The objectives of this study were to determine the optimum plot size (Xo) and the number of replications to evaluate grain yield and verify the variability of Xo among oat cultivars. Thirtytwo uniformity trials of 3 × 3 m were performed, being 8 from each cultivar (URS Charrua, URS Taura, URS Estampa, and URS Corona). Each uniformity trial was divided in 36 basic experimental units (BEU) of 0.5 × 0.5 m. Grain yield was determined in each BEU. The Xo was determined by the method of maximum curvature of the coefficient of variation model. Mean comparisons among cultivars were performed by the Scott-Knott test via bootstrap. The number of replications was calculated by an iterative process until convergence for experiments in completely randomized design (CRD) and randomized block CRop pRoduCTion And MAnAgeMenT-Article

O objetivo deste trabalho foi determinar o tamanho de amostra para a estimação do coeficiente de correlação linear de Pearson entre caracteres de três híbridos de milho. Para as análises, foram tomadas aleatoriamente 361, 373 e 416 plantas, respectivamente, de híbridos simples, triplo e duplo. Para cada planta, os seguintes caracteres foram mensurados: diâmetro maior e menor do colmo, altura da planta e altura, peso, comprimento e diâmetro da espiga, número de fileiras por espiga, peso e diâmetro de sabugo, massa de cem grãos, número de grãos por espiga, comprimento e produtividade de grãos. Para cada um dos 91 pares de caracteres e híbridos, foi determinado o tamanho de amostra a partir de "bootstrap", com reposição de 1.000 amostras, de cada tamanho de amostra simulado. Na estimação do coeficiente de correlação linear de Pearson com a mesma precisão, o tamanho de amostra (número de plantas) aumenta na direção de pares de caracteres com menor intensidade de relação linear, independentemente do tipo de híbrido. Para os 91 pares de caracteres estudados, 252 plantas são suficientes para a estimação do coeficiente de correlação linear de Pearson, no intervalo de confiança de "bootstrap" de 95%, igual a 0,30

RESUMOO objetivo do estudo foi estimar o tamanho de amostra para avaliar a altura de planta (H), o diâmetro do coleto (D) e a relação altura de planta/diâmetro do coleto (HD) de timbaúva (Enterolobium contortisiliquum) e verificar a variabilidade do tamanho de amostra entre tubetes, doses de fertilizante e idades de avaliação. Foram avaliados dez tratamentos, formados pela combinação de tamanhos de tubetes (110 e 180 cm3 ) e doses de fertilizante (0, 3, 5, 7 e 9 g L -1 de substrato), no delineamento em blocos, com quatro repetições. Em cinco idades foram determinadas H, D e HD. O tamanho de amostra para H, D e HD é dependente da idade de avaliação. Para os tamanhos de tubetes, doses de fertilizante e idades de avaliação, 22 plantas por unidade experimental (bandeja) são suficientes para estimar a média dessas características, para erro de estimação de 10% da média, com grau de confiança de 95%. Palavras-chave:Enterolobium contortisiliquum, número de plantas, amostragem. Sample Size for Height and Diameter Evaluation of Timbauva Plants ABSTRACTThe objective was to estimate the sample size to evaluate height (H), collar diameter (D) and relation height/collar diameter (HD) of timbauva plants (Enterolobium contortisiliquum) and to verify its variability among tubes, dosages of fertilizer and ages of evaluation. Ten treatments were organized in blocks designed with four replication and formed by the combination of sizes of tubes (110 and 180 cm 3 ) and dosages of fertilizer (0, 3, 5, 7 e 9 g L -1 of substrate). The H, D and HD variables were evaluated in five ages. The sample size to evaluate H, D and HD is dependent on age evaluation. For the tubes, dosages of fertilizer and ages of evaluation, 22 plants per experimental unit (pot) are enough to predict the plants variables, with estimation error equal to 10% of estimated average, with a reliable rating of 95%.

Studies on growth models for productive character of sunn hemp are important to know the behavior of the culture. Therefore, the objective of this research was to adjust non-linear models, Gompertz and Logistic, in the description of productive traits of sunn hemp in two sowing periods. Two uniformity trials were performed. The evaluations began on October the 29 th 2014 and December the 16 th 2014, totaling 94 and 76 evaluation days for periods 1 and 2, respectively. After the emergence of the seeds of sunn hemp, for first period from 7 days after sowing, and from 2 to 13 days after sowing, on each day, they were collected randomly four plants. The traits: fresh matter leaf, stem, root, shoot, and total, and dry matter leaf, stem, root, shoot, and total. For both models the confidence interval was calculated of parameters a, b and c. The adjustment quality of the Gompertz and Logistic models was verified by the determination coefficient, the Akaike information criteria, residual standard deviation, mean absolute deviation, mean absolute percentage error and mean prediction error. The Gompertz model when compared between the sowing periods through the confidence interval of the parameters, for the productive traits, differs. The same result was found for the Logistic model. The growth models of Gompertz and Logistic presented good adjustment quality.

