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In the past, genetic improvement of dairy cattle was focused on high milk production. This led to deterioration of health and fertility traits and in consequence increased veterinary treatment costs and culling rates (Butler and Smith, 1989; Oltenacu and Broom, 2010). To prevent these negative effects, new traits (conformation, fertility, survival) were consecutively incorporated into selection indices in many countries including Poland. Recently, traits connected with the energy balance of cows have drawn the interest of researchers. Energy balance is defined as the difference between energy intake and energy requirements for milk output and maintenance (Buttchereit et al., 2010). Negative energy balance has serious consequences for body function and in turn determines cow health and fertility. Cows with a negative energy balance are more prone to mastitis, lameness, digestive and locomotive problems and metabolic diseases such as ketosis (Goff and Horst, 1997; Heuer et al., 1999; Collard et al., 2000; Negussie et al., 2013). Energy balance can be calculated to indicate the metabolic status of a cow, but the costs of meaABSTRACT. The aim of the study was to estimate the genetic parameters of milk fat-to-protein ratio in the first three lactations of Polish Holstein-Friesian cows. Data included 104 875 test-day records of 6299 cows calving from years 2000–2012. Genetic parameters were estimated with a multitrait random regression model using the Bayesian method via Gibbs sampling. The linear model for fat-to-protein ratio and milk traits (milk yield, lactose percentage, milk urea concentration) included fixed herd-test-day effect, fixed regressions within age at calving by season of calving subclasses, and random regressions for additive genetic and permanent environmental effects. All regressions were modelled using fourth-order Legendre polynomials. The average daily heritability of fat-to-protein ratio ranged from 0.24 to 0.31. Fat-to-protein ratio was negatively genetically correlated with milk yield for almost every day in milk in each lactation, with means of −0.52, −0.24 and −0.05 in the first, second and third lactations, respectively. Average genetic correlations of fat-to-protein ratio with lactose percentage and milk urea concentration were rather low or close to zero (−0.08 to 0.10) except for the genetic correlation with milk urea content in the second lactation (0.32). The results suggest that fat-to-protein ratio is a heritable trait and might be used in the selection of Polish Holstein-Friesians assuming that the relationship between fat-to-protein ratio and economically important traits will be investigated. Received: 4 September 2018 Revised: 10 January 2019 Accepted: 7 April 2019

Genetic parameters of milk fat-to-protein ratio in first three lactations of Polish Holstein-Friesian cows