# ABSTRACT:

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 m2. 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 m2, 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.

Key words:
Lolium multiflorum L.; uniformity trials; experiment planning; maximum curvature method.

# RESUMO:

Palavras-chave:
Lolium multiflorum L.; ensaios de uniformidade; planejamento experimental; método da curvatura máxima.

# 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., 2018BISCAÍNO, L.L. et al. Beef heifers performance in ryegrass pasture supplemented with rice bran with or without monensin. Arquivo Brasileiro de Medicina Veterinária e Zootecnia, v.70, p.881-887, 2018. Available from: <Available from: https://dx.doi.org/10.1590/1678-4162-9463 >. Accessed: Mar. 07, 2019. doi: 10.1590/1678-4162-9463.
https://dx.doi.org/10.1590/1678-4162-946...
). 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., 2011CASSOL, L. C.et al. Yield and structural composition of oat and ryegrass subjected to different periods of cutting and nitrogen fertilization. Revista Ceres, v.58, p.438-443, 2011. Available from: <Available from: http://dx.doi.org/10.1590/S0034-737X2011000400006 >. Accessed: Set. 17, 2019. doi: 10.1590/S0034-737X2011000400006.
http://dx.doi.org/10.1590/S0034-737X2011...
). 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., 2009RIBEIRO FILHO, H. M. N. et al. Herbage intake and milk yield of dairy cows grazing Italian ryegrass at two herbage allowances. Revista Brasileira de Zootecnia, v.38, p.2038-2044, 2009. Available from <Available from http://dx.doi.org/10.1590/S1516-35982009001000026 >. Accessed: Set. 17, 2019. doi: 10.1590/S1516-35982009001000026.
http://dx.doi.org/10.1590/S1516-35982009...
). 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., 2018VIZIOLI, B. et al. Influence of ryegrass managements on the physical properties of a Haplohumox. Pesquisa Agropecuária Brasileira, v. 53, p.952-960, 2018. Available from: <Available from: https://doi.org/10.1590/S0100-204X2018000800010 >. Accessed: Mar. 29, 2019. doi: 10.1590/S0100-204X2018000800010.
https://doi.org/10.1590/S0100-204X201800...
).

