In breeding of autogamous plants, breeders often deal with the evaluation of progenies derived from multiple populations. We hypothesize that selection strategies that account for the heterogeneous genotypic variability of progenies within these populations associated with the population means may improve progeny selection. Thus, the objective of this work was to use two mixed models with progenies nested to population effects to obtain and evaluate indexes for the genotypic values of progenies. We used simulations and a real dataset from a multipopulation recurrent selection program of common bean (Phaseolus vulgaris L.). Progenies from 20 populations were evaluated for grain yield in two different generations. The three studied indexes consider the merit of populations, but differently account for the genotypic variability of progenies within populations: index gM uses a mean estimate, index gH is based on heterogeneous estimates, and the index gW also uses a mean estimate but is weighted by the selection accuracy within populations. The studied populations were highly diverse in both generations, justifying the implementation of the two models to obtain the population means and specific estimates of genotypic variability of progenies for each population. The comparison among indexes suggested that index gW more appropriately explored the information from the genotypic profiles of the common bean studied populations in the genotypic values of progenies. Thus, the index gW has the potential to help breeders of self‐pollinated plant species to improve progeny selection from multiple populations.

In common bean (Phaseolus vulgaris L.) breeding, several trials are carried out in field conditions to predict the genotypic values, but experimental designs may not be sufficient to capture the field heterogeneity in the experimental area. The objective of this work was to evaluate the potential of spatial models to correct data from a common bean breeding program for spatial trends and improve the prediction of genotypic values. We used real data from 19 field trials from a common bean breeding program and three experimental designs. The traditional statistical model with design effects and independent errors was fitted and used as the basic model. Later, we fitted a sequence of spatial models to include different residual (co)variance structures for local trends and fixed and random effects based on plot position information to capture global and extraneous trends. The basic model and the best-fit spatial model were compared regarding the estimates of heritability, accuracy, prediction error variance, and discordance in the top-ranking genotypes. In most cases, the use of spatial models improved the estimates of heritability and accuracy or, at least, reduced the estimates of prediction error variance. Also, changes in the genotypic values classification were observed. Because no single model presented the best fit for all trials, some of the tested models were recommended for future trials based on the patterns of spatial trends observed. Thus, the use of spatial models helped to improve the data analysis and the prediction of genotypic values by capturing the field heterogeneity in our common bean field trials.