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The cultivation of onion Allium cepa L. is of extreme economic importance globally, and, because of this, research must be constantly updated in order to increase productivity. This study was designed to estimate the optimal plot size, sample size and number of repetitions for experiments evaluating variables in the onion crop. Uniformity tests were carried in the years 2016 and 2017 in the experimental area of the Crop Science Department at Universidade Federal de Santa Maria, Santa Maria (RS), Brazil. Each plant was considered a basic experimental unit. Bulb mass, bulb height, and bulb diameter were measured for each basic experimental unit. The optimal plot size, sample size, and number of repetitions were estimated by the method of maximum curvature of the variation coefficient. For onion culture, the optimal plot size to evaluate the bulb mass, bulb height and bulb diameter is eight, six and six, respectively. The optimal sample size for evaluating the bulb mass of the onion crop is six plants, while for the height and diameter variables the optimal sample size is four plants in the direction of the row considering a semi-amplitude of the confidence interval (D%) equal to 20% of the average. Bulb mass variables require 10 repetitions to assess up to 20 treatments in a randomized block design for the least significant difference of the Tukey’s test, expressed as a percentage of the average of 35%. Bulb height and bulb diameter require just six repetitions for the same assessment.

The aim of this work was to use growth models as an alternative analysis of experiments with tomatoes. The data were obtained from field experiments of tomatoes carried out in the 2015/2016 and 2016/2017 growing seasons. Six and nine harvests were carried out in 2015/2016 and 2016/2017, respectively. In each harvest, the number and mass of fruits per plant were assessed. The ANOVA for repeated measures was performed to analysis of the data, and the residuals were assessed. Also for each variable, the Brody, Gompertz, Logistic and von Bertalanffy growth models were fitted as a function of the accumulated values per plant in each harvest and days after the transplant of the seedlings. The assumptions of normality, homogeneity and independence of residuals were verified by the Shapiro-Wilk, Breusch-Pagan and Durbin-Watson tests, respectively. The bias of the parameters was evaluated by the intrinsic and parametric nonlinearity, by the difference between OLS-based and the mean of 10.000 bootstrap-based parameter estimates, and by evaluating the symmetry of the sampling distributions of such parameters. Among the models tested, the one that presented a high coefficient of determination and less non-linearity was selected. The parameters of the selected model were compared by the F test. From the second-, third- and fourth-order derivatives with respect to x (days after transplant), the maximum acceleration point, inflection point, maximum deceleration point, and point of asymptotic deceleration were estimated. The residuals increased with the mean when ANOVA was used, and the data transformation did not fix the violated assumption. The violation of the model's assumptions motivated us to propose nonlinear models as an alternative to statistical analysis with ANOVAs. The logistic model had parameters close to being unbiased, and all assumptions have been meeting. Due to this, the logistic model was selected. The critical points of this model allowed assessing the productive precocity, crop concentration period and productive behavior of the genotypes during the productive period. Finally, we have shown that growth models may be an interesting alternative to standard ANOVA procedures to analyze experiments with horticultural crops in future studies.

The objective of this study was to estimate the coefficient of repeatability and the number of measurements required for production and quality variables in a strawberry crop. An experiment was conducted with two strawberry cultivars from two origins grown in four substrate mixtures, totaling 16 treatments, evaluated in a randomized block design with four replications. Mass (MF) and number (NF) of fruits per plant were evaluated as measures of production, and total soluble solids (SST), titratable acidity (AT) and firmness (FIR) of fruits during the crop cycle were evaluated as measures of quality. Subsequently, the repeatability coefficient was estimated by the following methods: analysis of variance (ANOVA), principal component analysis using a correlation matrix (PCcor), principal component analysis using a variance-covariance matrix (PCcov) and structural analysis (SA). The number of measurements was adjusted for each studied variable based on determination coefficients of 0.80, 0.85, 0.90, and 0.95. The repeatability coefficients ranged from low to medium. The ANOVA method gave the lowest r values, while the PCcov method presented the highest values of r. When using the PCcov method, 3.6, 2.9, 6.2, 3.2, and 3.8 measurements were needed to reach 80% confidence for the variables MF, NF, SST, AT, and FIR, respectively, and this increased to 7.3, 14.0, 29.6, 15.4, and 18.1 for 95% confidence in the results for MF, NF, SST, AT, and FIR, respectively.