For research on ryegrass to be scientifically valid, it is essential to define the experimental planning. In ryegrass experiments, were used plots from four plants until plots with areas of 108 m2 and three to eight replications (FLORES et al., 2008FLORES, R.A. et al. Forage production of annual ryegrass populations in the state of Rio Grande do Sul, Brazil. Revista Brasileira de Zootecnia, v. 37, p.1168-1175, 2008. Available from: <Available from: http://dx.doi.org/10.1590/S1516-35982008000700005 >. Accessed: Mar. 29, 2019. doi: 10.1590/S1516-35982008000700005.
http://dx.doi.org/10.1590/S1516-35982008...
; CASSOL et al., 2011CASSOL, L. C.et al. Yield and structural composition of oat and ryegrass subjected to different periods of cutting and nitrogen fertilization. Revista Ceres, v.58, p.438-443, 2011. Available from: <Available from: http://dx.doi.org/10.1590/S0034-737X2011000400006 >. Accessed: Set. 17, 2019. doi: 10.1590/S0034-737X2011000400006.
http://dx.doi.org/10.1590/S0034-737X2011...
; AGOSTINETTO et al., 2017AGOSTINETTO, D. et al. Metabolic activity of wheat and ryegrass plants in competition. Planta Daninha, v.35, p.1-7, 2017. Available from: <Available from: http://dx.doi.org/10.1590/S0100-83582017350100044 >. Accessed: Mar. 29, 2019. doi: 10.1590/S0100-83582017350100044.
http://dx.doi.org/10.1590/S0100-83582017...
; VIZIOLI et al., 2018VIZIOLI, B. et al. Influence of ryegrass managements on the physical properties of a Haplohumox. Pesquisa Agropecuária Brasileira, v. 53, p.952-960, 2018. Available from: <Available from: https://doi.org/10.1590/S0100-204X2018000800010 >. Accessed: Mar. 29, 2019. doi: 10.1590/S0100-204X2018000800010.
https://doi.org/10.1590/S0100-204X201800...
). However; although, experimental planning has already been carried out for forage crops, such as oat (CARGNELUTTI FILHO et al., 2014; CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in vetch. Bragantia, v.76, p.178-188, 2017. Available from: <Available from: https://dx.doi.org/10.1590/1678-4499.084 >. Accessed: Mar. 07, 2019. doi: 10.1590/1678-4499.084.
https://dx.doi.org/10.1590/1678-4499.084...
LAVEZO et al., 2017LAVEZO, A. et al. Plot size and number of replications to evaluate the grain yield in oat cultivars. Bragantia, v.76, p.512-520, 2017. Available from: <Available from: https://dx.doi.org/10.1590/1678-4499.2016.410 >. Accessed: Mar. 07, 2019. doi: 10.1590/1678-4499.2016.410.
https://dx.doi.org/10.1590/1678-4499.201...
), forage pea (CARGNELUTTI FILHO et al., 2015CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in forage pea. Ciência Rural, v.45, p.1174-1182, 2015. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20141043 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20141043.
https://dx.doi.org/10.1590/0103-8478cr20...
), millet (BURIN et al., 2016BURIN, C. et al. Plot size and number of replicates in times of sowing and cuts of millet. Revista Brasileira de Engenharia Agrícola e Ambiental, v.20, p.119-127, 2016. Available from: <Available from: https://dx.doi.org/10.1590/1807-1929/agriambi.v20n2p119-127 >. Accessed: Mar. 07, 2019. doi: 10.1590/1807-1929/agriambi.v20n2p119-127.
https://dx.doi.org/10.1590/1807-1929/agr...
), vetch (CARGNELUTTI FILHO et al., 2017CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in vetch. Bragantia, v.76, p.178-188, 2017. Available from: <Available from: https://dx.doi.org/10.1590/1678-4499.084 >. Accessed: Mar. 07, 2019. doi: 10.1590/1678-4499.084.
https://dx.doi.org/10.1590/1678-4499.084...
) and rye (CHAVES et al., 2018CHAVES, G.G. et al. Plot size and number of replications for evaluation of the yield of grains in cultivars and dates of sowing of rye. Journal of Agricultural Science, v.10, p.122-132, 2018. Available from: <Available from: http://dx.doi.org/10.5539/jas.v10n1p122 >. Accessed: Mar. 07, 2019. doi: 10.5539/jas.v10n1p122.
http://dx.doi.org/10.5539/jas.v10n1p122...
), no experimental planning studies were reported for ryegrass.

