Experimental optimization of the number of blocks by means of algorithms parameterized by confidence interval in popcorn breeding.

The objective of this study was to determine the optimal number of repetitions to be used in competition trials of popcorn traits related to production and quality, including grain yield and expansion capacity. The experiments were conducted in 3 environments representative of the north and northwest regions of the State of Rio de Janeiro with 10 Brazilian genotypes of popcorn, consisting by 4 commercial hybrids (IAC 112, IAC 125, Zélia, and Jade), 4 improved varieties (BRS Ângela, UFVM-2 Barão de Viçosa, Beija-flor, and Viçosa) and 2 experimental populations (UNB2U-C3 and UNB2U-C4). The experimental design utilized was a randomized complete block design with 7 repetitions. The Bootstrap method was employed to obtain samples of all of the possible combinations within the 7 blocks. Subsequently, the confidence intervals of the parameters of interest were calculated for all simulated data sets. The optimal number of repetition for all of the traits was considered when all of the estimates of the parameters in question were encountered within the confidence interval. The estimates of the number of repetitions varied according to the parameter estimated, variable evaluated, and environment cultivated, ranging from 2 to 7. It is believed that only the expansion capacity traits in the Colégio Agrícola environment (for residual variance and coefficient of variation), and number of ears per plot, in the Itaocara environment (for coefficient of variation) needed 7 repetitions to fall within the confidence interval. Thus, for the 3 studies conducted, we can conclude that 6 repetitions are optimal for obtaining high experimental precision.