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• For the first time for rubber tree breeding, this work investigate correlation, path analysis and canonical correlation. • There is an association between the production traits (yield, girth and the laticiferous system) and the morphological traits. • Selection for the number of leaf storeys may increase at least three of the traits (yield, girth, bark thickness and number of latex vessel rings). • Selecting for Girth and the number of leaf storeys will increase the efficiency of early selection for yield in young plants. The present work evaluated the relationship of rubber yield with morphological and structural traits of the laticiferous system in rubber tree [ Hevea brasiliensis (Willd. ex Adr. de Juss.) Muell. Arg] open-pollinated progenies to understand the cause and effect relationships between traits in order to enable future early selection. The progenies were installed in Jaú, Pindorama and Votuporanga in a randomized block design, with five replications and 10 plants per plot at a spacing of 2.0 × 2.0 m. The traits evaluated at three years of age were rubber yield (Yld); girth (Grt), expressed by the stem perimeter; bark thickness (BT); number of latex vessel rings (RG); length (PL), diameter (PD) and petiole index (PI); leaflet length(LFL) and width (LFW); leaf width (LW), area (LA) and index (LI); and number of leaf storeys (NLS). Coefficients of the genotypic correlations were used for a graphical representation of the correlation network created in the Genes program. Subsequently, the diagnosis of multicollinearity, as well as the analysis of the direct and indirect genotypic correlations of bark anatomical traits, leaf morphological traits, girth, and rubber yield, were performed. The traits that showed significant genotypic correlations with rubber yield at the three evaluated sites were girth, bark thickness, and number of leaf storeys. The girth character had the largest direct effect on rubber yield. Canonical correlation analysis showed that selection for the number of leaf storeys may increase at least three of the traits (yield, girth, bark thickness, and number of latex vessel rings) for most locations studied. There is an association between the yield traits (yield, girth, and the laticiferous system) and the morphological traits. [ABSTRACT FROM AUTHOR]