Comparison of Random Regression Models with Different Order Legendre Polynomials for Genetic Parameter Estimation on Race Completion Speed of Arabian Horses

SIMPLE SUMMARY: This study aimed to compare different order Legendre polynomials for Arabian racing horses. The present work’s results indicated that the L(2,2) Legendre polynomial (that suggests generalizations and connections to the various mathematical structures and numerical applications) model could be reliably used to estimate heritability values for the racing speed of Arabian horses in the presence of repeated observations. ABSTRACT: This work aimed to compare the fitting performance of the random regression models applied to the different order orthogonal Legendre polynomials on the race completion speed (m/s) of Arabian racing horses. Legendre polynomial function for additive genetic, permanent environmental variances and heritability values with the L(2,2), L(2,3), L(3,2) and L(3,3) models (where L(i,j) means L(order of fit for additive genetic effects, order of fit for permanent environmental effects)) was estimated. A total of 233,491 race speed records (m/s) of Arabian horses were taken from the Jockey Club of Turkey between 2005 and 2016. The mean and standard deviation of heritability values were estimated as 0.294 ± 0.0746, 0.285 ± 0.0620, 0.302 ± 0.0767 and 0.290 ± 0.1018 for L(2,2), L(2,3), L(3,2), and L(3,3), respectively. The steady decreasing trend of permanent environmental variances for L(2,2) provided stationery for heritability values. According to Akaike information criterion (AIC) and Bayesian information criterion (BIC) values, the L(2,2) model could be reliably used to estimate heritability values for the racing speed of Arabian horses in the presence of repeated observations.