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AbstractThe prediction of seed longevity (P50) is traditionally performed by the use of the Probit model. However, due to the fact that the survival data are of binary origin (0,1), the fit of the model can be compromised by the non-normality of the residues. Consequently, this leads to prediction losses, despite the data being partially smoothed by Probit and Logit models. A possibility to reduce the effect of non-normality of the data would be to apply the principles of the central limit theorem, which states that non-normal residues tend to be normal as the n sample is increased. The Logit and Probit models differ in their normal and logistic distribution. Therefore, we developed a new estimation procedure by using a small increase of the n sample and tested it in the Probit and Logit functions to improve the prediction of P50. The results showed that the calculation of P50 by increasing the n samples from 4 to 6 replicates improved the index of correctness of the prediction. The Logit model presented better performance when compared with the Probit model, indicating that the estimation of P50 is more adequate when the adjustment of the data is performed by the Logit function.

Seed longevity is characterized as the time for which seed remains viable during storage. Seed longevity can be estimated by a Probit model that determines the period in which 50% of seeds have lost viability (P 50 ). The transformed data are binary and when they are not normally distributed, it is necessary to modify the Probit model or apply other functions to estimate longevity. This work aimed studied the use of the Logit, Cauchy, and Cauchy-Santos-Sartori-Faria (Cauchy-SSF) functions to estimate the longevity of soybean seed [Glycine max (L.) Merr.] and compared Probit longevity models for the ordinary least squares (OLS) adjustment method and the generalized linear model (GLM). Ten seed lots were used to estimate water content, germination, and longevity. The P 50 data were transformed via the Probit, Logit, Cauchy, and Cauchy-SSF functions to estimate the coefficients of determination, the Akaike information criterion, deviance, dispersion, and the regression residuals. The effect on the results was observed, depending on the link function. The Cauchy-SSF function as part of the OLS method estimated longevity in eight seed lots within the interval of interest (II), and the Cauchy function as part of the GLM estimated longevity in nine seed lots. The Cauchy, Cauchy-SSF, and Logit models were capable of estimating the longevity of soybean seeds (P 50 ) slightly better than the Probit model. We suggest the Cauchy-SSF function for the OLS method and the Cauchy function for the GLM method to estimate soybean seed longevity when the data are not normally distributed. core Ideas• The Cauchy, Cauchy-Santos-Sartori-Faria Cauchy-SSF, and Logit functions estimated longevity in soybean seeds more robustly than the Probit function. • The ordinary least squares method combined with the Cauchy-SSF function is as good as the generalized linear model method with the Cauchy function. • The selection of the function changes the estimated time when 50% of seeds have lost viability, emphasizing the importance of the correct choice.Abbreviations: Cauchy-SSF, Cauchy-Santos-Sartori-Faria; GLM, generalized linear model; II, interval of interest; OLS, ordinary least squares; P 50, period in which 50% of seeds have lost viability, σ, standard deviation. bIoMetrY, ModeLInG, And stAtIstIcsPublished in Agron.

h i g h l i g h t s • An inexpensive strategy was used to valorize fish canning industry by products. • Urea complexation was more efficient than winterization. • The solid fraction contained 79.94% (w/w) of saturated and monounsaturated FAME. • The liquid fraction was further analysed by preparative HPLC analysis. • After HPLC analysis, an oil fraction containing 89.25% EPA (w/w) was obtained.

The identification of superior genotypes in plant breeding programs is not a quick and simple task and requires breeders to become aware of more suitable and efficient tools for evaluating crop performance. Univariate analyses are often too narrow for the scope of plant breeding because it lacks consideration of relations between variables. Therefore, the objective of this study was to select castor bean hybrids based on principal component analysis (PCA). Trials were conducted in 2017 with 31 hybrids in a randomized block design with 4 replications. The following variables were used to evaluate crop performance: plant height (PH), insertion height of the primary raceme (HPR), number of stem nodes (NN), number of racemes (NR), number of seeds (NS), stem diameter (SD), number of fruits (NF), 100-seed weight (S100) and seed oil content (SOC). The first three principal components (PCs) explained approximately 75.01 % of all the variability in the dataset. PC 1, 2 and 3 were particularly related to productivity (NS, NR, S100 and NF), plant size (SD, HPR and PH) and oil production (SOC), respectively. Hybrids 14 and 23 were the most suitable for grain production in commercial scale due to short-height, which favors mechanical harvesting. Commercial hybrid 26 showed high SOC, medium grain yield and medium-height.