Lima bean is an important crop in Northeastern Brazil and a source of food and income for farmers in the region. However, there have been few genetic studies on this species, which limits the knowledge available for use in breeding programs. The objective of this study was to estimate the relationship between cycle and production traits using canonical correlation analysis and to identify traits that can be used for the indirect selection of lima bean. The experiment was conducted at the Department of Plant Science of the Universidade Federal do Piauí, Teresina, in a randomized block design with five replications, in which 11 agronomic traits from six lima bean populations in the F3 generation originating from biparental crosses were evaluated in 2019. The data were subjected to canonical correlation analysis using the virtual environment R. The results showed that only the first coefficient of the canonical pair was significant (r = 0.5531) by the quisquare test, suggesting that the studied groups were not independent, as the cycle traits showed coefficients of large magnitudes in the relationship between groups. The canonical correlation results suggested that there is a linear association between cycle and production traits in lima beans, in which days to flowering, days to maturation, pod length, seed width, and seed thickness contribute the most to the association between groups.

- Based on its nutritional and economic value, the lima bean (Phaseolus lunatus L.) is the second most important species of the genus. It has high genetic diversity and potential for production and is considered an alternative food and income source. The objective of this study was to apply the restricted maximum likelihood/ best linear unbiased prediction (REML/ BLUP) methodology to estimate genetic parameters and predict genotypic values in F3 populations of lima beans. Twelve characteristics were evaluated in five populations with indeterminate growth habits (H39, H72, H53, H90, and H56). Model 83 from the Selegen program was used for analysis. Considering the genetic parameters, the highest values of genetic variance were for plant height and number of pods per plant. Pod thickness and seed width are favorable for breeding programs. Seed width selection gain was significant for populations H56 and H90 at 11.26 mm and 10.50 mm, respectively. As for the length and thickness of seeds, the gains were less significant, with population H53 showing the greatest gain. The REML/ BLUP methodology proved efficient in estimating genetic parameters and predicting gains in lima bean populations. The estimated selection gains indicated that the highest gains were obtained for plant height, the number of pods per plant, pod thickness, seed width, and the number of days to maturity. Populations H53 and H56 stood out for having large and white seeds, thus being potential populations for species improvement.