Application of Wilmink’s exponential term to estimate lactation curves of milk β-hydroxybutyrate concentration on days in milk for Holstein cows in Japan

Abstract

We examined the utility of including Wilmink’s exponential term in models to represent the trend of milk β-hydroxybutyrate (BHB) concentrations throughout the lactation period of Holstein cows in Japan. The data comprised 6,954,286 test-day records from first through fifth parities that occurred during 2017 through 2020. We compared four models to determine which provided the best fit of milk BHB concentrations during lactation: second-order Legendre polynomials (L2), third-order Legendre polynomials (L3), first-order Legendre polynomials with Wilmink’s exponential term (L1W), and second-order Legendre polynomials with Wilmink’s exponential term (L2W). Among the evaluated models, using L2W yielded the smallest mean squared error and mean residuals on days in milk in each lactation period for 1 through 5 parities. Including Wilmink’s exponential term will be beneficial for developing a model that recapitulates the trend in milk BHB throughout lactation in Holstein cows.