TEORIA DE VALORES EXTREMOS E TAMANHO AMOSTRAL PARA O MELHORAMENTO GENÉTICO DO QUANTIL MÁXIMO EM PLANTAS - ESCOBAR, José Alfredo Diaz; RESENDE, Marcos Deon Vilela de; AZEVEDO, Camila Ferreira; SILVA, Fabyano Fonseca e; BARBOSA, Márcio Henrique Pereira; NUNES, Andrei Caíque Pires; ALVES, Rodrigo Silva; NASCIMENTO, Moysés (Brazilian Journal of Biometrics, 2018)
This study aimed to propose and evaluate a statistical methodology to improve the extreme value of the distributions. Such an approach is based on the upper quantiles of GEV (Generalized Extremes Values Distribution) of individual genotypic values between and within families. From real and simulated data sets from sugarcane families, generalized extreme value distributions (Gumbel, Fréchet and Weibull) were fitted to the maximum of each family. Stochastic simulations and experimental data resampling consistently indicated that the evaluation of 200 families is enough to maximize the efficiency in order to select extreme individuals. Weibull distribution fitted best and indicated an increase in selection efficiency is about 1.10 (gain of 10%) when going from 20 to 100 individuals per family and 1.12 (gain of 2%) when going from 100 to 200 individuals. These numbers are approximately constant regardless of the number of evaluated families. A good practical option would be the evaluation of 200 families with 100 individuals, in a total of 20,000 individuals. The methodology is also suitable to classify the families or progenies ability to generate exceptional individuals and inform the sample sizes to be practiced in every family to capture these individuals.