The objective of this work was to evaluate the interference of sample size on multicollinearity diagnosis in path analysis. From the analyses of productive traits of cherry tomato, two Pearson correlation matrices were obtained, one with severe multicollinearity and the other with weak multicollinearity. Sixty-six sample sizes were designed, and from the amplitude of the bootstrap confidence interval, it was observed that sample size interfered on multicollinearity diagnosis. When sample size was small, the imprecision of the diagnostic criteria estimates interfered with multicollinearity diagnosis in the matrix with weak multicollinearity.

The aim of this study was to select growth models to describe strawberry (Fragaria x ananassa)fruit production. To do this, data on 16 treatments (combination of 2 cultivars [Albion and Camarosa], ...

The objective of this study was to identify and estimate the relationships between production component variables and fruit yields in tomatoes. This experiment was conducted in a randomized block design with a 2x3x3 factorial arrangement, with two tomato hybrids (Netuno and San Vito), three doses of boron (H3BO3 - 0, 2, 4 g/pit) and three calcium floral applications (no application; application every 7 days; and application every 14 days), totaling 18 treatments with four replications and 20 plants per plot. Pearson correlation coef ficients were estimated between the measured variables and, after that, those with greater significance were selected for productivity with the Stepwise method and verification of multicollinearity using the number of condition and inflation factor of the variance. The correlations of the selected variables were decomposed into direct and indirect effects on fruit productivity with path analysis. There was a strong correlation be tween the variables, excluding the variables height, diameter and average mass of the fruits. Thus, there were cause and effect relationships between the independent variable total mass of the fruits and the principal variable total fruit yield. The variables diameter and total number of fruits did not contribute to an increased tomato production. RESUMEN El objetivo de este trabajo fue identificar y estimar las relaciones entre variables componentes de producción y rendi miento de frutos en tomate. El experimento se realizó con diseño de bloques al azar con un arreglo factorial 2x3x3, correspondiendo a dos híbridos de tomate (Netuno y San Vito), tres dosis de boro (H3BO3 - 0, 2, 4 g/sitio) y calcio (si aplicación, aplicación cada 7 días y aplicación cada 14 días), para un total de 18 tratamientos, cuatro repeticiones y 20 plantas por parcela. Se estimaron los coeficientes de correlación de Pearson entre las variables medidas, poste riormente, se seleccionaron aquellos con mayor significancia para la productividad mediante el método Stepwise y la verificación de la multicolinealidad por el número de condiciones y el factor de inflación de la varianza. Las correla ciones de las variables seleccionadas fueron descompuestas en efectos directos e indirectos sobre la productividad de los frutos mediante el análisis de coeficientes de trayectoria. Se encontró una fuerte correlación entre las variables, excluyendo las variables altura, diámetro y masa promedio de los frutos. Por lo tanto, existen relaciones de causa y efecto entre la variable independiente la masa total de frutos y la variable principal de productividad total de frutos, y las variables diámetro y número total de frutos no contribuyeron a aumentar la productividad de tomate.

Ethnopharmacological relevance Chamomilla recutita (Asteraceae) is used worldwide as a soothing, anti-inflammatory and aromatherapy. In Brazil, it is one of the most cultivated medicinal species. However, the cultivation form may alter the production of compounds in the secondary metabolism and compromise the therapeutic purpose of this species. Aim of the study Evaluation of antiproliferative and genotoxic effects of infusions and essential oil of chamomile, cultivated with homeopathy, on the cell cycle of Allium cepa, as well as the determination of the phenolic compounds present in the infusions of the chamomile inflorescences. Material and methods For the Allium cepa test, two concentrations of 10 and 40 g L−1 of inflorescences of chamomile were used for the preparation of the infusions and essential oil diluted to 0.10%, referring to the six treatments obtained in field cultivation, in which were carried out the applications of homeopathy from the emergence to the harvest of the plants. Distilled water and ethanol were used as negative control and glyphosate 2% as a positive control. The determination of phenolic compounds present in the infusions was carried by liquid chromatography in a UHPLC apparatus. Results Chamomile infusions at concentrations of 10 and 40 g L−1 of inflorescence reduced mitotic index and emphasized antiproliferative activity on the cell cycle of Allium cepa. However, the treatments related to essential oil diluted to 0.10% showed a response variation dependent on the dynamization used, as well as for apigenin concentration. Conclusions Therefore, cultivation with homeopathy does not induce a genotoxic effect in the use of infusions and essential oil of chamomile and it emphasize antiproliferative activity on the cell cycle of Allium cepa, favoring the sustainable cultivation and the safe use of this medicinal species when cultivated with homeopathy.

