“…Permanent environment, animal genetics, residuals, and mating sire were analyzed as a random effect influences on the reproductive traits. Lambing season (1, 2, 3), and the year of calving (2018, 2019, 2020) were fixed effects for LS, and the module was [ 26 ]: where Y is the LS observation; b is fixed effects; a is the vector of solutions for the coefficients of direct animal (additive) genetic random effects; pe is the vector of solution for permanent environmental effects; s is the random effect of the service sire in the year of calving; e is the vector of residual effects; X , Z , W , and T are the correspondent incidence matrices of the fixed effects and additive genetic, permanent environmental random effects due to repeated records per ewe and random effect of the service sire, respectively.…”