In experimental planning, the optimal plot size can be defined by the maximum curvature method of the variation coefficient model proposed by PARANAÍBA et al. (2009PARANAÍBA, P.F. et al. Optimum experimental plot size: proposition of estimation methods. Revista Brasileira de Biometria, v.27, p.255-268, 2009. Available from: <Available from: http://jaguar.fcav.unesp.br/RME/fasciculos/v27/v27_n2/Patricia.pdf >. Accessed: Mar. 07, 2019.
http://jaguar.fcav.unesp.br/RME/fascicul...
). 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., 2014CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in black oat. Ciência Rural, v.44, p.1732-1739, 2014. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20131466 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20131466.
https://dx.doi.org/10.1590/0103-8478cr20...
, 2015CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in forage pea. Ciência Rural, v.45, p.1174-1182, 2015. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20141043 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20141043.
https://dx.doi.org/10.1590/0103-8478cr20...
, 2017CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in vetch. Bragantia, v.76, p.178-188, 2017. Available from: <Available from: https://dx.doi.org/10.1590/1678-4499.084 >. Accessed: Mar. 07, 2019. doi: 10.1590/1678-4499.084.
https://dx.doi.org/10.1590/1678-4499.084...
). Using these methods, was recommended: a plot size of 4.14m2 and four replications to evaluate the fresh matter of black oats (CARGNELUTTI FILHO et al., 2014CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in black oat. Ciência Rural, v.44, p.1732-1739, 2014. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20131466 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20131466.
https://dx.doi.org/10.1590/0103-8478cr20...
); a plot size of 5.03 m2 and four replications to evaluate the fresh matter of forage pea (CARGNELUTTI FILHO et al., 2015CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in forage pea. Ciência Rural, v.45, p.1174-1182, 2015. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20141043 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20141043.
https://dx.doi.org/10.1590/0103-8478cr20...
); a plot size of 4.97m2 and five replications to evaluate millet shoot fresh matter (BURIN et al., 2016BURIN, C. et al. Plot size and number of replicates in times of sowing and cuts of millet. Revista Brasileira de Engenharia Agrícola e Ambiental, v.20, p.119-127, 2016. Available from: <Available from: https://dx.doi.org/10.1590/1807-1929/agriambi.v20n2p119-127 >. Accessed: Mar. 07, 2019. doi: 10.1590/1807-1929/agriambi.v20n2p119-127.
https://dx.doi.org/10.1590/1807-1929/agr...
); a plot size of 1.57m2 and four replications to evaluate grain yield in four oat cultivars (LAVEZO et al., 2017LAVEZO, A. et al. Plot size and number of replications to evaluate the grain yield in oat cultivars. Bragantia, v.76, p.512-520, 2017. Available from: <Available from: https://dx.doi.org/10.1590/1678-4499.2016.410 >. Accessed: Mar. 07, 2019. doi: 10.1590/1678-4499.2016.410.
https://dx.doi.org/10.1590/1678-4499.201...
); a plot size of 4.52 m2 and four replications to evaluate the fresh matter of vetch (CARGNELUTTI FILHO et al., 2017CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in forage pea. Ciência Rural, v.45, p.1174-1182, 2015. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20141043 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20141043.
https://dx.doi.org/10.1590/0103-8478cr20...
); and, a plot size of 6.08 m2 and seven replications to evaluate grains yield of rye (CHAVES et al., 2018CHAVES, G.G. et al. Plot size and number of replications for evaluation of the yield of grains in cultivars and dates of sowing of rye. Journal of Agricultural Science, v.10, p.122-132, 2018. Available from: <Available from: http://dx.doi.org/10.5539/jas.v10n1p122 >. Accessed: Mar. 07, 2019. doi: 10.5539/jas.v10n1p122.
http://dx.doi.org/10.5539/jas.v10n1p122...
). 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., 2012WREGE, M.S. et al. Atlas climático da Região Sul do Brasil: Estados do Paraná, Santa Catarina e Rio Grande do Sul. 2ª ed. Brasília: EMBRAPA , 2012. 333 p.) and the soil is classified as “Haplic Plinthosol” (SANTOS et al., 2013SANTOS, H.G. et al. Sistema brasileiro de classificação de solos. Brasília: EMBRAPA, 2013. 353 p.).

The ryegrass seeds were sown to haul on June 9, 2015, in an area of 720 m2, with 25 kg of seeds per hectare. Fertilization was carried out according to the crop recommendation (CQFS, 2004CQFS - Comissão de Química e Fertilidade do Solo. Manual de adubação e de calagem para os Estados do Rio Grande do Sul e de Santa Catarina. 10ª ed. Porto Alegre: Sociedade Brasileira de Ciência do Solo. 2004, 400 p. ). The cultural practices were performed evenly, as recommended for the uniformity trials (STORCK et al., 2016STORCK, L. et al. Experimentação vegetal. 3ª ed. Santa Maria: UFSM, 2016. 200 p. ). Then, in the experiment central area were delimited 20 uniformity trials, each one of size 8 m2 (4 m × 2 m), was divided into 16 basic experimental units (BEU) of 0.5 m2 (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 (s2), mean (m, g), variation coefficient of the trial (CVtrial, %), optimal plot size (Xo, in BEU and m2) and the variation coefficient in the optimal plot size (CVXo, %). The estimate of ρ was obtained in the direction of the rows, according to the equation described by PARANAÍBA et al. (2009PARANAÍBA, P.F. et al. Optimum experimental plot size: proposition of estimation methods. Revista Brasileira de Biometria, v.27, p.255-268, 2009. Available from: <Available from: http://jaguar.fcav.unesp.br/RME/fasciculos/v27/v27_n2/Patricia.pdf >. Accessed: Mar. 07, 2019.
http://jaguar.fcav.unesp.br/RME/fascicul...
).

