Modelling lactation curves of dairy goats by fitting random regression models using Legendre polynomials or B-splines

Abstract

A total of 17 356 test-day milk yield (TDMY) records from 642 first lactations of Alpine goats were used to model variations in lactation curve using random regression models (RRM). Orthogonal Legendre polynomials and B-splines were evaluated in order to obtain adequate and parsimonious models for the estimation of genetic parameters. The analysis were performed using a single-trait RRM, including the additive genetic, permanent environmental and residual effects. We estimated the mean trend of milk yield, and the additive genetic and permanent environmental covariance functions through random regression using different orders of Orthogonal Legendre polynomial (three to six) and B-spline functions (linear, quadratic and cubic, with three to six knots). This study further evaluated different number of classes of residual variances. The covariance components and the genetic parameters were estimated using the Restricted Maximum Likelihood method. Heritability estimates presented similar trends for both functions. RRMs with a higher number of parameters better described the genetic variation of TDMY throughout the lactation. The most suitable RRM for genetic evaluation of TDMY of Alpine goats is a quadratic B-spline function with six knots, for the mean trend, curves of additive genetic and permanent environmental effects and five classes of residual variance.

Temporal covariance structure of multi-spectral phenotypes and their predictive ability for end-of-season traits in maize

“…Additionally, the high correlation between consecutive records can create computational issues. As an alternative to repeatability and multi-trait mixed models, random regression models have been implemented to model such repeated measurements that are recorded in a continuous scale, such as time or age (Kirkpatrick et al 1990 ; Huisman et al 2002 ; Boligon et al 2012 ; Lopes et al 2012 ; Brito et al 2017 ). Random regression models commonly use Legendre polynomials to model the variance and covariance of measurements at and among the time points (Meyer 2005 ).…”

Diversity of dairy goat lactation curves in France

“…Some authors have focused on finding mathematical models that describe the biological processes of milk production by mammary gland cells (Pollott, 2000;Elvira et al, 2013a). Others have proposed a statistical approach by modeling the shape of the curve from elementary controls such as random regression testday models including genetic and nongenetic effects (Menéndez-Buxadera et al, 2010;Mucha et al, 2014;Brito et al, 2017) or by using methods such as principal component analysis (PCA) to sum up the information contained in the data (Carta et al, 2014). Principal component analysis is a dimension-reduction tool that reduces a large set of variables to a small set containing most of the original information.…”

Use of Spline function for the characterisation on peak yield, peak day and persistency in lactation curves in Murciano-Granadina goats

“…This biomodeling of LC by an animal, allowed the adjustment of two or more straight lines that describe the production until and after the peak of lactation. Likewise, the general form of the function is in accordance with that presented by Brito et al (2017) and Meyer (2005), the equation being stated as follows:…”

“…The path of the LC can be done through the use of empirical mathematical models and predicting the yield on each day of lactation with minimum error; but not all models fit a typical lactation curve (Fern andez et al 2002;Gonz ales-Peña et al 2012). Therefore, the importance of mathematical models (citing Spline model) as useful tools for the description and analysis of LC (Brito et al 2017) and that the MG breed has proven to be the best fit than several other common functions (Wood, Cappio-Borlino, Cobby and Le Du, Wilmink and Legendre) (Le on et al 2012). Therefore, it is interesting to summarise the phenomenon of lactation in a few descriptive parameters, so that they can be interpreted biologically; referring to the rate of increase and decline of production before and after peak respectively, as well as the environmental factors that affect these parameters.…”