Modelling growth in Suffolk and Charollais sheep populations using random regression models and validation of constrained polynomial correlation values

Random regression modelling has been used across multiple animal species to model longitudinal data. The random regression model for growth accounts for the genetic correlation between measures of the same trait over time and the wide environmental variability in growth, but this requires adequate weight records across the age range.
However, contemporary management practices in sheep in the United Kingdom (UK) generally focus on growing lambs and neglect mature weight recordings. This study examined modelling strategies for growth data in Suffolk and Charollais sheep, provided by the Agriculture and Horticulture Development Board (AHDB), with polynomial random regression modelling with many early life weight recordings but limited weight recordings in mature animals. Two methods were employed to model the data. In Method A missing mature weight records were predicted for those animals that did not have a recorded mature weight. The animals were sorted into groups based on the identity of their sires and the year in which the animal was born. Mature weight values were predicted within each group with a multiple regression model.
The dataset, including predicted values, was analyzed with random regression models using polynomials and simple linear regression for animal and permanent environmental (PE) effects. In Method B the dataset with missing mature weight records was analyzed using a random linear regression animal model with random animal and PE effects. Due to problems of convergence because the parameters were close to the boundary space, fixing the correlation between the intercept and slope of the Legendre polynomial at different levels was investigated. The heritability values resulting from the model with a fixed correlation between intercept and slope parameters at 0.5 for the Suffolk dataset resulted in heritability values ranging from 0.2 to 0.5 from 1 to 619 days of age. Corresponding estimates for the Charollais dataset ranged from 0.18 to 0.49
from 1 to 640 days of age. For the Suffolk data the genetic correlations ranged from 1.00 to 0.08 between weight at day 1 to weight at day 619, while for the Charollais the correlations ranged from 1.00 to 0.05 from 1 to 640 days of age. Validation procedures were undertaken using a multi-trait approach to examine the estimated breeding values (EBV) when the correlation between the intercept and slope are fixed at different levels. The results indicated that fixing the correlation at 0.5 gave the most appropriate estimates for the Suffolk and Charollais datasets.
appropriate estimates for the Suffolk and Charollais datasets