Based on the maximum curvature method of the variation coefficient model, proposed by PARANAÍBA et al. (2009PARANAÍBA, P.F. et al. Optimum experimental plot size: proposition of estimation methods. Revista Brasileira de Biometria, v.27, p.255-268, 2009. Available from: <Available from: http://jaguar.fcav.unesp.br/RME/fasciculos/v27/v27_n2/Patricia.pdf >. Accessed: Mar. 07, 2019.
http://jaguar.fcav.unesp.br/RME/fascicul...
), the optimal plot size $\mathit{Xo}=\left(10\sqrt[3]{2\left(1-{\rho }^{2}\right){s}^{2}\mathit{m}\right)}\right)/\mathit{m}$ and the variation coefficient in the optimal plot size ${\mathit{CV}}_{\mathit{Xo}}=\left(\sqrt{\left(1-{\rho }^{2}\right){s}^{2}/{m}^{2}}\right)/\sqrt{\mathit{Xo}}×100$ were determined. The means comparisons of the statistics ρ, s2, m, CV, Xo, and CVXo 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, 2014FERREIRA, D.F. Sisvar: A guide for its bootstrap procedures in multiple comparisons. Ciência e Agrotecnologia, v.38, p.109-112, 2014. Available from: <Available from: http://www.scielo.br/pdf/cagro/v38n2/a01v38n2.pdf >. Accessed: Mar. 07, 2019.
http://www.scielo.br/pdf/cagro/v38n2/a01...
).

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, $d=\left({q}_{\alpha \left(i;\mathit{DFE}\right)}\sqrt{\mathit{MSE⁄r}}\right)\mathit{⁄m}×100$where qα(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 $\left(\mathit{CV}=\sqrt{\mathit{MSE}}/\mathit{m}×100\right)$, in percentage, in the expression for the calculation of d and isolating r, we have $r={\left({q}_{\alpha \left(i;\mathit{DFE}\right)}\mathit{CV}/d\right)}^{2}$. In the study, the CV is expressed as a percentage and corresponds to the CVXo, since this is the CV expected for the experiment with the optimal plot size (Xo) determined.

From the mean of CVXo, 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, 2014FERREIRA, D.F. Sisvar: A guide for its bootstrap procedures in multiple comparisons. Ciência e Agrotecnologia, v.38, p.109-112, 2014. Available from: <Available from: http://www.scielo.br/pdf/cagro/v38n2/a01v38n2.pdf >. Accessed: Mar. 07, 2019.
http://www.scielo.br/pdf/cagro/v38n2/a01...
)

# RESULTS AND DISCUSSION:

There were no differences between the three evaluation times for estimates of the first-order spatial autocorrelation coefficient (ρ), variance (s2), mean (m), variation coefficient of the trial (CVtrial), optimal plot size (Xo) and the variation coefficient in the optimal plot size (CVXo) 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.

Table 1
First-order spatial autocorrelation coefficient (ρ), variance (s2), mean (m), variation coefficient of the trial (CV), optimal plot size (Xo, in BEU of 0.5m2 and in m2) 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.

