Multiple-trait analysis of a long-term selection experiment for non-destructive deformation in White Leghorns: Evolution of genetic parameters for traits related to eggshell strength

•Long-term two-way selection for non-destructive deformation was effective and resulted in significant genetic improvement.•Non-destructive deformation displayed moderate heritability for both the strong and weak lines (0.388±0.032 and 0.415±0.030).•Non-destructive deformation displayed strong genetic correlations with other eggshell traits, for both lines.•The breeding values revealed an asymmetric response between the two lines, even after selection ceased.