The objective of this study was to assess the sample size required for estimating the direct effects of explanatory variables on the grain yield of corn in the combinations formed by three types of hybrids x two harvests x nine scenarios of explanatory variables x two types of path analyses x four levels of accuracy. A total of 6340 plants were evaluated (361, 373, and 416 plants from single-, triple-, and double-cross hybrids in the 2008/2009 harvest, respectively, and 1777, 1693, and 1720 plants from single-, triple-, and double-cross hybrids in the 2009/2010 harvest, respectively). Eleven explanatory variables were measured in each plant: plant height, ear insertion height, ear weight, number of grain rows per ear, ear length and diameter, cob weight and diameter, 100-grain mass, number of grains per ear, grain length and, the main variable, grain yield. Thus, nine scenarios were planned (scenarios 1, 2, 3, 4, 5, 6, 7, 8, and 9 with 0, 1, 2, 3, 4, 5, 6, 7, and 8 explanatory variables excluded, respectively) and two types of path analyses conducted (traditional and ridge path analyses). The sample size required for estimating the direct effect of each explanatory variable on grain yield was assessed using resampling with replacement at four accuracy levels [95% confidence interval ranges (95%CI) of 0.15, 0.25, 0.35, and 0.45]. The use of the ninth scenario of path analysis is recommended regardless of hybrid and harvest given the smaller sample size required compared to the previous scenarios. To estimate direct effects with the maximum 95%CI of 0.25, 10 to 530 plants are required depending on the type of hybrid, harvest, scenario, type of path analyses, and explanatory variables. To estimate the direct effects in the ninth scenario with a maximum 95%CI of 0.25, 120 plants suffice regardless of the type of hybrid, harvest, or type of path analyses.

The objectives of this study were to determine the optimum plot size (X o ) and the number of replications to evaluate the grains yield of rye (Secale cereale L.) and investigate the variability of X o between two cultivars and three sowing dates. Eighteen uniformity trials were conducted with rye. The X o was determined by the method of maximum curvature of the coefficient of variation model. The number of repetitions 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 0.05 of probability, by Tukey test, expressed in percentage of the average of the experiment (d = 10, 12, ... 30%). There is variability in optimum plot size to evaluate the grains yield among the cultivars BRS Progresso and Temprano and among sowing dates in the rye crop. The optimum plot size to evaluate the grains yield of rye is 6.08 m 2 . Seven replicates are sufficient to evaluate the grains yield of rye in experiments with up to 50 treatments, and identify, as significant at 5% probability by Tukey test, differences among averages of treatments of 29.65% of the mean of the experiment in designs completely randomized and randomized block.

ABSTRACT. The State of Rio Grande do Sul (RS) stands out as the largest wheat producer in Brazil. Wheat is the most emphasized winter cereal in RS, attracting public and private investments directed to wheat genetic breeding. The study of genetic progress should be performed routinely at breeding programs to study the behavior of cultivars developed for homogeneous regions of cultivation. The objectives of this study were: 1) to evaluate the genetic progress of wheat grain yield in RS; 2) to evaluate the influence of cultivar competition trial stratification in homogeneous regions of cultivation on the study of genetic progress. Grain yield data of 122 wheat cultivars evaluated in 137 trials arranged in randomized block design with three or four replications were used. Field trials were carried out in 23 locations in RS divided into two homogeneous regions during the period from 2002 to 2013. Genetic progress for RS and homogeneous regions was studied utilizing the method proposed by Vencovsky. Annual genetic progress for wheat grain yield during the period of 12 years in the State of RS was 2.86%, oscillating between homogeneous regions of cultivation. The difference of annual genetic progress in region 1 (1.82%) in relation to region 2 (4.38%) justifies the study of genetic progress by homogeneous regions of cultivation.

R E S U M ONo Planalto do Rio Grande do Sul, Brasil, local de clima subtropical, o cultivo da segunda safra de verão com a cultura da soja (safrinha), semeada após o cultivo de milho, vem agregando importância econômica, aumentando progressivamente sua área de cultivo e possibilitando maior produção de grãos durante o período de verão. Estudos dos caracteres dos genótipos semeados nessa condição específica, com efeito da redução da luminosidade, podem auxiliar nas futuras seleções em programas de melhoramento vegetal da cultura. O objetivo do trabalho foi avaliar as relações lineares entre caracteres de soja (Glycine max L.) e identificar caracteres para a seleção indireta, em segunda safra de cultivo de verão, em região subtropical. Dezoito cultivares de soja foram avaliadas em três locais do Rio Grande do Sul. As semeaduras foram realizadas em 09/01/2013, 10/01/2013 e 24/01/2013, para os experimentos conduzidos em Barra do Guarita, Vista Gaúcha e Tenente Portela, respectivamente. Foi utilizado o delineamento de blocos ao acaso, com quatro repetições. Foram mensurados os caracteres altura de inserção do primeiro legume, altura de planta, massa de cem grãos e produtividade de grãos. Realizou-se a análise de variância dos caracteres. Foi investigada a relação entre os caracteres por meio de análises de correlação e de trilha. No cultivo de soja em época de safrinha (segunda safra de verão), em clima subtropical, a altura de planta tem relação linear positiva com produtividade de grãos e pode ser usada para seleção indireta de cultivares mais produtivas. Palavras-chave: Glycine max L., relações lineares, seleção indireta. A B S T R A C TIn the highlands of Rio Grande do Sul, Brazil, with subtropical climate, the cultivation of the second summer crop with soybean (off-season), sowed after maize, has been adding economic importance, increasing progressively its cultivation area, and allowing greater grain yield during the summer period. Studies of traits of genotypes sown in this particular condition, with reducing luminosity effect, can assist in future selections in soybean plant breeding programs. The objective of this study was to evaluate the linear relations among soybean traits (Glycine max L.) and identify traits for indirect selection in the second crop of summer cultivation, in subtropical region. Eighteen soybean cultivars were evaluated in three locations of Rio Grande do Sul. Sowing was performed on Jan/09/2013, Jan/10/2013, and Jan/24/2013 for the experiments carried out in Barra do Guarita, Vista Gaúcha, and Tenente Portela, respectively. The randomized block design with four replications was utilized. The traits insertion of the first pod height, plant height, one hundred grains weight, and grain yield were measured. The traits analysis of variance was performed. Relation among traits was investigated through correlation and path analysis. In off-season soybean cultivation (second summer crop) in subtropical climate, plant height has positive linear relation with grain yield and it can be used for in...