The fresh matter weight of ryegrass ranged between 1166 and 1705 g per BEU of 0.5 m2, 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, 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)PIMENTEL-GOMES, F. Curso de estatística experimental. 15ª ed. Piracicaba: FEALQ, 2009. 451 p.. 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 m2, with a mean value of 2.19 m2. 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)PIMENTEL-GOMES, F. Curso de estatística experimental. 15ª ed. Piracicaba: FEALQ, 2009. 451 p.. The optimal plot size to determine fresh matter weight of ryegrass (2.19 m2) is lower than that described in the literature to determine fresh matter weight of other foragers as black oats (4.14m2 - CARGNELUTTI FILHO et al., 2014CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in black oat. Ciência Rural, v.44, p.1732-1739, 2014. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20131466 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20131466.
https://dx.doi.org/10.1590/0103-8478cr20...
), forage pea (5.03 m2 - CARGNELUTTI FILHO et al., 2015CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in forage pea. Ciência Rural, v.45, p.1174-1182, 2015. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20141043 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20141043.
https://dx.doi.org/10.1590/0103-8478cr20...
), millet (4.97 m2 - BURIN et al., 2016BURIN, C. et al. Plot size and number of replicates in times of sowing and cuts of millet. Revista Brasileira de Engenharia Agrícola e Ambiental, v.20, p.119-127, 2016. Available from: <Available from: https://dx.doi.org/10.1590/1807-1929/agriambi.v20n2p119-127 >. Accessed: Mar. 07, 2019. doi: 10.1590/1807-1929/agriambi.v20n2p119-127.
https://dx.doi.org/10.1590/1807-1929/agr...
) and vetch (4.52 m2 - CARGNELUTTI FILHO et al., 2017CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in vetch. Bragantia, v.76, p.178-188, 2017. Available from: <Available from: https://dx.doi.org/10.1590/1678-4499.084 >. Accessed: Mar. 07, 2019. doi: 10.1590/1678-4499.084.
https://dx.doi.org/10.1590/1678-4499.084...
). However, the variation coefficient in the optimal plot size (CVXo = 9.79%) was similar to that described for other forages in the abovementioned studies (9.25%≤CVXo≤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., 2014CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in black oat. Ciência Rural, v.44, p.1732-1739, 2014. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20131466 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20131466.
https://dx.doi.org/10.1590/0103-8478cr20...
, 2015CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in forage pea. Ciência Rural, v.45, p.1174-1182, 2015. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20141043 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20141043.
https://dx.doi.org/10.1590/0103-8478cr20...
, 2017CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in vetch. Bragantia, v.76, p.178-188, 2017. Available from: <Available from: https://dx.doi.org/10.1590/1678-4499.084 >. Accessed: Mar. 07, 2019. doi: 10.1590/1678-4499.084.
https://dx.doi.org/10.1590/1678-4499.084...
; BURIN et al., 2016BURIN, C. et al. Plot size and number of replicates in times of sowing and cuts of millet. Revista Brasileira de Engenharia Agrícola e Ambiental, v.20, p.119-127, 2016. Available from: <Available from: https://dx.doi.org/10.1590/1807-1929/agriambi.v20n2p119-127 >. Accessed: Mar. 07, 2019. doi: 10.1590/1807-1929/agriambi.v20n2p119-127.
https://dx.doi.org/10.1590/1807-1929/agr...
; LAVEZO et al., 2017LAVEZO, A. et al. Plot size and number of replications to evaluate the grain yield in oat cultivars. Bragantia, v.76, p.512-520, 2017. Available from: <Available from: https://dx.doi.org/10.1590/1678-4499.2016.410 >. Accessed: Mar. 07, 2019. doi: 10.1590/1678-4499.2016.410.
https://dx.doi.org/10.1590/1678-4499.201...
; CHAVES et al., 2018CHAVES, G.G. et al. Plot size and number of replications for evaluation of the yield of grains in cultivars and dates of sowing of rye. Journal of Agricultural Science, v.10, p.122-132, 2018. Available from: <Available from: http://dx.doi.org/10.5539/jas.v10n1p122 >. Accessed: Mar. 07, 2019. doi: 10.5539/jas.v10n1p122.
http://dx.doi.org/10.5539/jas.v10n1p122...
), indicating the infeasibility of experimental conduction at this precision level.

Table 2
Number of replications for experiments in the completely randomized 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 = 2.19m2) and the variation coefficient in optimal plot size (CVXo = 9.79%).