Nitrogen fertilizer management modifies oat (Avena sativa) panicle components and its grain yield. The work aims to study the potential of the variables of oat (A. sativa) panicle with N-fertilizer, and to simulatate its grain yield using multiple linear regression in succession systems of high and reduced N-residual release. The study was done in 2013 and 2014. The experiment was done in a complete randomized block of 4×2 factorial design, with four replications. The treatments include: nitrogen fertilizer of four doses (0, 30, 60 and 120 kg ha-1), oat (A. sativa) cultivars at two levels (Barbarasul and Brisasul) and succession system at two levels (soybean/oat (A. sativa) and corn/oat (A. sativa). The multiple linear models were efficient in the harvest index of panicle of soybean/oat (A. sativa) system, regardless of the dose evaluated. However, at high doses, the number of grain per panicle was included. In the corn/oat (Avena sativa) system, the harvest index of panicle, the number of grains and spikelets panicle were adjusted based on the model. The multiple linear regression efficiently simulates N-fertilizer to affect the grain yield of oat (Avena sativa) and one or more potential variables of panicle in the succession systems. Key words: Inflorescence, succession system, stepwise, multiple linear regression.

Growth regulator in oat can reduce lodging with effects on yield indicators. The objective of the study is to define the optimum dose of growth regulator to reduce lodging in oats under different conditions of nitrogen (N) fertilization (reduced, high and very high) and the effects on yield indicators in the succession systems. In each succession system (soybean/oats and corn/oats), two experiments were conducted, one to quantify biomass yield and the other to estimate grain yield and lodging. In the four experiments, the design was randomized blocks with four replicates in 3 x 4 factorial scheme, for N-fertilizer doses (30, 90 and 150 kg ha-1) and growth regulator doses (0, 200, 400 and 600 mL ha-1), respectively. Growth regulator reduces lodging in oat plants, with the ideal doses of 500 mL ha-1 in the soybean/oat system and 400 mL ha-1 in the corn/oat system, regardless of the reduced, high and very high N doses. There is a linear reduction of biological and straw yields, and a quadratic trend in the expression of grain yield and harvest index as a function of the growth regulator doses, regardless of succession systems (soybean/oats and corn/oats). RESUMO O regulador de crescimento em aveia pode reduzir o acamamento com reflexos nos indicadores de produtividade. O objetivo do estudo é a definição da dose ótima do regulador de crescimento para redução no acamamento de plantas de aveia, em condições de reduzida, alta e muito alta fertilização com nitrogênio e os reflexos sobre os indicadores de produtividade nos sistemas de sucessão. Em cada sistema de sucessão (soja/aveia e milho/aveia), dois experimentos foram conduzidos, um para quantificar a produtividade de biomassa e, o outro, para estimativa da produtividade de grãos e o acamamento. Nos experimentos, o delineamento foi o de blocos casualizados com quatro repetições em fatorial 3 x 4 para doses de N-fertilizante (30, 90 e 150 kg ha-1), fonte ureia, e doses de regulador de crescimento (0, 200, 400 e 600 mL ha-1) de princípio ativo Trinexapac-Ethyl, respectivamente. O regulador de crescimento reduz o acamamento de plantas de aveia, com a dose ideal em 500 mL ha-1 no sistema soja/aveia e de 400 mL ha-1 no sistema milho/aveia, independentemente da dose reduzida, alta e muito alta de nitrogênio. Há redução linear da produtividade biológica e de palha, e comportamento quadrático na expressão da produtividade de grãos e índice de colheita em função das doses de regulador, independentemente dos sistemas de sucessão (soja/aveia e milho/aveia).

