 2020; Burin et al. (2015); Chaves et al. (2018); Lavezo et al. (2018); and Toebe et al. (2020aToebe et al. ( , 2020b], the greater is the term i, and the lower is the d, the greater will be the number of replicates. In this sense, the use of five, six, seven, and eight replicates is sufficient to identify differences Table 1. First order spatial autocorrelation coefficient (ρ), variance (s 2 ), mean (m), coefficient of variation of the trial (CV trial, %), optimal plot size (Xo, in BEUs of 0.51 m 2 and in m 2 ), and the coefficient of variation of the optimal plot size (CV Xo , %) for the fresh weight of 'Barjumbo' ryegrass (Lolium multiflorum), sowed in rows and evaluated in uniformity trials at 130 and 131 days after sowing (DAS).
Using the same methods of the present study to determine plot size and the number of replicates (in black oats, oat, forage pea, millet, rye, Sudan grass, triticale, and vetch), the plot size ranged from 1.66 to 7.95 m 2 , and the number of replicates ranged from four to eight (Cargnelutti Filho et al., 2014a, Table 2. First order spatial autocorrelation coefficient (ρ), variance (s 2 ), mean (Me), coefficient of variation of the trial (CV, in %), optimal plot size (Xo, m 2 , in BEUs of 0.51 m 2 ), and the coefficient of variation in the optimal plot size (CV Xo , %), for the fresh weight of 'Barjumbo' ryegrass (Lolium multiflorum) sowed in rows and evaluated in uniformity trials at 133, 134, and 137 days after sowing (DAS).

DAS
Trial (  (2) For the statistics ρ, s 2 , Me, CV, Xo, and CV Xo , the means followed by equal letters, in the columns (comparison of means between the evaluation days), do not differ by Tukey's test, at 5% probability, via bootstrap with 10,000 resamplings.
Pesq. agropec. bras., Brasília, v.57, e02976, 2022 DOI: 10.1590/S1678-3921.pab2022.v57.02976 Table 3. Number of replicates of experiments in a completely randomized design, in scenarios formed by the combinations of i treatments (i = 3, 4, ..., 50) and d least differences between treatment means to be detected as significant by Tukey's test, at 5% probability, expressed as percentage of the overall experimental mean (d = 10, 11, ..., 20%), to evaluate the fresh weight of 'Barjumbo' ryegrass (Lolium multiflorum) sowed in rows of the optimal plot size (Xo = 2.29 m 2 ), and the coefficient of variation in the optimal plot size (CV Xo = 10.04%).  Table 4. Number of replicates for experiments in a randomized 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 by Tukey's test, at 5% probability, expressed in percentage of the overall experimental mean (d = 10, 11, ..., 20%), to evaluate the fresh weight of 'Barjumbo' ryegrass (Lolium multiflorum) sowed in rows in the optimal plot size (Xo = 2.29 m 2 ), and coefficient of variation in the optimal plot size (CV Xo = 10.04%). 2020; Burin et al., 2015;Chaves et al., 2018;Lavezo et al., 2018;Toebe et al., 2020b). The combination of these plot sizes and numbers of replicates allowed to identify as significant the differences between treatment means ranging between 20.00 and 44.75% of the experimental mean, by Tukey's test, at 5% probability. Such differences for plot sizes and number of replicates between surveys are due to the intrinsic variability of each crop, between cultivars, the local of experimental conduction and crop year, among other factors.
In broadcast-seeded ryegrass , the optimal plot size to determine the fresh weight was 2.19 m 2 , with a coefficient of variation of 9.79% (Toebe et al., 2020a). According to these authors, the use of eight replicates is recommended to identify differences of 20% between treatment means as significant, in experiments with up to 50 treatments. In the study developed by Toebe et al. (2020a), the CV values of the uniformity trials, optimal plot size, CV in the optimal plot size, and the number of replicates were similar to those of the present study. This fact shows the consistency of these statistics for ryegrass, even considering different cultivation systems and cultivars. This may not be the case for other crops, such as turnip, for which Cargnelutti Filho et al. (2014b) recommended a greater plot size to evaluate the fresh weight in broadcastedseeding experiments than the plot size of experiments sowed in rows. This can be explained by differences of soil, agricultural years, and, especially, by the different response of crops to the spatial arrangement. Other researchers - Flores et al. (2008) and Vizioli et al. (2018) -have used larger plot sizes than the one recommended in the present work for ryegrass, that is, 3-100 m 2 plots. However, the useful area of evaluation and the number of replicates were generally lower than the values obtained in the present study. Thus, this work contributes to the definition of experimental protocols for ryegrass cultivation, with the use optimization of experimental resources and the quality guarantee of inferential data analysis.
In the present study, for the combination of a higher number of treatments (50 treatments) and lower precision (d = 20%), the number of replicates was 8.19 (Tables 3 and 4), which cannot be used in practice.
Thus, differences between treatment means of 20.24% of the experimental mean are identified as significant, by Tukey's test, at 5% probability, in experiments with up to 50 treatments and eight replicates. It is noteworthy, however, that very large agricultural experiments (with many treatments) occupy large areas and, therefore, they have usually greater variability, which sometimes makes it difficult to detect significant differences between treatments. Hence, experiments with more than 50 treatments and more than eight replicates should be avoided, to minimize the experimental variability.

Conclusions
1. The optimal plot size to evaluate the fresh weight of ryegrass (Lolium multiflorum) sowed in rows is 2.29 m 2 .
2. In experiments with up to 50 treatments, eight replicates are required to identify as significant the differences between treatment means of 20.24%.