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 = 2.19m2) and the variation coefficient in optimal plot size (CVXo = 9.79%).

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., 2014CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in black oat. Ciência Rural, v.44, p.1732-1739, 2014. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20131466 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20131466.
https://dx.doi.org/10.1590/0103-8478cr20...
, 2015CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in forage pea. Ciência Rural, v.45, p.1174-1182, 2015. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20141043 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20141043.
https://dx.doi.org/10.1590/0103-8478cr20...
, 2017CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in vetch. Bragantia, v.76, p.178-188, 2017. Available from: <Available from: https://dx.doi.org/10.1590/1678-4499.084 >. Accessed: Mar. 07, 2019. doi: 10.1590/1678-4499.084.
https://dx.doi.org/10.1590/1678-4499.084...
; BURIN et al., 2016BURIN, C. et al. Plot size and number of replicates in times of sowing and cuts of millet. Revista Brasileira de Engenharia Agrícola e Ambiental, v.20, p.119-127, 2016. Available from: <Available from: https://dx.doi.org/10.1590/1807-1929/agriambi.v20n2p119-127 >. Accessed: Mar. 07, 2019. doi: 10.1590/1807-1929/agriambi.v20n2p119-127.
https://dx.doi.org/10.1590/1807-1929/agr...
; LAVEZO et al., 2017LAVEZO, A. et al. Plot size and number of replications to evaluate the grain yield in oat cultivars. Bragantia, v.76, p.512-520, 2017. Available from: <Available from: https://dx.doi.org/10.1590/1678-4499.2016.410 >. Accessed: Mar. 07, 2019. doi: 10.1590/1678-4499.2016.410.
https://dx.doi.org/10.1590/1678-4499.201...
; CHAVES et al., 2018CHAVES, G.G. et al. Plot size and number of replications for evaluation of the yield of grains in cultivars and dates of sowing of rye. Journal of Agricultural Science, v.10, p.122-132, 2018. Available from: <Available from: http://dx.doi.org/10.5539/jas.v10n1p122 >. Accessed: Mar. 07, 2019. doi: 10.5539/jas.v10n1p122.
http://dx.doi.org/10.5539/jas.v10n1p122...
). 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 CVXo. This pattern has also been reported in the literature (CARGNELUTTI FILHO et al., 2014CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in black oat. Ciência Rural, v.44, p.1732-1739, 2014. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20131466 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20131466.
https://dx.doi.org/10.1590/0103-8478cr20...
, 2015CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in forage pea. Ciência Rural, v.45, p.1174-1182, 2015. Available from: <Available from: https://dx.doi.org/10.1590/0103-8478cr20141043 >. Accessed: Mar. 07, 2019. doi: 10.1590/0103-8478cr20141043.
https://dx.doi.org/10.1590/0103-8478cr20...
, 2017CARGNELUTTI FILHO, A. et al. Plot size and number of repetitions in vetch. Bragantia, v.76, p.178-188, 2017. Available from: <Available from: https://dx.doi.org/10.1590/1678-4499.084 >. Accessed: Mar. 07, 2019. doi: 10.1590/1678-4499.084.
https://dx.doi.org/10.1590/1678-4499.084...
; BURIN et al., 2016BURIN, C. et al. Plot size and number of replicates in times of sowing and cuts of millet. Revista Brasileira de Engenharia Agrícola e Ambiental, v.20, p.119-127, 2016. Available from: <Available from: https://dx.doi.org/10.1590/1807-1929/agriambi.v20n2p119-127 >. Accessed: Mar. 07, 2019. doi: 10.1590/1807-1929/agriambi.v20n2p119-127.
https://dx.doi.org/10.1590/1807-1929/agr...
; LAVEZO et al., 2017LAVEZO, A. et al. Plot size and number of replications to evaluate the grain yield in oat cultivars. Bragantia, v.76, p.512-520, 2017. Available from: <Available from: https://dx.doi.org/10.1590/1678-4499.2016.410 >. Accessed: Mar. 07, 2019. doi: 10.1590/1678-4499.2016.410.
https://dx.doi.org/10.1590/1678-4499.201...
; CHAVES et al., 2018CHAVES, G.G. et al. Plot size and number of replications for evaluation of the yield of grains in cultivars and dates of sowing of rye. Journal of Agricultural Science, v.10, p.122-132, 2018. Available from: <Available from: http://dx.doi.org/10.5539/jas.v10n1p122 >. Accessed: Mar. 07, 2019. doi: 10.5539/jas.v10n1p122.
http://dx.doi.org/10.5539/jas.v10n1p122...
).