portuguesO objetivo deste trabalho foi determinar o tamanho de amostra necessario para estimar o coeficiente de correlacao de Pearson entre variaveis do tomate cereja. Foram instalados dois ensaios de uniformidade em ambiente protegido na primavera/verao de 2014. As variaveis observadas em cada planta foram comprimento medio de fruto, largura media de fruto, peso medio de fruto, numero de cachos, numero de frutos por cacho, numero de frutos e peso total de frutos, sendo calculada a matriz de correlacao de Pearson entre elas. Foram planejados 68 tamanhos de amostra em uma estufa e 48 em outra, com tamanho inicial composto de 10 plantas e os demais obtidos acrescentando cinco plantas. Para cada tamanho de amostra planejado foram obtidas 3000 estimativas do coeficiente de correlacao de Pearson atraves de reamostragens “bootstrap” com reposicao. O tamanho de amostra de cada coeficiente de correlacao foi determinado quando o valor da amplitude do intervalo de confianca de 95% foi menor ou igual a 0,4. A obtencao das estimativas do coeficiente de correlacao de Pearson com elevada precisao e dificil para caracteres com relacao linear fraca e, consequentemente, maior e o tamanho amostra necessario para estima-los. As relacoes lineares envolvendo as variaveis relacionadas com o tamanho e o numero de frutos por planta tem menor precisao. Para estimar o coeficiente de correlacao entre variaveis produtivas do tomate cereja, com intervalo de confianca de 95% igual a 0,4, e necessario amostrar 275 plantas na estufa de 250m², e 200 plantas na estufa de 200m². Palavras-chave: Solanum lycopersicum var. cerasiforme; amostragem; reamostragem; ”bootstrap”. EnglishThe aim of this study was to determine the required sample size for estimation of the Pearson coefficient of correlation between cherry tomato variables. Two uniformity tests were set up in a protected environment in the spring/summer of 2014. The observed variables in each plant were mean fruit length, mean fruit width, mean fruit weight, number of bunches, number of fruits per bunch, number of fruits, and total weight of fruits, with calculation of the Pearson correlation matrix between them. Sixty eight sample sizes were planned for one greenhouse and 48 for another, with the initial sample size of 10 plants, and the others were obtained by adding five plants. For each planned sample size, 3000 estimates of the Pearson correlation coefficient were obtained through bootstrap re-samplings with replacement. The sample size for each correlation coefficient was determined when the 95% confidence interval amplitude value was less than or equal to 0.4. Obtaining estimates of the Pearson correlation coefficient with high precision is difficult for parameters with a weak linear relation. Accordingly, a larger sample size is necessary to estimate them. Linear relations involving variables dealing with size and number of fruits per plant have less precision. To estimate the coefficient of correlation between productivity variables of cherry tomato, with a confidence interval of 95% equal to 0.4, it is necessary to sample 275 plants in a 250m² greenhouse, and 200 plants in a 200m² greenhouse. Key words: Solanum lycopersicum var. cerasiforme; sampling; resampling; bootstrap.

The plot size estimation is based on uniformity trials, however little is known about and how the size of uniformity trial affects the estimate of the plot size. That way, the aim of this study was to determine the influence of uniformity trial size on the estimation of plot size in the eggplant crop. Two uniformity trials were performed with the eggplant culture in a plastic tunnel. The fresh mass of fruit and number of fruits were assessed in six harvests, with a seven-day interval between harvests. For each trial (Tunnel 1 and 2), 25 uniformity trials of different sizes were simulated (3, 4, 5, … 28 BEU) per harvest and harvest row (individual and grouped) since they presented heteroscedasticity. For each planned uniformity trial, bootstrap procedure was used to estimate 3,000 plot sizes by the maximum coefficient of variation curvature method. The mean and 95% confidence interval width was calculated by the difference between the 97.5th and 2.5th percentiles. The AIC95% and plot size averages were higher in individual harvests than grouped harvests. As the size of the simulated uniformity trial increased, it was verified a reduction of the AIC95% of the plot size. However, the mean plot size did not change with increasing uniformity trial size. In this way, it is possible to state that the size of the uniformity trial affects accuracy the plot size estimation because trials with few numbers of basic experimental units present high experimental variability and inaccurate estimates.

Homeopathic medicines may present differentiated responses in the cultivation of medicinal plants, altering the plant metabolism. The aim was to verify and describe the pathogenic symptoms caused by the application of Phosphorus in the cultivation of chamomile, aiming at the production of flowers. Four dynamizations, 3CH, 6CH, 12CH and 30CH (centesimal scale: CH = centesimal hahnemannian), were evaluated in the Mandirituba chamomile cultivar. Control pots received only distilled water and 70% alcohol in the same amount and proportion of homeopathic medicine. The variables analyzed from the harvest of the flowers are related to the parameters of inflorescence and plant production of chamomile. There was no difference between the dynamizations applied for the number of flowers plant-1, dry mass plant-1, dry mass hectare-1, number of branches and plant height. The characters of flowers mass plant-1, and production of fresh and dried flowers did not differ from the averages presented by the witnesses; however, in the 30CH dynamization, values higher than the others were observed, as well as for fresh mass plant-1 and hectare-1. The diameter and the height of the flower expressed better results in the 3CH dynamization. The application of Phosphorus promotes pathogenesis in the cultivation of chamomile with increases in the characters related to the inflorescence.