Bayesian Models combining Legendre and B-spline polynomials for genetic analysis of multiple lactations in Gyr cattle

Abstract

We aimed with this study to combine Legendre polynomials (LEG) and linear B-splines (BSP) to describe simultaneously the first and second lactation of Gyr dairy cattle under a multiple-trait random regression models (MTRRM) framework. Additionally we proposed the application of self-organizing map to define the classes of residual variances under these models. A total of 26,438 and 23,892 milk yield test-day records were used, respectively, for the first and second lactations of 3253 Gyr cows. Two preliminary MTRRM analyses considering 10 residual classes were performed: the first one was based on LEG for systematic and random effects for both lactations; and the second one was based on BSP. Three classes were defined by using a self-organizing map: from 6 to 35; 36–185 and 186–305 days in milk. After definition of residual variance classes, a total of 16 MTRRM combining LEG and BSP were compared. The MTRRM based on BSP to describe the systematic effects of the first and second lactation, BSP to describe the random effects of the first lactation and LEG to describe the random effects of the second lactation (BSP-BSP-BSP-LEG) outperformed all other models. From the BSP-BSP-BSP-LEG model, heritability estimates for milk yield over time ranged from 0.1107 to 0.2902, and from 0.2036 to 0.3967, for the first and second lactation, respectively. In general, additive genetic correlation estimates between days in milk within each lactation and between lactations had medium magnitude (mean of genetic correlations were 0.6630, 0.6226 and 0.4749 for the first, second and between both lactations, respectively). We concluded that combining different functions under a MTRRM framework is a feasible alternative for genetic modeling of lactation curves in Gyr dairy cattle.