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

$d=\frac{{q}_{5%\left(50;350\right)}×9.79}{\sqrt{8}}=\frac{5.699681×9.79}{\sqrt{8}}=19.73%$

and for the randomized complete block design

$d=\frac{{q}_{5%\left(50;343\right)}×9.79}{\sqrt{8}}=\frac{5.700775×9.79}{\sqrt{8}}=19.73%$

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 m2 (1.5 m × 2 m) in one site and of 6 m2 in another site, with a collection area of 0.25 m2 per plot (0.5 m × 0.5 m) (FLORES et al., 2008FLORES, R.A. et al. Forage production of annual ryegrass populations in the state of Rio Grande do Sul, Brazil. Revista Brasileira de Zootecnia, v. 37, p.1168-1175, 2008. Available from: <Available from: http://dx.doi.org/10.1590/S1516-35982008000700005 >. Accessed: Mar. 29, 2019. doi: 10.1590/S1516-35982008000700005.
http://dx.doi.org/10.1590/S1516-35982008...
). 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 100m2 (10 m × 10 m) to evaluate soil physical components under no-till (VIZIOLI et al., 2018VIZIOLI, B. et al. Influence of ryegrass managements on the physical properties of a Haplohumox. Pesquisa Agropecuária Brasileira, v. 53, p.952-960, 2018. Available from: <Available from: https://doi.org/10.1590/S0100-204X2018000800010 >. Accessed: Mar. 29, 2019. doi: 10.1590/S0100-204X2018000800010.
https://doi.org/10.1590/S0100-204X201800...
). 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., 2017AGOSTINETTO, D. et al. Metabolic activity of wheat and ryegrass plants in competition. Planta Daninha, v.35, p.1-7, 2017. Available from: <Available from: http://dx.doi.org/10.1590/S0100-83582017350100044 >. Accessed: Mar. 29, 2019. doi: 10.1590/S0100-83582017350100044.
http://dx.doi.org/10.1590/S0100-83582017...
). Already to evaluate the yield and structural composition of oat and ryegrass subjected to different periods of cutting and nitrogen fertilization, CASSOL et al. (2011CASSOL, L. C.et al. Yield and structural composition of oat and ryegrass subjected to different periods of cutting and nitrogen fertilization. Revista Ceres, v.58, p.438-443, 2011. Available from: <Available from: http://dx.doi.org/10.1590/S0034-737X2011000400006 >. Accessed: Set. 17, 2019. doi: 10.1590/S0034-737X2011000400006.
http://dx.doi.org/10.1590/S0034-737X2011...
) used a randomized complete block design with four replications and plots of 108 m2 (6 m × 18 m) and subplots of 36 m2 (6 m × 6m).

# CONCLUSION:

The optimal plot size to determine the fresh matter weight of ryegrass seeded at the haul is 2.19m2, 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.

# ACKNOWLEDGEMENTS

To the Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul (FAPERGS - Process no. 16/2551-0000257-6 ARD/PPP) by financial support. To Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq - Process no. 304652/2017-2) for the research grant of the second author. To the CNPq, to the FAPERGS, to the Programa de Educação Tutorial do Ministério da Educação and to the Universidade Federal do Pampa by scholarships. To the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brasil - Finance code 001.

# REFERENCES

• CR-2019-0195.R2

# Publication Dates

• Publication in this collection
31 Jan 2020
• Date of issue
2020